A SEARCH FOR NEUTRINOLESS TAU DECAYS TO THREE LEPTONS
by
JEFFREY A. KOLB
A DISSERTATION
Presented to the Department of Physics
and the Graduate School of the University of Oregon
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
June 2008
11
University of Oregon Graduate School
Confirmation of Approval and Acceptance of Dissertation prepared by:
Jeffrey Kolb
Title:
"A Search for Neutrinoless Tau Decays to Three Leptons"
This dissertation has been accepted and approved in partial fulfillment of the
requirements for the degree in the Department of Physics by:
David Strom, Chairperson, Physics
Eric Torrence, Advisor, Physics
Nilendra Deshpande, Member, Physics
Michael Raymer, Member, Physics
Michael Kellman, Outside Member, Chemistry
and Richard Linton, Vice President for Research and Graduate StudieslDean of the
Graduate School for the University of Oregon.
June 14, 2008
Original approval signatures are on file with the Graduate School and the University of
Oregon Libraries.
iii
An Abstract of the Dissertation of
Jeffrey A. Kolb
in the Department of Physics
for the degree of
to be taken
Doctor of Philosophy
June 2008
Title: A SEARCH FOR NEUTRINOLESS TAU DECAYS TO THREE LEPTONS
Approved:
Dr. Eric Torrence, Advisor
Using approximately 350 million 7+7- pair events recorded with the BaBar
detector at the Stanford Linear Accelerator Center between 1999 and 2006, a search
has been made for neutrinoless, lepton-flavor violating tau decays to three lighter
leptons. All six decay modes consistent with conservation of electric charge and
energy have been considered. With signal selection efficiencies of 5-12%, we obtain
90% confidence level upper limits on the branching fraction B(7 ~ eU) in the range
(4-8) x 10-8 .
iv
CURRICULUM VITAE
NAME OF AUTHOR: Jeffrey A. Kolb
PLACE OF BIRTH: Williamsport, Pennsylvania
DATE OF BIRTH: December 18, 1979
GRADUATE AND UNDERGRADUATE SCHOOLS ATTENDED:
University of Oregon, Eugene
Taylor University, Upland, IN
DEGREES
Doctor of Philosophy in Physics, 2008, University of Oregon
Master of Science in Physics, 2005, University of Oregon
Bachelor of Science in Engineering Physics, 2002, Taylor University
ACADEMIC INTERESTS
Tau decays
Lepton flavor violation
Distributed computing in high energy physics
PROFESSIONAL EXPERIENCE
Research Assistant, Department of Physics, University of Oregon, Eugene,
2005-2008
Teaching Assistant, Department of Physics, University of Oregon, Eugene,
2002-2004
PUBLICATIONS
BaBar Collaboration, B. Aubert, et al., Improved Limits on the
Lepton-Flavor Violating Decays T-- ---? g-g+g-, Phys. Rev. Lett. 99, 251803
(2007)
K. Kiers, J. Kolb, T. Klein, S. Price, and J.C. Sprott, Chaos in a Nonlinear
Analog Computer, International Journal of Bifurcation and Chaos 14,
2867-2873 (2004)
K. Kiers, J. Kolb, J. Lee, A. Soni, and G.-H. Wu, Ubiquitous CP Violation in
a Top-Inspired Left-Right Model, Phys. Rev. D 66, 095002 (2002).
vACKNOWLEDGMENTS
First of all, I would like to acknowledge the support and guidance of my advisor,
Eric Torrence, who has been unfailingly happy to share from his impressive
knowledge of experimental particle physics. Eric's enthusiasm for doing physics has
catalyzed the development of my interest in the field, and his sound advice over the
years has led me down a path on which I'm pleasantly surprised to find myself.
I would also like to acknowledge the many friends who have traveled with me for
all or part of this physics journey. I am grateful to The Men of the Man Ranch
(Adam, Adam, Paul, Chuck, Brian), AI, Iva, Tiffany, the K Center folks, and the
rest of my Eugene friends for their support. I also acknowledge all the wonderful
people from Solid Start and small group who have been so encouraging.
Finally, I acknowledge my family, who have always cared for and supported me.
And Ruthie, who has loved me well.
Vi
DEDICATION
This dissertation is dedicated to Dr. Ken Kiers. Ken's kindness is inspiring and
his overwhelming dedication to his students allowed this student to pursue a dream.
Chapter
vii
TABLE OF CONTENTS
Page
I INTRODUCTION 1
1 Overview. 1
2 Theoretical Motivation. 3
2.1 Lepton Flavor . 4
2.2 The Standard Model of Electromagnetic and Weak
Interactions. . . . . .. 4
2.3 Flavor Structures Beyond the Standard Model 8
3 Previous Experimental Work . . . . . . . . . 9
3.1 Search for Neutrinoless Muon Decays 9
3.2 Search for Neutrinoless Tau Decays 11
II THE BABAR EXPERIMENT 15
1
2
3
4
5
Introduction .
Particle Acceleration for the BABAR Experiment
2.1 Beam Production
2.2 Beam Storage .
2.3 Beam Energy .
2.4 Interaction Region .
2.5 Performance....
The BABAR Detector . . . .
3.1 Detector Goals and Constraints
3.2 Charged Particle Tracking .
3.3 Pion and Kaon Identification
3.4 Electromagnetic Calorimetry
3.5 Muon Detection .....
Simulations . . . . . . . . . . . .
Data Acquisition and Triggering
15
16
17
17
18
18
19
19
22
26
36
37
44
47
51
Chapter
6
5.1 nigger Requirements and Design.
5.2 Level One nigger .
5.3 Level Three Trigger .....
Offline Data Processing . . . . . . .
6.1 Prompt Data Reconstruction
6.2 Data Skimming
Vlll
Page
51
52
57
57
58
59
III DATA ANALYSIS . 61
1
2
3
4
5
6
7
8
Introduction to Analysis .
1.1 Branching Fractions
1.2 Upper Limits ....
1.3 Incorporating Uncertainties into Upper Limits
1.4 Overview of Analysis Steps .
1.5 Analysis Optimization and Expected Upper Limits.
Selection of the Data.
Event Preselection . . . . . . . .
Particle Identification . . . . . .
Mass and Energy Determination
Event Selection . . . . . . . . . .
Estimation of Background . . . .
7.1 Backgrounds from cc and uds .
7.2 Background from T+T-
7.3 QED Background . .
7.4 Final Background Fit
Systematic Uncertainties
8.1 Signal Efficiency ...
8.2 Background Estimation
8.3 Other Systematics .
61
62
63
66
69
70
71
72
73
80
82
85
85
88
88
90
97
97
101
105
IV RESULTS AND CONCLUSIONS. 107
1
2
3
Results .
Discussion of Results .
2.1 Implications for Theory
Conclusion
107
108
108
111
APPENDICES . . . . . 113
A TRACK LISTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 113
Chapter
1
2
3
4
The CalorClusterNeutral List ..
The ChargedTracks List . . . . .
The GoodTracksVeryLoose List
The gammaConversionDefault List
IX
Page
113
113
113
113
B PARTICLE IDENTIFICATION ALGORITHMS 115
1
2
3
The eMicroTight Selector
The muNNLoose Selector
The KLHTight Selector
115
116
117
C AUXILIARY PLOTS ... 118
1
2
3
Optimization Plots .
N-1 Plots .
Plots of Background Fits
118
125
132
REFERENCES . . . . . . . . . . . . . 136
xLIST OF FIGURES
Figure Page
11.1 The PEP-II interaction region around the BABAR detector. 20
11.2 Integrated' luminosity at BABAR as a function of time. 21
II.3 Sideview of the BABAR detector. 24
II.4 Endview of the BABAR detector. . 25
II.5 Longitudinal schematic view of the SVT. 27
II.6 Transverse schematic view of the SVT. 28
II.7 Longitudinal view of the DCH, with dimensions in mm. 29
II.8 Schematic layout of the drift cells for the four innermost superlayers. The
lines between the wires have been added to show the cell boundaries. The
line below the first layer is the 1-mm-think beryllium inner wall. . . 30
11.9 The magnetic field components Bz and B r as a function of z for various
radial distances r (in meters). . . . . . . . . . . . . . . . . . . . . . . .. 31
11.10 Relative magnitude of the magnetic field transverse to a high momentum
track as a function of track length from the IP for various polar angles (in
degrees). The data are normalized to the field at the origin. . . . . . .. 32
II.ll SVT hit reconstruction efficiency, as measured on p,+p,- events for (a)
forward half-modules and (b) backward half modules. Vertical lines
delineate the five different layers. . . . . . . . . . . . . . . . . . . . . .. 33
11.12 SVT hit resolution in (left) z and (right) ¢ coordinate in microns, plotted
as a function of track incident angle in degrees. . . . . . . . . . . . . .. 34
II.13 DCH position resolution as a function of the drift distance in layer 18, for
tracks on the left and right side of the sense wire. The data are averaged
over all cells in the layer. . . . . . . . . . . . . . . . . . . . . . . . . . .. 35
II.14 Measurements of dEjdx in the DCH as a function of track momentum.
The curves show the Bethe-Bloch predictions for each particle type. 35
Xl
Figure Page
II.15 Transverse momentum resolution, as determined from cosmic ray muons
traversing the DCH and SVT. . . . . . . . . . . . 39
II.16 Longitudinal view of the DIRC. . . . . . . . . . . 39
11.17 Detail of the DIRC bars and the imaging region. 40
II.18 Longitudinal view of the EMC. . . . . . . . . . . 41
11.19 A schematic of the wrapped crystal and the readout electronics on the
back end. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42
11.20 Energy resolution of the EMC for photons and electrons, as measured for
various processes. The solid line is from the fit (Equation II.4), and the
shaded area denotes the fit error. . . . . . . . . . . . . . . . . . . . . .. 43
11.21 Angular resolution of the for photons from?fo decays. The solid line is the
fit (Equation II.5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 44
II.22 Overview of the IFR: barrels sectors and forward (FW) and backward
(BW) endcaps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., 45
11.23 Cross section of a planar RPC, with schematic of the high voltage
connections. . . . . . . . . . . . . . 46
11.24 Track Segment Finder pivot group. . . . . . . . . . . 53
II.25 Single track Zo for all L1 tracks without a cut on Z00 55
IIL1 The efficiency for muon identification in data and MC by the
muNNLoose selector, as a function of muon momentum for (a) positively
charged muons, and (b) negatively charged muons. Plot (c) shows the
ratio of the data efficiency to the MC efficiency. . . . . . . . . . . . . .. 78
III.2 The efficiency for e+ / e- identification in data and MC by the
eMicroTight selector, as a function of particle momentum for (a)
positrons, and (b) electrons. Plot (c) shows the ratio of the data efficiency
to the MC efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78
IIL3 The mis-ID rate for pions in data and MC by the eMicroTight selector,
as a function of particle momentum for (a) positively charged pions, and
(b) negatively charged pions. Plot (c) shows the ratio of the data mis-ID
rate to the MC mis-ID rate. . . . . . . . . . . . . . . . . . . . . . . . .. 78
Xll
Figure Page
IlIA The mis-ID rate for pions in data and MC by the muNNLoose selector,
as a function of particle momentum for (a) positively charged pions, and
(b) negatively charged pions. Plot (c) shows the ratio of the data mis-ID
rate to the MC mis-ID rate. . . . . . . . . . . . . . . . . . . . . . . . .. 79
III.5 The mis-ID rate for kaons in data and MC by the eMicroTight selector,
as a function of particle momentum for (a) positively charged kaons, and
(b) negatively charged kaons. Plot (c) shows the ratio of the data mis-ID
rate to the MC mis-ID rate. . . . . . . . . . . . . . . . . . . . . . . . .. 79
III.6 The mis-ID rate for kaons in data and MC by the muNNLoose selector,
as a function of particle momentum for (a) positively charged kaons, and
(b) negatively charged kaons. Plot (c) shows the ratio of the data mis-ID
rate to the MC mis-ID rate. . . . . . . . . . . . . . . . . . . . . . . . .. 80
III.7 The (b.M, b.E) distributions for the signal channels after preselection
and particle identification. The box shows the borders of the signal
region. The histogram borders correspond to the large box. The z-axis is
logarithmically-scaled. . . . . . . . . . . . . . . . . . . . . . . . . . . " 82
III.8 r- --} /1- /1+ /1-: uds background. The histograms show the average PID-
weight per bin as a function of b.M (left) and b.E (right). . . . . . . .. 86
III.9 r- --} e-e+e- channel: PDFs with MC-fitted shapes are scaled to data;
a) b.E projection of the data (points) and the sum of the background
PDFs (curve); b) b.M projection of the data (points) and the sum of
the background PDFs (curve); c) PDF (b.M, b.E) distribution; d) data
(b.M, b.E) distribution. The filled black boxes and open red box show
the signal region (blinded for data). 91
III.lOr- --} /1-e+e- channel: PDFs with MC-fitted shapes are scaled to data;
a) b.E projection of the data (points) and the sum of the background
PDFs (curve); b) b.M projection of the data (points) and the sum of
the background PDFs (curve); c) PDF (b.M,b.E) distribution; d) data
(b.M, b.E) distribution. The filled black boxes and open red box show
the signal region (blinded for data). 92
------ ------------
xiii
Figure Page
III.117- ~ f-L+e-e- channel: PDFs with MC-fitted shapes are scaled to data;
a) !:::.E projection of the data (points) and the sum of the background
PDFs (curve); b) !:::.M projection of the data (points) and the sum of
the background PDFs (curve); c) PDF (!:::.M, !:::.E) distribution; d) data
(!:::.M, !:::.E) distribution. The filled black boxes and open red box show
the signal region (blinded for data). 93
III.127- ~ e+f-L-f-L- channel: PDFs with MC-fitted shapes are scaled to data;
a) !:::.E projection of the data (points) and the sum of the background
PDFs (curve); b) !:::.M projection of the data (points) and the sum of
the background PDFs (curve); c) PDF (!:::.M, !:::.E) distribution; d) data
(!:::.M, !:::.E) distribution. The filled black boxes and open red box show
the signal region (blinded for data). 94
III. 13 7- ~ e- f-L+ f-L- channel: PDFs with MC-fitted shapes are scaled to data;
a) !:::.E projection of the data (points) and the sum of the background
PDFs (curve); b) !:::.M projection of the data (points) and the sum of
the background PDFs (curve); c) PDF (!:::.M, !:::.E) distribution; d) data
(!:::.M, !:::.E) distribution. The filled black boxes and open red box show
the signal region (blinded for data). 95
III. 14 7- ~ f-L- f-L+ f-L- channel: PDFs with MC-fitted shapes are scaled to data;
a) !:::.E projection of the data (points) and the sum of the background
PDFs (curve); b) !:::.M projection of the data (points) and the sum of
the background PDFs (curve); c) PDF (!:::.M, !:::.E) distribution; d) data
(!:::.M, !:::.E) distribution. The filled black boxes and open red box show
the signal region (blinded for data). 96
III.l57- ~ f-L- f-L+ f-L- a) generated MC Dalitz distribution after preselection; b)
efficiency to pass all selection except SB as function of Dalitz distribution;
c) selection efficiency as a function of invariant mass squared of the pair
of same-sign leptons; d) selection efficiency as a function of invariant mass
squared of the pair of opposite-sign leptons; e) efficiency for all selection
cuts except PID as a function of invariant mass squared of the pair of same-
sign leptons; e) efficiency for all selection cuts except PID as a function of
invariant mass squared of the pair of opposite-sign leptons; 99
'.i
f
XIV
Figure Page
III.16a) The distribution of p~ms versus p!j.ms for the T- --+ e- e+e- channel after
preselection and PID. The z-axis is logarithmic. The red line shows the
cuts applied to select the two-photon control sample. b) The (b..M, b..E)
distribution of these events plotted without the cut on p!j.ms. 104
IV.1 Observed data shown as dots in the (b..M, b..E) plane and the boundaries
of the signal region for each decay mode. The dark and light shading
indicates contours containing 50% and 90% of the selected MC signal
events, respectively. 109
IV.2 Feynman diagram of the leading Higgs-induced contribution to T- --+
/1- /1+J.C in the MSSM. . . . . . . . . . . . . . . . . . . . . . . . . . . 111
C.1 Expected upper limit on branching fraction as a function of p~ms. /1- e+e-
channel is excluded because the dimuon control sample does not have
a requirement on the maximum value of pFs (see section 7). Arrows
indicate optimized value for the selection cut. . . . . . . . . . . . . . .. 119
C.2 Expected upper limit on branching fraction as a function of the minimum
total transverse momentum p!j.ms. Arrows indicate optimized value for the
selection cut. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 120
C.3 Expected upper limit on branching fraction as a function of b..M~fn.
Arrows indicate optimized value for the selection cut. . . . . . .. 121
C.4 Expected upper limit on branching fraction as a function of b..M~~x'
Arrows indicate optimized value for the selection cut. 122
C.5 Expected upper limit on branching fraction as a function of b..E~fn'
Arrows indicate optimized value for the selection cut. 123
C.6 Expected upper limit on branching fraction as a function of b..E~~x'
Arrows indicate optimized value for the selection cut. 124
Figure
xv
Page
C.7 7- ~ e-e+e- channel a) total transverse momentum; b) I-prong
momentum; c) min 2-track mass; d) I-prong mass; e) (bool) one-prong
track has EMC energy. The points show the data distributions for
events in the grand sideband region with all other cuts applied. The
blue histogram shows the expected 7+7- background level, the green
histogram shows the expected Bhabha background level, and the yellow
histogram shows the expected uds background level, all normalized by
the background fits with all selection cuts applied. Arrow(s) indicate the
chosen cut value(s). For comparison, the red curve shows the MC signal
distribution for the large box with arbitrary normalization. . . . .. 126
C.8 7- ~ p,-e+e- channel a) total transverse momentum; b) I-prong
momentum; c) min 2-track mass; d) I-prong mass; e) (bool) one-prong
track has EMC energy. The points show the data distributions for
events in the grand sideband region with all other cuts applied. The
blue histogram shows the expected 7+7- background level, the green
histogram shows the expected dimuon background level, and the yellow
histogram shows the expected uds background level, all normalized by
the background fits with all selection cuts applied. Arrow(s) indicate the
chosen cut value(s). For comparison, the red curve shows the MC signal
distribution for the large box with arbitrary normalization. . . . .. 127
C.g 7- ~ p,+e-e- channel a) total transverse momentum; b) I-prong
momentum; c) min2-track mass; d) I-prong mass; e) (bool) one-prong
track has EMC energy. The points show the data distributions for
events in the grand sideband region with all other cuts applied. The
blue histogram shows the expected 7+7- background level, the green
histogram shows the expected Bhabha background level, and the yellow
histogram shows the expected uds background level, all normalized by
the background fits with all selection cuts applied. Arrow(s) indicate the
chosen cut value(s). For comparison, the red curve shows the MC signal
distribution for the large box with arbitrary normalization. 128
XVI
Figure Page
C.I0 T- -----> e+/F/-r channel a) total transverse momentum; b) I-prong
momentum; c) min 2-track mass; d) I-prong mass; e) (bool) one-prong
track has EMC energy. The points show the data distributions for
events in the grand sideband region with all other cuts applied. The
blue histogram shows the expected T+T- background level, the green
histogram shows the expected Bhabha background level, and the yellow
histogram shows the expected 'lJ,ds background level, all normalized by
the background fits with all selection cuts applied. Arrow(s) indicate the
chosen cut value(s). For comparison, the red curve shows the MC signal
distribution for the large box with arbitrary normalization. 129
C.llT- -----> e-p,+p,- channel a) total transverse momentum; b) I-prong
momentum; c) minimum 2-track mass; d) I-prong mass; e) (bool) one-
prong track has EMC energy. The points show the data distributions for
events in the grand sideband region with all other cuts applied. The green
histogram shows the expected Bhabha background level and the yellow
histogram shows the expected 'lJ,ds background level, all normalized by
the background fits with all selection cuts applied. Arrow(s) indicate the
chosen cut value(s). For comparison, the red curve shows the MC signal
distribution for the large box with arbitrary normalization. 130
C.12 T- -----> p,-p,+p,- channel a) total transverse momentum; b) I-prong
momentum; c) minimum 2-track mass; d) I-prong mass; e) (bool) one-
prong track has EMC energy. The points show the data distributions
for events in the grand sideband region with all other cuts applied. The
blue histogram shows the expected T+T- background level and the yellow
histogram shows the expected 'lJ,ds background level, all normalized by
the background fits with all selection cuts applied. Arrow(s) indicate the
chosen cut value(s). For comparison, the red curve shows the MC signal
distribution for the large box with arbitrary normalization. 131
XVll
Figure Page
C.13 uds background: Fit of the uds (.b.M, .b.E) MC distribution with PDF
described in the text. column 1) .b.M projection of the MC distribution
(points) and the PDF (curve); column 2) .b.E projection of the MC
distribution (points) and the PDF (curve); column 3) MC (.b.M, .b.E)
distribution; column 4) MC PDF (.b.M, .b.E) distribution; row 1) e-e+e-;
row 2) J..Ce+e-; row 3) e-J-l+e-; row 4) J-l-e+J-l-; row 5) e-J-l+J-l-; row 6)
J-l-J-l+J-l- . .b.M is plotted in (GeV/c2 ) and.b.E is plotted in (GeV). ... 133
C.14 T+T- background: Fit of the T+T- (.b.M, .b.E) MC distribution with PDF
described in the text. column 1) .b.M projection of the MC distribution
(points) and the PDF (curve); column 2) .b.E projection of the MC
distribution (points) and the PDF (curve); column 3) MC (.b.M, .b.E)
distribution; column 4) MC PDF (.b.M, .b.E) distribution; row 1) J-l-e+e-;
row 2) e-J-l+e-; row 3) J-l-e+J-l-; row 4) e-J-l+J-l-; row 5) J-l-J-l+J-l- . .b.M
is plotted in (GeV/ c2) and .b.E is plotted in (GeV). Only channels with
significant T+T- contributions in the LB are shown. 134
C.15 Bhabha and di-muon backgrounds: Fit of the Bhabha and di-muon
(.b.M, .b.E) MC distributions with PDF described in the text. column
1) .b.M projection of the control sample distribution (points) and the
PDF (curve); column 2) .b.E projection of the control sample distribution
(points) and the PDF (curve); column 3) control sample (.b.M, .b.E)
distribution; column 4) PDF (.b.M, .b.E) distribution; row 1) e-e+e-; row
2) J-l-e+e-; row 3) e-J-l+J-l- . .b.M is plotted in (GeV/c2 ) and.b.E is plotted
in (GeV). Only channels with significant QED contributions in the LB are
shown. 135
xviii
LIST OF TABLES
Table Page
11.1 Approximate production cross sections at BABAR, including experimental
acceptance factors. uds refers to the total continuum production to
uu, dd, ss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " 17
11.2 Integrated luminosity records for various time periods, in inverse picobarns
(pb) and inverse femtobarns (fb), where 1 barn = 10-28 m2 . 19
11.3 Properties of CsI(Tl). 40
IIA Primitive trigger objects constructed by the Levell trigger. 56
11.5 1FT trigger patter definitions, where J.L refers to a signal in a sector. 56
IIL1 Background MC samples used in the analysis. 72
IIL2 Preselection efficiencies in percent for signal MC, background MC, and
data samples. Cuts are applied sequentially and the marginal efficiencies
are quoted. For the signal samples, the loss in efficiency due to the one-
prong branching fraction is included in these numbers. 'Trigger' means
that L30utDch or L30utEmc tagbit is set. The bb efficiencies include
both B OEO and B+B- samples. Uncertainties on the total efficiency
numbers are from MC statistics. 74
IIl.3 Particle ID selectors used to identify the 3-prong tracks. 75
IlIA Efficiency for preselected events to pass the PID requirements. 79
IIL5 Signal region boundaries M 1 < b.M < M 2 , E1 < b.E < E2 for each decay
mode. The boundaries of the large box (LB) used in the background fits
is also shown in the last column. The last row shows the signal efficiencies
in percent for these signal regions (for the events passed preselection and
PID requirements). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81
XlX
Table Page
III.6 Signal efficiency for events passing preselection and PID to be in the signal
box or in the large box. 81
III.7 Efficiency for events after PID and LB requirements to pass the selection
cuts. As described in Section 7, the Bhabha and dimuon contributions
are modeled with data control samples. The corresponding selection
efficiencies are not shown. . . . . . . . . . . . . . . . . . . . . . . . . .. 84
III.8 Expected number of background events in the grand sideband (GS) and
signal box (SB) after the background fits. By construction, the total
number of expected background events in the GS is equal to the number
of data events in the GS. The luminosity is 376 fb-l. . . . . . . . . . .. 90
III.9 The number of expected (left) and observed (right) events in the boxes
neighbor to the signal box. Uncertainties on the sum of the expected
background for all four boxes are estimated from the uncertainty on the
expected background in the SB. Poisson errors are assigned to the sum of
the data for all four boxes. 103
III.10Systematic uncertainties expressed in relative percent. . . . . . . . . .. 106
IV.1 The total efficiency E, estimated background level in the signal region,
expected upper limit, observed number of events in the SB and 90% CL
upper limit on B(T ~ fU). 108
1CHAPTER I
INTRODUCTION
1 Overview
Tau lepton decays have always been observed to include at least one neutrino in the
final state. Furthermore, neutral leptonic currents such as the photon appear to
always generate pairs of leptons of the same type. These sort of observations have
led to the postulate that the number of leptons of each type (or flavor) are
separately conserved in all reactions. Recent observations of neutrino flavor
oscillations provide an unambiguous signature of the non-conservation of lepton
flavor, or lepton flavor violation (LFV). But do the interactions of charged leptons
still conserve lepton flavor? Many extensions of the standard theory of particle
physics naturally predict LFV. In fact, neutrinoless lepton decays could be the first
sign of physics beyond the standard theory. In particular, the heaviness of the third
generation lepton, the tau, makes it attractive for probing theoretical models with
new particles that couple preferentially to more massive particles.
In this work, we present a search for the neutrinoless tau decays T ~ UR, where
R= e, f..l, the two lighter charged leptons. We search for all such decays consistent
with the conservation of energy and electric charge:
2Throughout this work, the charge-conjugate modes are implied.
The construction and operation of the BABAR detector and the PEP-II storage
rings at the Stanford Linear Accelerator Center presents a unique opportunity to
search for rare tau decays such as 7 ----+ eee and to further test the assumption of
lepton flavor conservation. The PEP- II storage rings produce e+ e- collisions at a
center-of-mass (CM) energy of 10.58 GeV. The BABAR detector, constructed around
the e+e- collision point, is a multipurpose detector made up of a number of
sub-detector systems which are optimized to detect and record the many different
decay products of the e+ e- collisions. While the primary physics program is based
around the decays of B mesons, the accelerator also generates a high rate of 7+7-
pairs through the reaction e+e- ----+ 7+7-. The detector is capable of efficiently
identifying and recording the decays of these leptons. Furthermore, the detector's
excellent energy and momentum resolution gives the BABAR physicists a precise
knowledge of the missing energy associated with unobservable neutrinos.
This work is divided into chapters as follows:
• Chapter I begins with a discussion of the role of symmetry in fundamental
physics and a presentation of the standard theory of subatomic
electromagnetic and weak interactions. Particular attention is paid to the
structure of the interaction between the different generations (or families) of
leptons. An analogy with the quark interactions is presented and some
possibilities for new couplings beyond the standard theory are briefly
mentioned. Chapter I concludes with a review of the experimental history of
searches for neutrinoless lepton decays.
• Chapter II concerns the BABAR experimental apparatus. After an overview of
the accelerator and general detector functions, the detector sub-systems are
reviewed, with emphasis placed on lepton detection capabilities. Next is a
discussion of the computer simulations of the e+ e- collisions and of the decay
products' subsequent interactions with the detector. The chapter concludes
with sections detailing the operation of the trigger and data processing
procedure.
3• Chapter III deals with the data analysis itself. After an general discussion of
branching fractions and limits, the details of the upper limit setting procedure
are presented. Next the selection of the data and optimization of the analysis
are discussed. Background calculations and estimates of uncertainties
complete the chapter.
• Chapter IV presents the finals results and a discussion of their merit. The
implications are discussed for a variety of models of physics beyond the
standard theory.
2 Theoretical Motivation
Mathematical symmetries playa fundamental role in theoretical physics. As proven
by Emmy Noether in 1917, the existence of a continuous symmetry in a theory
implies the existence of a conserved quantity. In other words, if the equations of
motion are invariant under some operation, the theory will have a divergence-less
current. Therefore, the existence of symmetries in the theories of particle physics is
of great interest because they lead to conservation laws, which in turn are powerful
tools for predicting and testing. A simple example is the invariance of physical laws
under translations in three-dimensional space. Noether's theorem relates this
symmetry to the conservation of momentum. Similarly, the invariance of physics
under rotations about a point is related to the conservation of angular momentum.
If the operation under which the theory is symmetric is generated by a group,
then a conserved current is associated with each generator of the symmetry. This
perspective on symmetries is particularly useful for theories with internal
symmetries. Such theories contain some number of fields whose interactions do not
change under rotations in the space of those fields. An example of this sort of
internal symmetry can be seen in the strong interactions of the proton and the
neutron. Since these two baryons experience the strong force equally, then there is a
symmetry in the abstract isospin space in which the particle are basis vectors. This
symmetry leads to the conservation of the isospin quantum number in strong
interactions.
42.1 Lepton Flavor
Lepton flavor is a quantum number associated with the particular generation or
family in which the lepton resides. The charged electron and the neutral electron
neutrino (along with their antiparticles) reside in the first lepton generation, while
muon-like particles reside in the second generation, and tau-like particles in the
third. If lepton flavor is conserved, then the decays of the charged leptons will
always involve a neutrino of the same generation. Therefore, the neutrinoless decay
of any lepton is a lepton flavor violating process.
In contrast to the symmetry examples mentioned earlier, the conservation of
lepton flavor does not appear to be the result of any known symmetry. Due to the
almost total absence of right-handed neutrinos, the standard theory described in the
next section permits leptonic transitions only within the same generation. But this
is the result of the smallness of the neutrino mass and is not due to any
fundamental symmetry. Furthermore, the standard theory is know to be an
incomplete low-energy effective theory based on a more general model. Without a
symmetry to protect lepton flavor, we have no reason to expect its conservation in a
more general theory.
2.2 The Standard Model of Electromagnetic and Weak Interactions
In the Standard Model (SrvI) of particle physics, the electromagnetic and weak
interactions [1, 2] are described by a quantized field theory which is constructed to
be invariant under rotations by elements of the symmetry group SU(2) xU(l).
Left-handed leptons are assigned to SU(2) doublets in the following way:
(1/~) (1/~) (1/=) .
eLM L T L
(1.1 )
Right-handed charged leptons are observed to not participate in the weak
interactions, and are therefore assigned to SU(2) singlets. Right-handed neutrinos
can not exist as massless particles, and are not included in the theory. The quark
sector of the theory is similarly constructed, with the six left-handed quarks
assigned to 3 SU(2) doublets:
(1.2)
5In contrast to the lepton sector, both up-type and down-type quarks have
right-handed and left-handed components. The right-handed components are
assigned to SU(2) singlets.
The three generators for the SU(2) symmetry are
(1.3)
while the single generator for the U(1) symmetry is
(1.4)
A local SU(2)xU(1) rotation on some doublet field 'l/J can be parameterized in terms
of these generators and the local variables aa (a = 1,2,3) and {3,
01. UX"T" ~13/2"/,
.<j/ -------t e e 'f/ .
For the theory to be invariant under such rotations, all kinetic terms in the
Lagrangian must use the covariant derivative
(1.5)
(1.6)
which couples the 'l/J field to the fields AJ.L and B. Fields such as AJ.L and B, which
appear in the covariant derivative and are associated with a symmetry of a theory,
are often referred to as gauge fields. In this case, the fields A~ and the coupling
strength g are associated with SU(2) symmetry, and the field B and the coupling
strength g' is associated with the U(l) symmetry.
Because mass terms of the form ~m2ij;'l/J are not invariant under SU(2) rotations,
all particle masses in the theory must arise through the Higgs mechanism. The
complex scalar Higgs field is assigned to an SU(2) doublet. A potential of the form
(1.7)
results in spontaneous breaking of the SU(2) symmetry, and the Higgs field ¢
6acquires a vacuum expectation value (VEV) of the form
(¢) = _1 (0)V2 1I
After spontaneous symmetry breaking, a rotation with
(1.8)
(1.9)
still leaves (¢) invariant. This residual U(I)EM symmetry is associated with the
conservation of electric charge and the corresponding vector boson, the photon
(AlI ex g'A~ + gBII ) remains massless. The remaining three gauge boson fields
(W; ,Z) have mass terms in the covariant derivative which couples the Higgs boson
to the gauge bosons.
SM Flavor Structure for Quarks
Flavor violation, or mixing between different generations of fermions, arises in the
SU(2) xU(I) theory as a consequence of the so-called Yukawa coupling of the Higgs
field ¢ to the left-handed and right-handed fermions. For one generation of quarks
('U and d only), these couplings in the Lagrangian for the quarks are
where QL is the first left-handed quark doublets from Equation 1.2, dR and UR are
the associated right-handed quark fields, and A is the coupling strength. When the
vacuum expectation of ¢ (Equation 1.8) is inserted, Equation 1.10 contains mass
terms of the form
(1.11 )
where
1
md = jC)Ad ll.y2 ' (1.12)
Mass terms of this sort are allowed in the theory because they result from
Higgs-quark couplings which are originally invariant under SU(2)xU(1) rotations.
Extending the theory to 3 generations of quarks mixes the mass terms. With
left-handed quark doublets Qt and right handed quark singlets u-k and d-k,
7Equation 1.10 now becomes
A r _ \ijQ-i ~di dj abQ-i ~t j + H C
LJ.1-Jq - -Ad L'P R - AU E La'PbUR .., (1.13)
where Aij is not necessarily diagonal. The matrix A can always be diagonalized by
setting
(1.14)
and making the rotations
and
d i UijdjL -----7 d L'
(1.15)
(1.16)
Inserting the Higgs VEV from Equation 1.8 into the rotated form of Equation 1.13
leads again to mass terms of the form Equation 1.11 for the six quarks.
While the diagonal matrices D contain the quark masses, and the lV matrices
disappear from the theory, the U matrices show up elsewhere. The rotations of
Equation 1.15-1.16 must be applied to all left-handed quark fields, and could, in
principle, affect in the electromagnetic and weak couplings of the quarks. The
unitary rotation matrices cancel in the neutral electroweak interactions. They also
cancel from the kinetic terms. However, the effect of the rotations on the
charged-current coupling of the W± to the left-handed quarks takes the form
(1.17)
The matrix V = U~Ud is referred to as the CKI\I matrix, and describes the flavor
structure of the charged-current coupling of left-handed quarks in the basis where
the quark mass matrices in Equation 1.13 are diagonal. The diagonal elements of V
describe the rate of same-generation quark transitions relative to
different-generation transitions, which are described by the off-diagonal elements.
In summary, the presence of mixing between the quark generations in the weak
charged-current interaction arises from the fact that the quark mass eigenstates are
not the same as the flavor eigenstates which undergo weak interactions. The form of
8Vel{M, which describes the relationship between these bases, is not predicted by the
theory and must be measured experimentally.
SM Flavor Structure for Leptons
As with the quarks, the left- and right-handed leptons in the SU(2) xU(1) theory
are coupled by the Higgs field. The most general Higgs coupling to the leptons takes
the same form as Equation 1.13:
J\ I' _ \ ijL-i A.Zi dj abL-i A.t j + H C
UJ..,£ - -AI L'+' R - All E La'+'bVR . ./., (1.18)
where the left-handed lepton doublets L have replaced the left-handed quark
doublets Q. In the case that the neutrinos are absolutely massless, there are no
right-handed neutrinos (or left-handed antineutrinos), and the second term in
Equation 1.18 is zero. The charged lepton mass matrix Al can be diagonalized as
before,
but the rotations
i Uijdj
eL -----t I 'L'
(1.19)
(1.20)
remove the U£ and W£ matrices from the theory without changing the charged
current coupling. Thus, with massless neutrinos, the weak interactions only induce
transitions within lepton generations and decays such as T -----t U£ are not predicted.
2.3 Flavor Structures Beyond the Standard Model
While the existence of neutrino oscillations allows for a complete set of massive left-
and right-handed Dirac neutrinos and anti-neutrinos, the sum of the three neutrinos
masses of this sort are required to be less that 2.0 eV [3]. This situation severely
limits the possibility of lepton flavor violation through a CKM-like mechanism.
With this sort of LFV structure, the rate for two-body decays such as T- -----t j.L-, is
proportional to the ratio (llm2 /ivl'{;v)2, where llm is the mass difference between the
neutrino mass eigenstates and lVlw is the mass of the charged electroweak gauge
9boson. This ratio leads to decay rates on the order of 10-40 , which would be
completely unobservable at any conceivable experiment in the near future.
Three body decays such as T -t ea can be generated with light neutrinos at
somewhat higher rates via loop diagrams, such as those suggested by Pham [4]. In
certain diagrams, the cancellation produced by unitarity of the neutrino mixing
matrix is particularly mild, leading to rates of order 10-14 for a favorable choice of
neutrino mixing angles. Nevertheless, such rates remain well beyond the reach of
any foreseeable experiments.
When considering theories beyond the Standard Model with right-handed
neutrinos, the possibilities for lepton flavor violation are more numerous. Since these
theoretical models must simplify to the SM at the typical collider energy and below,
the models usually contain many new particles and lepton couplings. In general,
there is no reason to expect all new lepton couplings to be simultaneously diagonal.
The new physics model could be as simple as the addition of a new neutral Higgs
SU(2) doublet, leading to expanded Yukawa terms such as (tau couplings only)
(1.21 )
3
where the !:1iR parameters are the source for LFV. In fact, these models must be
further constrained just to suppress lepton flavor violating interactions to rates
below the current experimental bounds. More complicated theories such as
supersymmetry provide numerous new sources of LFV, both directly at tree level or
through loop effects where the unitarity suppression is relatively mild [5]. More
specific models will be noted in the discussion of the results in Section 2.
3 Previous Experimental Work
3.1 Search for Neutrinoless Muon Decays
Searches for non-conservation of lepton number and family have been performed at
least as far back as 1948, when E.P. Hincks and B. Pontecorvo performed studies of
the decays of what they thought was a meson with a lifetime of 2.2 f-JS [6]. A search
for the decays of this "mu meson" to an electron and a photon, each with energy
around 50 MeV, produced a null result. Once the muon was firmly established as a
second generation of lepton, other searches [7, 8, 9, 10, 11, 12, 13] for f-J- -t e-,
were made, but none with positive results. In 1959, Lee and Samios [14] used slow
10
muons in a bubble chamber to search for the decay fJ+ -----t e+e-e+. No events were
observed, and the experimenters estimated the ratio
(1.22)
In 1963, a search for the process fJ- -----t e-e+e- by the Babaev, Balats, Kaftanov,
Landsberg, Lyubimov, and Yu [15] also produced a null result. Two years later,
Parker, Anderson, and Rey [16] placed the first upper limit on the branching
fraction for the decay fJ- -----t e-,. Based on some technical breakthroughs of Babaev
et al., their experiment was designed to observe the simultaneous back-to-back
emission of an electron and a gamma ray. The large solid-angle coverage and good
angular resolution of their detector allowed significant improvement in background
rejection, and led to a 90% C.L. upper limit on B(fJ- -----t e-,) of 2.2 x 10-8 .
These 1960's era limits stood until the late 1970's. In 1977, a search for
fJ- -----t e-, at the Swiss Institute for Nuclear Research (SIN) generated rumors of a
positive result. This brought about a resurgence of interest in lepton flavor and
number conservation. Careful study of the SIN data led to upper limits on
fJ- -----t e-, around 1 x 10-9 [17, 18]. In 1988, the SINDRUM collaboration at SIN
placed what is still the best limit on B(fJ- -----t e-~ e+e-) [19]:
r(fJ -----t 3e) 12 ( 07( ) < 1.0 x 10- 90/0 C.L.).r fJ -----t e2v (1.23)
The SINDRUM detector is designed to detect the decays of fJ+'s which are stopped
at a rate of about 5 x 106/s. Electrons and positrons are detected in a spectrometer
of consisting of five concentric multiwire proportional chambers, and a cylindrical
array of 64 scintillation counters in a ,0.33 T magnetic field.
Experiments at the Los Alamos Meson Physics Facility (LAMPF) continue to
make improvements to the limits on fJ- -----t e-,. In 1988, the physicists used data
taken with the Crystal Box detector to set new limits on fJ- -----t e-"fJ- -----t e-",
and fJ- -----t e-e+e- [20]. The lVIEGA collaboration further lowered the fJ- -----t e-,
limit in 1999. Using a similar experimental setup to that of SINDRUrvI, the detector
is designed to observe the characteristic back-to-back positron/photon emission. By
making high quality measurements of timing, energy, and position, MEGA set an
11
upper limit [21] of
(1.24)
3.2 Search for Neutrinoless Tau Decays
In 1975, Martin Perl and his collaborators on the MARK-I experiment at SLAC's
SPEAR e+ e- rings made the somewhat unexpectedly discovery of a third generation
of lepton, the tau [22]. One year earlier, in the so-called November Revolution, the
charm quark had been observed in the form of the J /'lj; cc bound state. Mesons
consisting of charm and a lighter quark (D mesons) were soon after observed at
slightly higher collision energies. The existence of the charm quark resolved some
long-standing theoretical issues involving the observed absence of flavor-changing
neutral currents [1]. In contrast, the lack of theoretical motivation for a third
generation of leptons l , and the fact that the charmed D meson has a mass very close
to that of the tau, led to a great deal of initial skepticism over the tau discovery.
A closer analysis of the MARK-I data showed that the increase in cross section
around 3.6 GeV CM energy couldn't be easily explained by only D mesons. These
charmed mesons were expected to decay primarily to strange particles, yet the
experimentalists instead noticed an increase in events with missing momentum and
many extra electrons and muons. Further more, there were no peaks in the KIT and
K1f1f mass spectra. A careful analysis of events with one or more leptons pointed to
a new spin-1/2 particle decaying to leptons and invisible neutrinos. The DASP and
PLUTO collaborations at the DORIS facility in DESY confirmed the discovery in
1977-78.
Just four years later, collaborators with the MARK-II detector at SPEAR used
the world's first large sample of tau decays ( 20000 events) to make searches for
radiative, neutrinoless tau decays to an electron or muon [23]. The group also
searched for four different three-body, leptonic decays (e- e+ e-, ~ce+ e-, e- /1+~c,
~c fJ+~c), and for six decays to a lepton and a neutral meson (1fo, KO, pO). The
general-purpose, hermetic design of the detector allowed for signal acceptance rates
(signal efficiencies) up to 10%. Limits on the branching fractions were set in the
1Kobayashi and Maskawa noted in 1972 that a third generation of quark would allow for CP
violation in the charged weak interactions.
12
range 10-3 - 10-4 at the 90% confidence level. All limits cited in this section were
calculated at the 90% confidence level.
The next significant search for neutrinoless tau decays was performed with the
ARGUS detector and the DORIS accelerator at DESY, and published in 1987 [24].
Like BABAR, the ARGUS experiment was conducted at 10.58 GeV CM energy. This
energy range is far enough above the tau production threshold to provide good
separation of tau and multihadron events, but not so high that the 1/s dependence
of the cross section starts to negatively affects the tau production rate. ARGUS
achieved exceptionally good signal acceptances rate of around 25% for all search
channels. The ARGUS analysts make searches for all six T -----+ PRJ! modes and placed
limits of the order 10-5 , an order-of-magnitude better than MARK II. They also
placed similar limits on the decays T- -----+ P- h+h-, T- -----+ P+h-h-, and
T- -----+ P- p/K*(892), where P = e, f-L and h = Jr±, K-.
New upper limits on the branching fractions for neutrinoless tau decays
continued to be placed as collaborations generated tau samples of sufficient size. In
1988, collaborators with the Crystal Ball detector at DORIS placed limits just
above 1 x 10-4 on the branching fractions for T -----+ e" T -----+ eJr°, and T -----+ eTl [25].
The CLEO collaboration published the first of many limits on neutrinoless tau
decays in 1990 [26]. Their search consisted of the T -----+ PPP modes and T -----+ Phh, with
zero or one kaons in the final state. While the CLEO limits were still of the order
10-5 , the were generally lower than the ARGUS limits. ARGUS responded in 1992
with a large new set of upper limits, including the first searches for non-conservation
of baryon number in tau decays [27]. Searches for T -----+ p" T -----+ PJr°, and T -----+ PTl
yielded upper limits in the range (3 - 13) x 10-4 . This study also placed new upper
limits on T- -----+ e-, and T- -----+ f-L-, which were a factor of 2 and 10, respectively,
than the previous limits.
CLEO made two other searches for T -----+ PU and T -----+ Phh in the 1990's. The
1994 results [28] included the first search for T -----+ PK*, while the 1998 report [29]
included the first searches for T -----+ Phh channels with resonant and non-resonant
K+K- pairs. In the later analysis, CLEO placed limits in the range (1 - 8) x 10-6 .
The DELPHI group at the LEP experiment at CERN published searches for
T- -----+ e-, and T- -----+ f-L-, in 1995, based on a sample of 81k tau pairs [30]. While
their upper limit on T- -----+ e-, of 1.1 x 10-4 was slightly better that from ARGUS a
few years earlier, their limit on T- -----+ f-L-, was not competitive with CLEO limit of
4.2 x 10-6 from 1993 [31]. Other results from CLEO in the 1990's included new
13
limits on T- --> e-, and T- --> /-l-, [32], a search for tau decays to a lepton and
various combinations of 7fo,S and 17'S [33], and another search for baryon-number
non-conservation T --> p,/7fo/17/27fo/7fo17 [34]. Nearly all of these searches resulted in
new upper limits.
While the CLEO tau sample led to a steady decrease in the upper limits for
many neutrinoless tau decays, two newer experiments would soon acquire tau
samples which would dwarf that of CLEO. The B-factories, BABAR at SLAC and
Belle at the KEK accelerator facility in Japan, began running in 1999. In 2002,
CLEO published the results of a search for tau decays to a lepton and one or two
K s mesons, based on 13.9 fb- 1 of integrated luminosity [35]. For the first time,
limits less than 10-6 were placed on branching fractions for LFV decays. However,
in their first three years of running, both B-factories recorded approximately 100
fb- 1 of integrated luminosity. During this time, both collaborations presented a
number of initial results based on a few tens of million tau pairs, though their limits
were not yet competitive with those from CLEO.
In early 2004, the B-factories began publishing results based on data from nearly
100 fb- 1 of integrated luminosity. BABAR published first, producing limits on
T --> UP in the range (1 - 3) x 10-7 [36]. Soon after, Belle published limits in the
range (2 - 4) x 10-7 for the same channels [37]. Later that year, Belle also
published new limits for T --> /-l17 which were more restrictive than CLEO's previous
limits by a factor of nearly 50 [38]. The B-factories limits on canonical LFV
channels like T --> f££ were primarily due to the high luminosity of the machines.
Total signal acceptance rates were generally similar to those for previous
experiments. If anything, the high backgrounds at BABAR and Belle required tighter
cuts (particularly in particle identification criteria) and consequently lower signal
efficiencies. But in the end, the B-factories' ability to deliver consistently high
luminosity allowed the experiment to set increasingly stringent limits on the the
neutrinoless tau decay branching fractions.
By 2005, BABAR and Belle began to publish results based on more than 100
fb-l. Belle published a search for T --> £7fo /17/17' based on 154 fb-1 of data. ·With
signal detection efficiencies in the range 5 - 9%, Belle placed limits on the branching
fractions in the range (1.3 - 10) x 10-7 [39]. Soon after, BABAR published the first
of such limits below 10-7 . Based on 221 fb- 1 of data, BABAR placed a new upper
limit on T- --> /-l-, of 6.8 x 10-8 [40]. BABAR also placed the first limits from the
14
B-factories on T - ehh [41]. Belle responded with new limits on T- - A/An- [42]
and T - eKs [43], the later of which included limits as low as 4.9 X 10-8 .
Recent publications on neutrinoless tau decays include a new limit on T- - e-i
from BABAR [44], Belle's first results for T - ehh and T _ epo / K* / K* / ¢ [45], and
updates on T - eno/17/17' from BABAR [46] and Belle [47]. Many of these results
place limits on the branching fractions of the order 10-8 . The analysis detailed in
this paper was published in late 2007 [48]. Using 376 fb- 1 of data, we placed upper
limits on T - eu from (4 - 8) X 10-8 with signal efficiencies in the range 5.5 - 12%.
'While the April 2008 shutdown of BABAR brings to an end the data taking period
for the experiment, final limits based on the full tau data sample are expected in the
year following the shutdown. As the size of the data sample at Belle increases, Hew
lower limits will doubtless be set. Plans for a high-luminosity Super-B factory
present the possibility of setting limits of the order 10-9 - 10-10 . This, of course, is
under the assumption that no signal is found.
15
CHAPTER II
THE BABAR EXPERIMENT
1 Introduction
Most modern accelerator-based particle physics experiments are conducted by large
collaborations of scientists and engineers. The necessary experimental facilities
include acceleration and beam guidance devices, which create large numbers of
particles in the desired initial state. Detection facilities are also needed to observe
and record final states from the reactions. The design and operation of these large
.
facilities requires the dedication of hundreds of highly trained contributors. Most
recent large detectors have been constructed as general purpose machines, allowing
for the possibility of making many different measurements with the same data. As
these experiments typically produce large quantities of data, many scientists are
required to extract these measurements from the data.
The B-factory concept was proposed in 1987 to study the decays of B-mesons.
In this concept, electrons and positrons are collided at a CM energy of 10.58 GeV,
right at the peak of the Upsilon 4(8) resonance in the e+e- total cross section. The
Upsilon 4(8) has a mass just slightly greater than twice the ,mass of the B meson,
and it decays almost exclusively to pairs of B mesons. By using asymmetric beam
energies to create the 10.58 GeV CM energy system, the B mesons are produced
with a boost in the laboratory reference frame. This results in measurable lifetimes
and fiightlengths of the B mesons. By observing differences in decay properties of B
and anti-B (B) mesons, one can make careful studies of CP violation.
The relatively small branching fraction for B mesons to CP eigenstates
necessitates a machine which can produce large numbers of B mesons. The rate of
production for a final state F is RF = La-F, where L is the instantaneous luminosity
and a-F is the cross section for e+e- - F. For the collision of two bunches at
16
frequency j with nl particles in the first bunch and nz particles in the second, the
instantaneous luminosity is written as
£ = jn1n2 .
21TA
(11.1 )
The cross section A is the product of the transverse bunch widths in x and y, under
the assumption that the bunch densities can be described by Gaussian distributions.
For a given cross section (see Table 11.1), the production rate can be increased by
using bunches with more particles, by increasing the bunch-crossing frequency, or by
decreasing the bunch cross section. The instantaneous luminosity is a flux, and has
units of [lj(time x area)]. The integration of the instantaneous luminosity over the
running time gives a measure of the accumulated data. Unless otherwise noted, all
further references to the luminosity will refer to the time-integrated luminosity.
As seen in Equation 11.1, the instantaneous luminosity is a general property of
the colliding beam system and is not dependent on the final state F. Thus, the high
instantaneous luminosity required for B meson studies provides a high rate for other
final states as well. In fact, the cross sections at 10.58 GeV for
e+e- ---> UU, dd, 58, ee, /+/- are all similar to that for BB, effectively making the
B-factory a tau and charm factory as well (see Table 11.1). In fact, Babar has
recorded significantly more tau decays that any previous experiment. This large
sample of tau decays leads to better precision on SM measurements and
opportunities to place more stringent limits on unobserved processes, including
lepton-flavor violating decays.
In Section 2, we examine the production and collision of e+e- pairs at 10.58
GeV CM energy, and in Section 3 we consider the detection of the the decay
products of those collisions. In Section 6, we will focus on the computing and data
processing components of the experiment. JVIuch of the discussion in this chapter is
based on material from reference [49]. All figures are taken from this reference.
2 Particle Acceleration for the BABAR Experiment
The BABAR experiment makes use of SLAC's 2 mile linear accelerator (linac) facility
to produce beams of 9 GeV electrons and 3.1 GeV positrons. The beams of particles
are then injected into the 800 m diameter PEP-II storage rings. At the IR-2
interaction region, the beams are brought into collision. The BABAR detector,
17
bb
cc
uds
T+T-
fJ+fJ-
e+e-
cross-section/nb
1.05
1.30
2.09
0.89
1.16
c:::40
Table 11.1: Approximate production cross sections at BABAR, including experimental
acceptance factors. uds refers to the total continuum production to UU, dd, SS.
constructed around this interaction point (IP) detects the long-lived particles
coming from the final state of the e+e- interaction.
2.1 Beam Production
The Stanford Linear Accelerator has been used to accelerate particles for collisions
since its construction was completed in 1966. In its current role, linac is used to
generate 9.0 GeV electrons and 3.1 GeV positrons to be collided inside the BABAR
detector. Electrons are produced with a polarized electron gun at the far end of the
linac. The electrons are collected into bunches of about 500 billion particles apiece,
and magnetically steered through damping rings to optimize the shape of the
bunches. Oscillating electric and magnetic fields then accelerate the bunches down
the 2-mile-long linac. Before being injected into the PEP-II rings, some electrons
are diverted for positron production. A fixed tungsten target is bombarded with
these electrons, producing e+e- pairs. The resulting positrons are returned to the
far end of the linac, collected into bunches of similar size and shape to those of the
electrons, and accelerated back down the linac, out of phase with the electrons.
2.2 Beam Storage
At the near end of the linac, bunches of electrons at 9 GeV and bunches of positrons
at 3.1 GeV are injected into the PEP-II storage rings. A tunnel contains two
beampipes for the counter-rotating beams, along with steering magnets and
acceleration stations. The tunnel circles the SLAC research yard at a radius of 400
meters. The high energy ring (HER) contains the electron beam rotating clockwise,
18
while in the low energy ring (LER) the positrons flow counterclockwise. Particles in
both rings are kept in orbit by a combination of magnets and radio frequency (RF)
acceleration.
Bunches in the rings have a longitudinal length (along the direction of travel) of
about 1 cm. For a given bunch spacing in the ring, only a certain number of bunches
can be circulating at any time. Furthermore, the quality of the beams in the rings
deteriorates over time due to a number of factors including random e+e- collisions
and beam-gas interactions. With no further injection of bunches, this situation
leads to an effective beam lifetime of 2-4 hours. The luminosity also decreases as the
beam quality deteriorates. For the first few years of the BABAR experiment, the
solution was to dump the beam and refill the rings with fresh bunches from the
linac. Unfortunately, data could not be taken during the refill, which often took 40
minutes. The current solution, known as trickle injection, is to continuously inject
small numbers of bunches into the ring. Under trickle injection, the detector records
data almost continuously, with only a brief inhibit window where the detector
ignores data around a recently refilled bunch. Trickle injection was implemented for
the LER e+ beam in November 2003 and for the HER e- beam in March 2004.
2.3 Beam Energy
About 10% of the data recorded at BABAR is taken with the e+ e- eM energy
lowered by about 40 MeV to 10.54GeV. At this off-peak energy, the e+e- cross
section is sufficiently far below the Y4(S) resonance that the production is
effectively free of B-mesons. The cross section for ee, uds, and 7+7- production is
nearly flat through the entire energy region from the Y4(S) peak though the
off-peak energy range. The data recorded at the off-peak energy allow physicists
studying B meson decays to understand the contribution of the continuum
production to the total cross section at the Y 4(S) resonance. For physicists
studying 7 decays, data recorded on- and off-resonance are equally useful, since the
7+ 7-- cross section is essentially the same at both energies.
2.4 Interaction Region
The HER and LER beams are brought into collision at the interaction region (IR)
inside the BABAR detector. The incoming beams are focused and brought into
19
collision by a combination a dipole and quadrupole magnets. After colliding
head-on, the bunches are quickly separated so as not to disrupt the next incoming
bunch from the opposite beam. Figure 11.1 shows the layout of the beams and the
PEP-II magnets around the interaction region. The beampipe around the IP is 27.8
mm in radius, and constructed of double-walled beryllium. Beryllium is one of the
lightest elements, giving it a small radiation length, but it is also very stiff. Water
circulated in the 1.5 mm gap between the walls of the beampipe provides cooling.
The inner surface of the beampipe is coated with a 4 /-lm layer of gold, which
reduces synchrotron radiation at the IP. A support tube encloses the beampipe, the
innermost detector component, and the innermost magnets. The total material
corresponds 0.019 radiation lengths, with the beryllium, the gold, and the support
tube contributing approximately equal amounts.
2.5 Performance
The PEP-II B-factory has capably delivered luminosity to the BABAR detector for
the duration of the experiment. The record-high instantaneous luminosity of
1.21 x 1034 cm-2 S-2 was reached on August 16, 2007. Integrated luminosity records
are shown in Table II.2 for individual 8-hour shifts, days, and months. The total
integrated luminosity is shown in Figure 11.2.
3 The BABAR Detector
The BABAR detector is a general purpose detector which must provide tracking
capabilities for electrons, muons, protons, and charged kaons and pions. The
detector must also provide good angular and energy resolution for electrons and
Table II.2: Integrated luminosity records for various time periods, in inverse picobarns
(pb) and inverse femtobarns (fb), where 1 barn = 10-28 m2 •
Time Period
8 hours
24 hours
7 days
30 days
Integrated Luminosity
329.7 pb-1
891.2 pb- 1
5.25 fb- 1
18.84 fb- 1
20
PEP-II Interaction Region
/
/
/
7.5
QF5
/
/r---,I
/
/
/
9Gev
/
QD4
/
QF5
o-_-O~CJF,
/ /
/
/
/
/
10
20
-10
/ QD4
-20 /
/
/'
QF2 Detector
-30
,
-7.5 -5 -2.5 0 2.5 5
Meters
(/)
.....
Q)
......
Q)
E
.~
c
Q)
o
Figure 11.1: The PEP-II interaction region around the BABAR detector.
21
As of 2008/01/08 00:00
-- Delivered Luminosity
-- Recorded Luminosity··························
Off Peak
100
PEP II Delivered Luminosity: 504.13/fb
400 - BaBar Recorded Luminosity: 484.92/fb
Off Peak Luminosity: 52.20/fb
200
CI>
-
(l3
C)
CI>
-_ 300
:=. 500
.~
en
Figure II.2: Integrated luminosity at BABAn as a function of timC'.
22
photons. Identification of long-lived particles is important, particularly
differentiation between charged pions and kaons. Finally, the detector must be able
to reconstruct decay vertices, especially those of short-lived B mesons.
3.1 Detector Goals and Constraints
The design of the BABAR detector is driven by physical constraints from the
interaction region (IR) layout and by performance goals for specific physics
processes. The PEP-II focusing magnets nearest to the IP limit the total length
along the beam axis. The detector is offset by 37 cm in the direction of boost. This
offset increases the acceptance of the detector components in the CM frame. In
order to reduce perturbation of the beams by the tracking system solenoid, the
detector axis is offset by 20 mrad with respect to the beam axis in the horizontal
plane.
The high luminosity of the e+e- interactions creates an environment with high
levels of machine background signals unrelated to primary e+e- collisions. The
dipole and quadrupole magnets which steer the beams into collision produce large
amounts of synchrotron radiation. Though these high energy photons are generally
diverted away from the detector, they still provide the primary source of machine
background. Other sources of background include beam-gas interaction due to
imperfect vacuum conditions in the beampipe, and the interaction with the machine
of low energy particles from radiative Bhabha scattering. The detector components
have been designed to withstand background rates at nearly 10 times the design
luminosity for the duration of the expected 10-year lifetime.
The general physics program of the BABAR Collaboration sets some basic
performance goals for the detector:
• large and uniform acceptance, down to small polar angles,
• high efficiency for charged track reconstruction,
• good track momentum resolution,
• good energy and angular resolution in calorimeter, and
• efficient particle identification and low mis-ID rates.
The B-physics program brings about further constraints. Branching fractions to CP
eigenstates are of the order 10-4 , and the final states typically include two or more
23
charged particles and several 7fo,s. Therefore, further goals from precision B-physics
measurements include:
• good resolution on the displaced B decay vertex, and
• significant 7f /kaon separation.
While the T-- eRe search does not require the full set of BABAR detector
capabilities, the significance of the resulting measurement is still constrained by a
number of performance issues. The most important factors are:
• tracking efficiency and resolution, and
• electron and muon identification and hadron rejection.
The innermost component of the BABAR detector is the Silicon Vertex Tracker
(SVT). Moving radially outward, the cylindrical Drift Chamber (DCH) surrounds
the SVT and completes the inner tracking system. The Detector of Internally
Reflected Cherenkov light (DIRC) is located outside the tracker and provides
particle identification information. The Electromagnetic Calorimeter (EMC) lies
outside the DIRC and just inside the superconducting magnet. The outermost
system is the Instrumented Flux Return (IFR), which completes the magnetic
circuit and provides muon detection. Figure 11.3 shows a y - z cross-section of the
BABAR detector, and Figure 11.4 shows a x - y view. The BABAR coordinate system
follows the diagram in the upper left-hand corner of II.3, and is defined as follows:
• the origin is located at the center of the detector (not the IP).
• the y axis points radially upward.
• the x axis points radially outward in a plane parallel to the ground.
• the z axis point in the direction of the CM boost (in the direction of the
electron beam).
• the angle e is the polar angle, measured from the positive z axis toward the
positive y axis.
• the angle ¢ is the azimuthal angle, measured from the positive y axis toward
the positive x axis.
tv
~
e+
1J 3500
I
i t
-5 r 1375
4m
Figure II.3: Sideview of the BABAR detector.
detector t.
l INSTRUMENTED
i f FLUX RETURN IIFRI
IF I BARREL SUPERCONDUCTINGI I r COIL~. / ELECTROMAGNETICr 1015 I 1749 1149 --1 CALORIMETER
' J ~ 4050 I IEMCIr- 1149 .,. I -, DRIFTCHAMBERtit, I r- 370 r lOCH!I i: ' SILICON VERTEX
i ; TRACKER
I I In I ISVTI
\ J. "l"I, ,-}---'-]i-J---, ]1'~R
'! /ENDCAP
!II ~~-===:=-_~ /
BI
01
02
FLOOR
o Scale
BABAR Coordinate System
y
~
BUCKING COIL
CRYOGENIC
CHIMNEY
MAGNETIC SHIELD
FOR DIRC
CHERENKOV
DETECTOR
IDIRC)
GAP FILLERl
PLATES
3500
i
DCH
SVT
DIRC
~-- CORNER PLATES
I ~ 1-
a Scale 4 m
BABAR Coordinate System
y
) -x
z
\ cutaway Isection
IFR BARREL
SUPERCONDUCTING -
COIL
EMC
EARTH QUAKE
ISOLATOR
EARTH QUAKE
TIE-DOWN
~IV:I '~IIII~FLOOR ,5'~ ~_~_~~ __ : 3~¥4 ~=to-o-o--o~fl1i·
) --- ~
IFR CYLINDRICAL RPCs -
Figure Ir.4: Endview of the BAEAR detector.
tV
01
26
3.2 Charged Particle Tracking
The inner components of the BABAR detector are surrounded by a super-conducting
solenoid that produces a 1.5 Tesla magnetic field. Charged particles follow helical
trajectories in this field, and the component of the particle momenta transverse to
the field lines can be calculated from the curvature of the trajectories. These
trajectories are reconstructed from the interactions of the particles with the SVT
and the DCH.
The SVT records the trajectories of particles within approximately 10 cm of the
interaction point. As the name implies, the SVT plays an important role in
measuring the decay vertices of short lived particles. In fact, the design of the SVT
was primarily driven by the need to accurately measure the lifetime and flightlength
of B mesons, along with constraints from the PEP-II magnets and beampipe. The
SVT also provides an initial measurement of the energy loss due to ionization
(dEldx). Because of the magnetic field, charged particles with transverse
momentum less that 100 MeVIc do not reach the DCH, and the SVT provides the
only trajectory measurements for such particles. The vertexing capability of BABAR
is relatively unimportant for tau studies such as the search for T --t £ff. However,
initial trajectories from the SVT still play an important role in the tracking of
charged particles.
The DCH, with its capability of measuring charged particle trajectories
throughout most of its 800 mm radius tracking volume, plays a primary role in the
tracking of charged particles. Measurements of track curvature provide momentum
and dE/dx information and the DCH is capable of making these measurement for
particles with momentum greater than 100 MeVIc and with 0.1 GeVIc < Pt < 5.0
GeVIc. Because different particles such as electrons, pions, and muons have
different energy loss characteristics, dE/dx information acts as a form of particle
identification. For low momentum particles, this information is generally
complimentary to other particle identification information derived from the DIRC.
At extreme forward and backward angles, the DCH dE/dx measurement is the only
source of particle identification. Finally, the data acquisition system uses signals
from the DCII to create primitive trigger signals, as described in Section 5.
27
Silicon Vertex Tracker
The SVT consists of five layers of double-sided silicon strips. The inner three layers
are built from six modules in r/J and are fiat along the direction of the beam. The
inner layers are built as close as possible to the beam pipe to minimize the effect of
multiple scattering on vertex measurements. The outer two layers are constructed
as arches and contain 16 (layer 4) or 18 (layer 5) modules. These layers are close to
the inner radius of the DCH, and allow for better linking of hits in the SVT to
tracks in the DCH. A longitudinal schematic view of the SVT can be seen in
Figure II.5. The strips on opposite sides of each layer are oriented orthogonally to
each other, with the r/J strips running parallel to the beam and the z strips oriented
transversely to the beam axis. To provide full azimuthal coverage and to aid in
alignment, the inner layers are tilted by a small amount in r/J, and the outer layers
are divided into two sub-layers. Figure II.6 shows a transverse schematic view of the
SVT. Each layer is divided into half-modules, which are read out at each end of the
detector by radiation-hard circuits. The total number of readout channels is
approximately 150, 000. Radiation is a major factor for any component so close to
the beam pipe. The SVT is required to withstand radiation doses of 1 Rad/day for
layers 1-3 and 0.1 Rad/day for the outer two layers.
Figure II.5: Longitudinal schematic view of the SVT.
28
- Beam Pipe 27.8mm radius
Figure 11.6: Transverse schematic view of the SVT.
Drift Chamber
The DCH measures 276 cm in length, with an inner radius of 23.6 cm and an outer
radius of 80.9 cm. Figure 11.7 shows a longitudinal view of the drift chamber. The
chamber is filled with a 80:20 mixture of helium:isobutane gas at 4 mbar above
atmospheric pressure, and consists of 7104 hexagonal drift cells arranged in 40
cylindrical layers. The layers are grouped by four into superlayers (see Figure II.8),
with alternating superlayers offset by ±45 to±76 mrad azimuthally to provide
longitudinal position information. Each cell consists of one grounded
tungsten-rhenium sense wire surrounded by six aluminum field wires held at
approximately +1900 VI. Charged particles passing through the chamber ionize the
gas, and the ionization shower, guided by the field created by the field wires, drifts
to the sense wire to be read out at the backward end-plate. Each signal on the sense
wire gives a measurement of drift time, which is used to calculate track trajectories,
as well as a measurement of integrated charge, from which energy loss can be
calculated. The choice of low-mass wires and and helium-based gas mixture leads to
minimal electromagnetic scattering in the DCH, about 0.2% of the radiation length
for the material.
1DCH voltage has been set to slightly different values over the course of the experiment. Early
data were recorded at 1900 V and 1960 V. The majority of the data has been recorded at 1930 V.
29
163011015 ' · 1749----'11 68
l;~en~~l_ il .,.,,! ? z < Z\ /[ J9
~ ~485j 2~.4 '=_:=+--11_3_58_8_e_~ 1_7-,-\t2__~3_6------'<lJ.f---
e- =1 464 r== 'PI If e+
469
t
1-2001
8583A13
Figure II.7: Longitudinal view of the DCH, with dimensions in mm.
The Magnet
The BABAR magnet system consists of a super-conducting solenoid, along with a
flux return which is instrumented from muon detection, and a field-compensating
bucking coil. The magnet also provides structural support for many of the detector
components. Figures II.3 and 11.4 show many of the key components of the magnet
system, as well as some of the nearby PEP-II magnets. To optimize the detector
acceptance for the asymmetric collision energy, the detector is offset by 370 mm in
the direction of the electron beam. The z-component of the magnetic field lies along
the z-axis of the detector coordinate system; this is also the approximate direction
of the electron beam.
The solenoid contains 10.3 km of cable made of filaments of super-conducting
niobium-titanium wound into wires and co-extruded with aluminum. The 4.5K
operating temperature is maintained by the circulation of liquid helium through
channels welded to the solenoid support cylinder. While the flux return provides
important support for the detector components, its design was driven by the much
larger magnetic forces and by earthquake considerations. Asymmetries and
imperfections in the flux return steel result in large axial forces, and a quench of the
magnet could generate sizable forces via eddy currents. Four earthquake isolators
limit horizontal acceleration to 0.4 g, and the detector components have been
30
16 0
15 0
14 0
13 0
12 -57
11 -55
10 -54
9 -52
8 50
7 48
6 47
5 45
4 0
3 0
2 0
1 0
Layer Stereo
=
I- -I
4cm
+ Sense o Field • Guard x Clearing
1-2001
8583A14
Figure II.8: Schematic layout of the drift cells for the four innermost superlayers.
The lines between the wires have been added to show the cell boundaries. The line
below the first layer is the I-mm-think beryllium inner wall.
31
designed to tolerate vertical acceleration up to 0.6 g. The bucking coil is a
water-cooled copper coil placed around the beampipe at the backward end of the
detector This coil reduces field leakage into the PEP-II components and shields the
DIRe photomultipliers. The magnetic field has been carefully studied (see
Figure II. 9), and shown to be of uniformly high quality. Within the tracking
volume, the azimuthal component B¢ does not exceed 1 mT. The variation of the
field transverse to the trajectory of a high momentum track is at most 2.5% from
maximum to minimum within the tracking volume, as seen in Figure 11.10
1.55
1.45
E
N
co
1.35
0.05
C -0.05
co~
-0.15
0.54
0.80
IP
,.. 1D~ift Chamber _I
1-2001
8583A2
-1.0 0.0
Z (m)
1.0
Figure II.9: The magnetic field components B z and HI' as a function of z for various
radial distances r (in meters).
32
1.02 r------.---.----~--_,_,
~ 1.00 r--=:;.....e::..._
2-
~
2:
of
2.01.0
Track Length (m)
0.98 '----_-----J'--_----l__----l__----l.....J
0.0
1-2001
8583A1
Figure n.10: Relative magnitude of the magnetic field transverse to a high momentum
track as a function of track length from the 1P for various polar angles (in degrees).
The data are normalized to the field at the origin.
Tracking Performance
The performance of the SVT under normal running conditions can be studied in
terms of efficiency and spatial resolution. The efficiency can be calculated for each
half-module by comparing the number of tracks crossing the active area of the
detector to the number of associated hits read out. The efficiency for a sample of
events recorded in July 2000 is plotted in Figure n.ll. The combined hardware and
software efficiency for these events is 97%, excluding the effect of defective readout
sections.
The spatial resolution is calculated from hit information for events with two
high-momentum tracks. The track momentum is compared to the hit location, and
the difference is projected onto the wafer plane along either the z or ¢ direction.
The width of these distributions gives the resolution, which are shown in
Figure 11.12. Averaged over the whole SVT, the spatial resolution for normal tracks
ranges from 10 - 15 J.1m for the inner layers to 30 - 40 J.1m for the outer layers.
The position resolution of the DeB can be measured by studying the precise
relationship between measured drift time and drift distance in e+e- and J.1+ J.1~
events. This drift distance is computed from an estimate of the distance of closest
33
I
- --- -
...........---- -
.. -+-
542 + 3
= --~-
0.9 f- a)
f- 10.8
>-.
o
~ 0.7 -
o + +
:::::: 0.6 i-L-,---I--+--I+--'--,.-----J-t__+--+---l+--+:-+-+--+-+--+---Ili-l-+--+--t-~r_'__+~I
WI
-t
0.9 b) -
0.8 - '1 2 3 4 5 ~-
+ +0.7 - -
0.6 I ,
, I
0 10 20 30 40 50
Half-module number
Figure lI.ll: SVT hit reconstruction efhciency, as measured on fJ +~C events for (a)
forward half-modules and (b) backward half modules. Vertical lines delineate the five
different layers.
angle (degrees)
- (b) -
Layer 1 Layer 2
- -
-+- -+-
-+- -+-
-+--+--+-
-+-
......
Layer 3 Layer 4
-+-
-+--+--+--+-
-+--+-
-50 0 50
Layer 5 angle (degrees)
--..
60
40
20
e
~ 0
:~ 60
] 40
o
~
..: 20
-e-
o
60
40
20
o
-50 o 50
60
40
20
e 0
~
= 60
o
:g 40
'0
~ 20
N
o
60
40
20
o
- Layer 1 - Layer 2 (a)
-+-
..
-+- ...
-+--+-
-+- -+--+-
-+--+-......-+- -+- -+-
......
Layer 3 Layer 4 -+-
-+- -+-+ -+--+--+--+---..
-+--+-......-+--+-
-50 0 50
Layer 5
-+- angle (degrees)
--.. -+--+-
......
-50 0 50
angle (degrees)
34
Figure 11.12: SVT hit resolution in (left) z and (right) ¢ coordinate in microns, plotted
as a function of track incident angle in degrees.
approach between the track and the sense wire. The drift distances and drift times
are averaged all the wires in the layer, but are separated by into two sets: those
tracks passing to the left of the sense wire, and those tracks passing to the right.
Figure 11.13 shows the position resolution as a function of drift distance, for tracks
on the left and right side of the sense wire.
The specific energy loss for charged particles traversing the DCH is computed by
measuring the total charge deposited. The charge from each traversed cell is
corrected for gain variations, pedestal-subtracted, and integrated over a time range
of about 1.8 /-lS. Further corrections are made on account of variations in gas
pressure and temperature, cell geometry, signal saturation, and entrance angle to
the cell. Measurements of dE/dx in the DCH are plotted as a function of
momentum in Figure 11.14. Resolution of just over 7% is achieved.
The total tracking efficiency is based on the combined performance of the SVT,
the DCH, and the algorithms used in the software reconstruction of the tracks.
While relatively simple track finding algorithms are used to quickly generate input
signals for the trigger, the offline reconstruction of charged particle tracks (see
Section 6.1) makes use of a variety of sophisticated search methods which refit each
track multiple times, searching for stub tracks and missed hits to better the
35
0.4 I. I I I I
•
0.3 - -
E
-S • •
c •0 0.2 - -
·S
0
• •(f) •(l) •a::
• •0.1 •••• ••••- -
0 I I I I
-10 -5 0 5 10
1-2001
Distance from Wire (mm)8583A19
Figure I1.13: DCH position resolution as a function of the drift distance in layer 18,
for tracks on the left and right side of the sense wire. The data are averaged over all
cells in the layer.
1-2001
8583A20
10-1 1
Momentum (GeV/c)
10
Figure I1.14: Measurements of dE/dx in the DCH as a function of track momentum.
The curves show the Bethe-Bloch predictions for each particle type.
36
resolution. The absolute tracking efficiency for the DCB can be measured by simply
comparing the number of tracks detected in the SVT to the number of
reconstructed tracks in the DCB. This efficiency varies based on the voltage of the
sense wire, with a maximum efficiency of 89% for the initial voltage of 1960 V, and
a slightly lower efficiency for the final voltage choice, 1930 V.
Fully reconstructed tracks are parameterized by five values (and the associated
error matrix) which are measured at the point of closest approach to the z-axis.
The distances from the origin of the coordinate system are do and zo, in the x - y
plane and along the z-axis, respectively. The angle cPo is the azimuthal angle, while
/\ is the dip angle relative to the transverse plane and w = l/pt is the curvature.
As measured for Bhabha (e+e-) and di-muon events, the resolutions on the first
four of these parameters are
0"do = 23 f1m
0"Zo = 29 f1m
O"¢o = 0.43 mrad
O"tauA = 0.53 . 10-3 .
The most important resolution for the purpose of the T -----+ U£ analysis is that of the
transverse momentum Pt. This resolution can be parameterized by the linear
function
O"Pt/Pt = (0.13 ± 0.01)% + (0.45 ± 0.03)%, (II.2)
where Pt is measured in GeV/c. This curve and the resolution data are shown in
Figure 11.15.
3.3 Pion and Kaon Identification
The DIRC is an innovative detector which provides particle identification via a
measurement of the particle's velocity. Velocity measurements, when coupled with
the momentum measured in the DCB, provide discrimination between particles of
different mass, particularly charged hadrons such as pions and kaons. \iVhile 7f/K
separation is extremely important for the flavor-tagging of B meson decays and the
identification of rare two-body B decays, the T -----+ U£ searches are naturally less
sensitive to the quality of charged hadron identification. Nevertheless, electron
identification makes some use of the DIRC 2 and kaon rejection is highly dependent
2The algorithm used for electron identification in this analysis does not actually use information
from the DIRe. However, an updated electron selection procedure based on likelihood ratios does
37
on this detector. The momentum range of the DIRC is set in part by the need for
1f/K separation in time-dependent asymmetry measurements, for which the typical
hadron momentum is below 1 GeV. For rare two-body B meson decays, the hadron
momenta lie between 1.7 and 4.2 GeV. The DIRC is designed to provide 4(T 1f/K
separation over the full momentum range.
Figure II.16 shows a sideview of the major DIRC components. The detector
contains of a layer of rectangular silica (quartz) bars oriented parallel to the beams
with an inner radius of 810 mm. The 144 bars are arranged in a 12-sided polygonal
barrel. Each bar is 4.9 m long and constructed from four 1.225 m pieces glued
end-to-end. The bars are 17.25 mm thick and 35 mm wide.
As charged particles with velocity exceeding the Cherenkov threshold pass
through the bars, Cherenkov photons are emitted in a cone about the track
momentum vector with an opening angle Be given by
1
cos(Be )= /3n' (11.3)
where /3 is the velocity divided by the speed of light, and n is the index of refraction
for the bars. The photons are transmitted down the bars and the angle Be is
maintained via total internal reflection (TIR). At the forward end of the the
detector, mirrors reflect the light toward the opposite end. At the back end of the
detector, the bars terminate at the conical, water-filled standoff box (SOB).
Photomultiplier tubes (PMTs) line the rear of the SOB and detect the photons
coming from the bars. A trapezoidal wedge of silica is fixed to the end of each bar.
By reflecting the photons at large angle with respect to the bar axis, the silica
wedge reduces losses due to TIR at the silica/water interface, and reduces the
density of PMTs needed for a given resolution. Figure 11.17 shows the details of the
bar end region, including the wedge and the SOB.
3.4 Electromagnetic Calorimetry
While the inner detectors (the vertex tracker, drift chamber, and Cherenkov
counter) are specifically designed to have a minimal and predictable impact on a
particle's momentum, the electromagnetic calorimeter does just the opposite. The
make use of the DIRe. This updated selector is used for essentially all electron identification in
recent BABAR analyses.
38
EMC is constructed of a material which induces electromagnetic showers, the
products of which are read out and used to make measurements of energy and
angular position. For the general program of B meson physics at BABAR, the design
and performance of the EMC is driven by the need to detect photons from the
decays of neutral pions and TJ mesons. In many analyses, including the T ----t fJ!jl-
analysis, the energy deposition in the EMC is used to identify electrons.
Calorimetry Requirements and Design
The EMC is designed to measure electromagnetic showers over the range of energy
from 20 lVIeV to 9 GeV. The lower bound comes from the need for efficient
reconstruction of B meson decays containing neutral pions and TJ mesons decaying
to photons. The upper bound on the energy range is set by the need to measure
high energy electrons from the e+e- ----t e+ e- e+ e- and e+ e- ----t ''!'y processes which
are used for calibration. Energy resolution of 1 - 2% is required for rare processes
involving neutral mesons decaying to high energy photons. Measurement of these
rare processes also requires angular resolution of a few mrad at energies above 2
GeV. The EMC must also fulfill a number of physical and mechanical requirements,
including the ability to operate inside the 1.5 T magnetic field. Temperature and
radiation exposure must be carefully monitored and controlled, energy calibrations
must be easily performed over the full energy range, and the whole detector must
operate reliably over the expected ten-year lifetime of the machine.
To meet the stated physics requirements, the EMC was constructed from
thallium-doped cesium-iodide (CsI(Tl)) crystals in a finely-segmented array. The
crystals have a high light yield and a short radiation length relative the crystal
depth. The transverse size of the crystals is approximately the Moliere radius of the
material, which optimizes the angular resolution while appropriately minimizing the
number of readout channels for each shower. The relevant properties of CsI(Tl) are
shown in Table 11.3.
39
1-2001
8583A22
048
Transverse momentum (GeV/c)
Figure II.15: Transverse momentum resolution, as determined from cosmic ray muons
traversing the DCH and SVT.
BUCKING COIL
IRON GUSSET
MAGNU Ie
SHIELD
Figure 11.16: Longitudinal view of the DIRC.
365
40
PMT + Base "
10,752 PMT's~
Purified Water
17.25 mm Thickness
(35.00 mm Width) /\
Standoff
~
PMT Surface \
\
\
I
,I\
" \, \
,/ Light Catcher \
" \
" \
" \
Window
rBarBox/1Track '
Trajectory Wedge ,
\
I+-{4X14~92:m~}-- 1.17m ----1
glued end-to-end
8·2000
8524A6
Figure II.17: Detail of the DIRC bars and the imaging region.
Table II.3: Properties of CsI(Tl).
Parameter Values
Radiation Length
Moliere Radius
Density
Light Yield
Light Yield Temp. Coeff.
Peak Emission Amax
Refractive Index (Amax )
Signal Decay Time
1.85 cm
3.8 cm
4.53 g/cm3
50000 i/MeV
0.28%;aC
565 nm
1.80
680 ns (64%)
3.34 fJ,s (36%)
41
The EMC consists of a cylindrical barrel and a conical forward endcap. The
detector has full 360° azimuthal coverage and polar coverage from 15.8° to 141.8°,
corresponding to 90% coverage in the CM system. The crystals have a tapered
trapezoidal cross section and lengths which vary according to the polar position of
the crystal. A longitudinal cross section is shown in Figure 11.18. The barrel
contains 5760 crystals arranged in 48 rings in e, each containing identical 120
crystals evenly spaced in cP. The endcap contains 820 crystals arranged in 8 rings in
e. The innermost two rings in the endcap are primarily for shower containment, and
electrons at the corresponding polar angles are difficult to identify. To minimize the
amount of pre-showering, the crystals are supported from the outside and only a
thin gas seal separates the EMC from the DIRC.
1---------2359---I
External
Support
i1555----I------ 2295 -----1
1
920 1127-i---- 1801 ' "\ 26.8'
38.2' : 558 22 7'~ 15.8'
1 ,!. t
-'-----'-
1375
1979 1-20018572A03
Figure II.18: Longitudinal view of the EMC.
Each crystal is read out by a pair of photodiodes at the back of the crystal.
While most light is internally reflected by the crystal surfaces, each crystal is
wrapped in two layers of reflective material to enhance the number of photons which
reach the back of the crystal. Further layers of foil and epoxy provide shielding and
electrical isolation. Each photodiode is connected to a low-noise preamplifiers. The
amplified signal is passed on to a custom auto-range encoding circuit, which
provides different gains for different ranges of energy. Upon the reception of an L1
accept signal, features extraction is performed on a ±2f1s window around the
.... - _._----------
42
waveform peak. A schematic of the wrapped crystal and some of the readout
electronics is shown in Figure II.19.
Output
Cable
Diode
\.-----f----. Carrier
Plate
Aluminum _
Frame
Silicon -t-tti==*hl
Photo-diodes 1-'....---'L.J..L.----..:~L...----'tL-j
TYVEK
(Reflector)
Aluminum ----.TIll
Foil
(R.F. Shield)
Mylar----lH III
(Electrical
Insulation)
CFC---+lIIIII
Compartments
(Mechanical
Support)
Csl(TI) Crystal
11-2000
8572A02
Figure II.19: A schematic of the wrapped crystal and the readout electronics on the
back end.
CaloriInetry Performance
The energy resolution of the EMC is measured with a number of different sources
over a wide range of energy, and can be parameterized as
(JE
E
(2.3 ± 0.3)% EB (1.85 ± 0.12)%.
4JE(GeV) (11.4)
Figure 11.20 shows the measured energy resolution as well as the fitted function
(Equation 11.4). The first term in the fit comes from statistical fluctuations in the
~
~0.Q7
~
';' 0.06
0.03
0.02
0.01
• nO ---7 Yf
D 11 ---7 Yf
.. Bhabhas
a Xc ---7 J/\jI Y
...... MonteCarlo
I
Photon Energy (GeV)
43
Figure 11.20: Energy resolution of the EMC for photons and electrons, as measured
for various processes. The solid line is from the fit (Equation 11.4), and the shaded
area denotes the fit error.
number of photons and other electronic noise. The constant term b, which
dominates at high energies, is associated with light collection, leakage, and
absorption between and in front of the crystals. The angular resolution, which due
to the crystal cross section is the same in eand <P, is parameterized similarly:
rJ(J = (2.3 ± 0.3)% EB (1.85 ± 0.12)%.
-'----Jf'=E::::::::;=(C===e===V7) (11.5)
Figure 11.21 shows the angular resolution for photons from nO decays.
Electron identification make significant use of the EMC. While the dE/dx loss in
the DCB and the Cherenkov angle in the DIRC can be used to separate charged
hadrons from electrons, the most important variable for positive electron
identification is the ratio of the energy deposited in the calorimeter to the
momentum of the charged track, as measured in the DCB and SVT. This ratio
should be very near unity for electrons. The details of the electron identification
algorithm used in this analysis can be found in Appendix B. Plots of the electron
selection efficiency and hadron mis-ID rates for the electron identification algorithm
used in the analysis can be found in Section 4.
44
4
2
00 5O.
...... MonteCario
............................
1.5 2 2.5 3
Photon Energy (GeV)
Figure 11.21: Angular resolution of the for photons from nO decays. The solid line is
the fit (Equation II.5).
3.5 Muon Detection
The Instrumented Flux Return must efficiently identify muons over a wide range of
momenta and angles. The IFR was also designed to detect neutral hadrons, such
K£'s and neutrons, although in practice the IFR is rarely used to detect anything
but muon identification. In terms of the general BABAR physics program, muon
detection plays an important role in the measurement of leptonic and semileptonic
decays of Band D mesons. The IFR aids in the measurement of missing momentum
and can be used to veto charm decays. Muon identification plays a particularly
important role in the , ~ £U searches. Because some of the searches (particularly
,- ~ p,-p,+ p,-) are expected to produce muons with momentum lower than 500
MeV, the performance of the IFR for identification of muons over a large
momentum range is of great importance.
The IFR is an integration of the magnetic flux return and the muon
identification instrumentation. It consists of a central hexagonal barrel, which covers
50% of the solid angle in the eM frame, and two endcaps (Figure 11.22). The IFR is
3.75 m long, and has an outer radius of 3.01 m and and inner radius of 1.78 m.
The finely-segmented steel of the IFR provides a path for the solenoid's
magnetic field. The steel is segmented into layers ranging in thickness from 2 em to
10 em. The thickness was chosen based simulations of muon penetration and hadron
45
Figure 11.22: Overview of the IFR: barrels sectors and forward (FW) and backward
(BW) endcaps.
shower shapes in the steel. The IFR steel is interspersed with layers of detector
material: either resistive plate chambers (RPCs) or limited streamer tubes (LSTs).
Two-dimensional position measurements are made by using orthogonal readout
strips oriented in ¢ and z. In the original detector, the IFR instrumentation
consisted solely of RPCs. Currently, the hexagonal barrel is instrumented with
LSTs, while the forward and backward endcaps still contain RPCs.
The RPCs identify muons by detecting streamers between a high-voltage gap.
Each RPC strip consists of two Bakelite sheets, 2 mm thick and separated by by a
gas-filled 2 mm gap. The inside surfaces of the Bakelite are treated with linseed oil.
The outside surfaces are painted with graphite and kept at high voltage (about 8 kV
and ground). An insulating mylar film separates the high voltage graphite from the
aluminum readout layer. The cross-section of an RPC is shown in Figure II.23. A
charged particle crossing the RPC gap initiates an electric discharge which is read
out via capacitive coupling to the aluminum strips. The readout strips on opposite
sides of the RPC are oriented orthogonally to give a two-dimensional position
measurement.
46
Foam
Foam
>
I
r--,.----------~--- Aluminumj x StripsII Insulator
-~ Graphite
: 2 mm
~~~~"""''''''''''''''''''';'''''''~~~:..:>I: 2 mm
: 2 mmI~!!!!!!=====_c~ GraphiteInsulator
Y Strips
Spacers
--......... Aluminum
8-2000
8564A4
Figure II.23: Cross section of a planar RPC, with schematic of the high voltage
connections.
47
The LSTs identify muons by detecting streamer ionization on a high-voltage
wire. LSTs are constructed of a single 100 Mm diameter sense wire running down
the center of a 9mm x 9mm plastic section. Plastic structures, or profiles, contain 8
such sections side-by-side, with one side open. These profiles are coated with
graphite and inserted into plastic tubes of matching dimensions for gas containment.
Signals on the wires themselves provide a ¢ measurement, and strips on the outside
of the tubes running perpendicularly to the wire provide a z measurement.
The original IFR contained 19 layers of RPCs in the barrel, 18 layers in the
endcaps, and 2 cylindrical layers between the EMC and the magnet. The RPCs in
12 of the barrel layers were replaced with LSTs over the period 2004-2006. Six of
the remaining layers were filled with brass to compensate for the loss of absorbing
material.
Muon identification relies almost entirely on the IFR, although other systems
can provide limited information. Muons are detected as tracks in the SVT and the
DCB, and must behave like a minimum-ionizing particle in the EMG. The tracks
from the inner detector are extrapolated to the IFR, taking into account the
non-uniform magnetic field, multiple scattering, and the average energy loss.
Extrapolated tracks for real muons must appropriately intersect the observed
clusters of hits in the IFR. The depth of penetration into the IFR must also be
consistent with a muon of the given momentum and angle.
When developing selection criteria for the identification of muons, there is
always a trade-off between efficiency for muon and mis-ID rates for pions and other
hadrons. These numbers are parameterized in terms of particle momentum in the
lab frame, polar angle, and azimuthal angle. The IFR efficiency for identifying
low-momentum muons is one of the limiting factors for the T -----+ iff searches. In
particular, muons with momentum less than 1 GeV rarely reach the IFR. The
actual performance of the IFR for detecting muons from LFV tau decays is
discussed in Section 4.
4 Simulations
In the Babar experiment, simulations of e+ e- collisions and the subsequent detector
and trigger response play an important role. These simulations can be used to
compensate for detector inefficiencies, as well as providing theoretical predictions for
distributions. It is useful to simulate both the signal events for which one is
48
searching as well as the background events which mimic the signal. Simulations of
signal processes allow one to carefully study the effect of one's analysis on the signal
efficiency. Simulations of the background processes allow precise comparisons
between the distributions of the simulated events and distributions of the data
themselves. Once the validity of the background simulations are confirmed for a
general situation, they can then be used to make predictions of specific background
contributions. This method of background prediction is in contrast with predictions
made directly from data, in which biases can be introduced by extrapolating from a
potentially small number of data events. For the T -t eee analysis, simulations of the
expected background events are compared to real data events in a kinematical region
near where the signal is expected. Once the background simulation is verified, these
events can be used to predict the expected number of background events in the
signal region - all without actually counting data events in the signal region. This
procedure reduces sensitivity to potentially large statistical fluctuations in the
number of background events seen in the small signal region of the data sample.
The simulation of events at Babar starts with piece of software called an event
generator. The goal of such a generator is to reproduce the behavior of the colliding
e+e- pair. A minimal set of desirable behaviors includes the accurate simulation of
differential and total cross sections as well as initial and final state radiation, and
the proper treatment of spin, particularly for short-lived particles. Initial and final
state radiation refers to the emission of one or more photons from the initial
(incident) electron and positron or from the final (outgoing) particles. For the
T -t eee search at Babar, the T particles are produced in pairs via the reaction
e+e- -t T+ T-. Consequently, the final-state particles in the simulation of the
reaction are T particles, which have a lifetime of about 0.29 picoseconds and which
travel on average less than a tenth of a millimeter before decaying. A secondary
piece of software simulates the decay of the T particles and the radiation from the T
decay products. Other software simulates the detector response and the trigger.
The individual momentum four vectors for particles in simulated events are
generated using Monte Carlo (MC) techniques. In fact, the data sets containing the
simulated events are often referred to as "1\10nte Carlo". There are a number of
different elementary MC algorithms but the basic goal is the same: to use randomly
generated numbers to create data which follow a specified distribution. This process
can also be thought of as numerical integration of the distribution. A trivially
simple example is that of a flat, bounded distribution in one variable. In this case, n
49
random numbers are drawn from a uniform distribution,
{
l/(b - a) a < x < bf(x;a,b) = - -:
o otherwIse
(11.6)
As n becomes large, a histogram of the generated values reproduces the original
distribution.
Because it is computationally cheap to generate random numbers which follow a
uniform distribution, such numbers are often used as a seed for MC events which
are to follow a more complicated distribution. In the Acceptance-Rejection method
of Von Neumann, the desired probability density function (PDF) f(x) is enclosed by
a function C h(x), where C is a constant greater than 1 and h(x) is typically a
uniform distribution or a normalized sum of uniform distributions. To generate data
distributed according to f (x), a candidate x is first generated according to h(x). A
second candidate u is then drawn from a uniform distribution (0,1). The candidate
x is accepted into the data set if uC h(x) ::::; f(x); otherwise x is rejected and the
process starts over.
The event generator used for the simulation of T pair production at Babar is
KK2f [50]. Conceptually, the algorithm is simple: the differential cross section is
given by the squared, spin-summed matrix element times the phase space. Random
numbers are used to draw a specific value from the PDF for each independent
quantity, such as Ip-;I, ¢, e, etc. In practice, the allowance for arbitrary numbers of
initial and final state photons which can interfere with each other, plus the inclusion
of higher order QED and EW corrections, makes for a very complicated calculation.
The KK2f generator achieves significantly better precision than the previous
generators of its kind (e.g. KORALZ[51], KORALB[52]). For the simulation of other
background processes such as e+e- - qq (q = u, d, S, c, b), Babar uses the
EvtGen [53] and Jetset [54] packages.
The decay of the T particles is simulated by the TAUOLA software package [55].
For the T - a£ analysis, TAUOLA must generate two different classes of T decays:
generic decays in which the T decays according to 8M branching fractions and
differential decay widths, and specific LFV decays for which the distributions are
not known.
Generic T decay rates are defined in TAUOLA by a DECAYDEC file. The file
lists the most recent values of the T branching fractions from the Particle Data
50
Group (PDG) [56]. For a given 7, a specific decay mode is selected randomly with
weights given by the measured branching fractions. Then, an algorithm to specify
the outgoing particle momenta and angle must be chosen. For leptonic decays of the
7, the Sl\/1 matrix element is known. From the square of the matrix element one can
calculate the differential decay width, which leads directly to PDFs for parameters
of the outgoing leptons and neutrinos. Complete QED corrections of 0(0:) are
included in TAUOLA. For two-body semileptonic decays (7 ----> KVn 7 ----> 1WT ) , SM
calculations give the differential decay widths to zeroth order, with the pion and
kaon decay constants taken from experiment. Radiative corrections are included in
the leading logarithmic approximation.
For 7 decays with two or more hadrons in the final-state, one must chose a
specific parameterization for the hadronic portion of the matrix element. The choice
of this form factor is influenced by the observation that hadronic 7 decays are
dominated by intermediate resonances decaying to pions, kaons, and other
pseudoscalars. In TAUOLA, these form factors are thus parameterized as
Breit-vVigner functions corresponding to the intermediate vector and axial-vector
resonances3 . The masses and widths of these resonances must be taken from
experiment. For high-multiplicity decays, chains of these resonances are used, with
heavier intermediate particles decaying to lighter resonances along with final-state
pseudoscalars. For decays where the same final state can occur via different decay
chains, the relative contribution of each path is fixed to the experimental value.
In the search for neutrinoless 7 decays to three leptons, the TAUOLA program is
also used to simulate the LFV decays. Since these decays have never been observed,
and few (if any) models exist which predict the dynamics of the final-state leptons,
the choice is made to model these decays in the simplest way possible. The matrix
element is set to unity and the differential decay widths are proportional to only the
Lorentz-invariant phase space for three particles. This choice explicitly removes any
resonant behavior and does not allow for relative angular momentum between any
two outgoing leptons.
Radiation from the leptonic decay products of the 7 particles must be simulated
as well. For the BABAR experiment, this is done by the PHOTOS software
package [57].
3In the case of some higher-multiplicity T decays, these resonances could also be pseudoscalars.
51
The output of the event simulation is a set of four-vectors which describe the
kinematics of the long-lived particles in the event4 . The four-vectors are used as
inputs to GEANT4[58], a software package which simulates the passage of particles
through the Babar detector. This simulation models multiple scattering, leptonic
and hadronic ionization of the traversed material, leptonic bremsstrahlung and pair
production, positron annihilation, the photoelectric effect, and Compton scattering.
The simulation also incorporates the effect of background noise in the detector by
mixing in signals taken from real snapshots of the detector subsystem electronics.
Finally, the simulated detector output is passed to the L1 trigger simulation (see
Section 5). If the trigger simulation generates an Accept signal, the detector
simulation output is passed onto the L3 trigger and the reconstruction software, just
as if it were data corresponding to a real event.
5 Data Acquisition and Triggering
The high luminosity of PEP-II is achieved in part by shortening the space between
bunches, which corresponds to a higher bunch-crossing frequency at the IP. This
high event rate amounts to an essentially continuous stream of collisions, preventing
the synchronization of the detector readout with the bunch-crossings. The actual
physics rate, by which we mean qq, p+p-, and T+T- events, is only about 65 Hz at
an instantaneous luminosity of 1034 cm- 2 S-l. Bhabha scattering, which is generally
uninteresting for physics purposes, contributes around 500 Hz, and random
interactions of the beam produce detectable tracks and clusters at nearly 20 kHz.
Since the data storage rate is limited to 100-200 Hz, the triggering mechanism must
provide an event rate reduction of around two orders of magnitude.
5.1 Trigger Requirements and Design
The BABAR trigger is designed as a two-level system: a hardware-based Level One
(L1) trigger, and a software-based Level Three (L3) trigger. BABAR has no Level
Two trigger. The trigger is required to operate with very high efficiency for physics
processes of interest, and with good stability and easily measured and reproducible
41n defining which particles are long-lived, some care must be taken with particles of intermediate
lifetimes, such as K~ mesons, which decay a measurable distance from the IP. For the T -. £££ such
particles are relatively unimportant, as they only occur in the background and are not part of the
signal.
52
behavior. Specifically, the efficiency for triggering on BB pairs must exceed 99%,
and deadtime must not exceed 1%.
To achieve the necessary event-rate reduction, event data for the entire detector
is read into storage buffers every 67 ns. This time interval corresponds to 16
bunch-crossings, most of which are empty events with no interesting physics. The
storage buffers can hold data for up to 193 events. In parallel, a small subset of the
event data is sent to the trigger for processing. The size of the event buffer sets the
limit on the total time for the Ll trigger to make the choice to store an event for
further processing. This latency is about 13 f-tS.
The trigger algorithms must be sufficiently simple to allow for relatively easy and
accurate simulation. In order to meet these requirements, the trigger was designed
to recognize general topologies rather than specific physics processes. Orthogonal
selection criteria allow for independent calibrations of different components and
robustness against missing and fake signals. The data objects calculated as part of
the trigger algorithm are stored and made available for efficiency studies. Finally, a
small number of events are passed and stored regardless of the trigger decision.
These events provide further data for performance studies. The trigger is made to
as flexible as possible, with a maximum amount of configurable parameters.
5.2 Level One Trigger
The Level One trigger samples a small set of the DCH and EMC signals every 269
ns. The IFR is sampled every 134 ns. A decision whether to store the event for
further processing must be made within the 13 f-tS latency window. The Ll trigger
consists of three sub-triggers working in parallel: the Drift Chamber Trigger (DCT),
the El'vIC trigger (EMT), and the IFR trigger (1FT). A global Ll trigger (GLT)
collects outputs from the 3 sub-triggers and forms a number of configurable trigger
lines. The values of these lines are passed to the Fast Control and Timing System
(FCTS), which makes the final decision to read out the event buffers and send the
event for further processing. In order to limit the load on L3, the Ll output rate is
configured to be no more than 1-2 kHz.
53
Level One Drift Chamber Trigger
The input to the DCT consists of a single bit for each DCll sense wire. The output
is a set of 16-bit ¢-maps which represent candidate tracks. These maps are
generated through use of three different modules. First, DCll signals are combined
to form track segments by set of 24 Track Segment Finder (TSF) modules.
Information about these segments is then passed to the Binary Link Tracker (BLT)
module, where the segments are linked to form complete tracks. In parallel with the
BLT, TSF outputs are also sent to a set of eight ZO/PT Discriminator (ZPD)
modules, which select tracks based on a fit to their transverse momentum (PT) and
distance of closest approach to the z-axis (zo). Prior to 2004, Transverse Momentum
Discriminator (PTD) modules were used to select tracks with high PT. PDT
modules did not fit for Zo0 With the projected increase in background in mind, the
ZPD modules were designed to better reject backgrounds by discarding events with
Zo > 20 cm.
The Track Segment Finder modules are responsible for finding track segments in
the 1776 overlapping groups of eight DCll cells called pivot groups (see
Figure 11.24). Each group contains one pivot cell and each cell contains one sense
wire. The signals on every DCll sense wire are sampled every 269 ns. Each signal
found increments a two-bit counter for the cell and the counters for all eight cells in
the group form a 16-bit value that is used to address a lookup table. In the case
that the group value corresponds to a valid segment, the lookup tables provide
position and time information which form the basis of the output data. The TSF
algorithm is capable of refining the event time and its uncertainty such that the
output data can be forwarded to the BLT and the ZPD every 134 ns.
Super
layer ..---..----r~
8 Cell Template
---- Pivot cell layer
Figure II.24: Track Segment Finder pivot group.
54
The Binary Link Tracker receives hit information from the TSF and maps it
onto the DCH geometry in terms of a map of supercells: 32 sectors in ¢ and 10
radial superlayers (SL). The segments are combined in such a way that dead or
inefficient supercells do not degrade the track-finding efficiency. The linking
algorithm is based on the CLEO-II trigger [59], and starts from the innermost
superlayer and works its way outward. Linked track segments are classified by the
outermost superlayer reached. Short tracks are defined by reaching the middle
superlayer, and long tracks must reach the outermost superlayer. See Table II.4 for
the definition of these and other DCT output objects. These tracks are sent to the
GLT in the form of a 16-bit ¢-map.
The ZO/PT Discriminator modules provide further background rejection by
evaluating candidate tracks according to their Zo value. Figure 11.25 shows the
distribution in Zo of tracks reconstructed by L3 without a cut on ZOo The ZPD
algorithm first searches seed track segments from the TSF and fits them for an
initial measurement of PT and the dip angle (A). Other segments are added to the
candidate track and, by using information from the DCH stereo superlayers,
subsequent fits give a value for Zo and refined values for PT and A. Tracks reaching
SL 7 and with PT and Zo values within an adjustable range are send on to the GLT.
Table II.4 shows these and other DCT output objects.
Level One Calorimeter Trigger
The Electromagnetic Calorimeter Trigger searches for calorimeter showers above
specified energy levels, and sends corresponding location information to the GLT.
The EMT operates in terms of towers, 240 8 x 3 (e x ¢) arrays of crystals in the
barrel and 40 19-22 crystal wedges in the endcap. Every 269 ns, all crystal energies
above 20 MeV are summed over each tower and sent to the EMT. The conversion of
the tower energy to ¢-maps for the GLT is done by 10 Trigger Processor Boards.
These boards determine the total energy in the 40 sectors in ¢, while summing over
different e ranges. These energy sums are compared against the trigger objects
shown in Table 11.4. After an estimation of the time of the energy deposit and a
conection for timing jitter, the results are sent to the GLT.
55
o 40 80
L3 Track Zo (em)
-40
o l...d:'~-L--l-----,------,-----L......-.L----,--,----,-~~~~
-80
<fJ
~ 8000
ro
~
'"'-o
06000
Z
2000
4000
Figure 11.25: Single track Zo for all L1 tracks without a cut on zoo
Level One lV1lion Trigger
The Level One Muon Trigger (1FT) is used to trigger on muon pairs from the IP and
cosmic rays. The output of the 1FT is used primarily for calibration and diagnostic
purposes. For the purpose of the trigger, the 1FT is split into ten sectors: one for
each of the six barrel sextants, and one for each half end-door. The input to the
1FT is an OR of all ¢-strips in eight selected layers in each sector. The 1FT module
samples these sectors every 134 ns and generates a three-bit trigger word (U) in
which is encoded the values for the seven 1FT trigger conditions (see Table 11.5).
Global Level One Trigger
The inputs to the Global Level One Trigger are the 11 trigger objects (stored in the
form of ¢-maps) listed in Table 11.4, plus the 1FT summary word U. First, the GLT
synchronizes the incoming signals by accounting for different latencies in the L1
components. Next, an additional set of ¢-maps are formed from back-to-back tracks
and clusters, and pairs of tracks and clusters with similar ¢ values. The ¢-maps are
used to address lookup tables for a count of the number of each trigger object in the
Table II.4: Primitive trigger objects constructed by the Level 1 trigger.
DCT Object PT cut Zo cut
A Short tracks reaching SL5 120 MeV/c -
B Long tracks reaching SL5 150 IvIeV/c -
Z Standard Z tracks reaching SL7 200 MeV/c 12 cm
Zt Tight Z tracks reaching SL7 200 MeV/c 10 cm
Z' High PT tracks reaching SL7 800 MeV/c 15 cm
Zk Tracks reaching SL7 (asymmetric cut) 200 MeV/c (e-) 12 cm
800 MeV/c (e+)
EMT Objects energy cut
M Minimum ionizing clusters 130 MeV -
G Intermediate energy clusters 350 MeV -
E High energy electron/photon 900 l\'1eV -
X M object in forward endcap 130 MeV -
y Backward barrel electron 1000 MeV -
U 1FT hit pattern from IFR - -
Table 11.5: 1FT trigger patter definitions, where f1 refers to a signal in a sector.
U Trigger condition
1 2: 2f1 topologies other than U = 5,6,7
2 If1 in backward endcap
3 If1 in forward endcap
4 1f1 in barrel
5 2 back-to-back f1S in barrel + 1 forward f1
6 1 f1 in barrel + 1 forward f1
7 2 back-to-back f1S in barrel
56
57
event, and trigger lines are formed by logical combinations of these counts. The time
of the trigger is derived from the timing distribution of the highest priority trigger.
The GLT sends the value of each trigger line to the FCTS, which can optionally
mask or scale any of those triggers. If a valid trigger remains, the FCTS issues an
L1 Accept signal, and the FEE buffers are read out for the appropriate time.
5.3 Level Three Trigger
The L3 trigger performs fast track finding and fitting by using segments from the
TSF and then taking actual DCH information to better the resolution on the track
parameters. First, the time of the track is determined from the TSF segments.
Then, the segments compatible with this time are used to address a lookup table.
This table is populated with data corresponding to simulated tracks above a cutoff
transverse momentum and which originate within a certain adjustable distance from
the IP. Tracks from the table are then refit for all five track parameters. This full fit
allows for tracks which do not originate from the IP.
The L3 trigger processes the EMC data in two steps: first, crystals with energy
above a threshold are identified, and second, clusters are formed from these crystals.
Individual crystal energy measurements are rejected if they are below 20 MeV or if
their timestamp lies outside the 1.3 p,s event window. The remaining crystal energy
measurements are added, along with their times, to a list. Clusters are formed by
using a lookup table addressed by the crystal positions and energies in the list.
Clusters must have energy greater than 100 MeV.
Based on the fitted tracks and the reconstructed clusters, the L3 trigger
performs a variety of filtering processes that classify events and reduce backgrounds.
A Bhabha filter identifies and vetos one- and two-prong events with E/p
measurements consistent with the expectation for Bhabha events. Other filters flag
radiative Bhabha, II, and cosmic events for calibration and luminosity monitoring.
6 Offline Data Processing
Events which are selected by the Level Three trigger are stored for further
processing. These events are grouped into runs, with each run representing
approximately an hour's worth of data-taking. The full set of detector signals for a
58
run of events is written to a single data file, usually referred to as an extended
tagged container (XTC) file. The raw size of each event in the XTC is about 30 KB,
and XTC files are typically a few tens of GB in size.
6.1 Prompt Data Reconstruction
In recent years, the full processing of the event data has been conducted offline,
meaning that the data are not fully processed in real-time (i.e. as the signals are
recorded by the detector). Instead, all subsequent processing operates groups of
events corresponding to one run (and one XTC file). These data are processed in a
two-pass system. First, calibration conditions are calculated from a subset of the
events in the run and written to the conditions database. This step is referred to as
Prompt Calibration (PC). Secondly, all the events are reconstructed based on the
conditions in the database, and are written out to event collections. This step is
referred to as Event Reconstruction (ER).
The PC step of the data processing makes use of only a subset of the events in a
run. For technical reasons, these events are also stored in a secondary data file
called a calib-XTG. The calib-XTC file for each run is filled with events passing a
particular set of L3 trigger output lines, all of which are designed to provide a
constant output rate of 1 or 2 Hz, depending on the trigger line. These output lines
select Bhabha events, di-muon events, cosmic muons, and low-multiplicity hadronic
events. The PC processing software runs on these events and writes out a set of
calibrations which give a picture of the detector conditions at the moment the
events were recorded.
To better account for changing detector conditions, the PC processing software
makes use of rolling calibrations. In this method, the calibration constants from
previous runs are stored and used as additional input information for the calculation
of the current run's calibrations. This method also effectively provides for larger
statistics without actually increasing the sampling rate for the calibration events.
vVhen all the calibration events in a run have been processed, the results are
collected and passed to a final processing module. This module calculates the final
calibration constants for that run and writes them to a temporary database where
they are made available for the next run. The calibration constants are also written
to the main conditions database, and assigned a validity interval corresponding to
the time interval over which the run was recorded. During a period of high
I •
59
luminosity typical of the later years of BABAR running, the PC processing step was
performed on computers at SLAC, utilizing around 30 CPUs.
The Event Reconstruction step processes the full set of events in the XTC file.
Because the detector has already been calibrated for the run period, the event
,
reconstruction can process the events in any order. This task is accomplished by a
farm of a few hundred multi-CPU computers at Padova, Italy, along with (more
recently) a similar farm at SLAG.
The actual reconstruction of an event (both PC and ER) is done by a software
application called Elf. In contrast to the trigger algorithms, this software uses the
full event data to reconstruct tracks in the DCH and SVT and clusters in the EMC
and IFR. Elf also creates lists of diHerent particles by running particle identification
(PID) algorithms on the reconstructed tracks (see Section 4 for a full description of
the algorithms using in the analysis). Finally, Elf fills a set of Boolean variables
called tags which provide a way of quickly classifying events based on very general
characteristics. Background filter and trigger information are also stored as tags.
The charged-track lists, neutral particle lists, PID lists, and tag variables are
written out to files called event collections, which are made available for further
procesl3ing and analysts' use. Simulated data are also reconstructed with Elf, but
are not run through the prompt reconstruction system. The event generator
software is bundled with the detector simulation software and with Elf to form one
integrated production package which directly outputs events collections.
6.2 Data Skinlnling
l\!lost physics measurements made with the BABAH data involve only a specific type
of event. Often these events constitute only a small fraction of the total data set.
To facilitate the many BABAR analysts, one final step of centralized data processing
takes place before the typical user sees the data. Once a run is processed by the
prompt reconstruction system, the output collections are skimmed. A skim refers to
a subset of reconstructed events which fulfill some basic criteria. Groups of
physicists working with similar analyses define a skim by choosing a simple set of
criteria that selects an acceptably large fraction of the events of interest. BABAH
analysts have defined hundreds of skims over the years, and some number of these
skims are chosen to be calculated for the data and MC events. Using a large farm of
computers at SLAC, each event in an event collection is processed and assigned a
60
true or false value for each skim being run. A deep-copy skim is a physical copy of
the reconstructed data for each event that passes a particular skim. A pointer skim
is a collection of pointers to the data for event that passes the skim. Pointer skims
are much smaller, but the redundant data of deep-copy skims provides better
computing performance with large numbers of users.
The T --+ eu analysis only uses data and MC events which pass the TaulN
skim. This skim selects events for which the following criteria are true (see
Appendix A for track and neutral list definitions):
• Event passes either DCH L3 trigger or E~!IC L3 trigger (always true for data,
not necessarily true for MC).
• Event passes one or more of the following background filters:
BGFMultihadron, BGFNeutralHadron, BGFTau, BGFMuMU,
BGFTwoProng. Analysis will later require BGFMultiHadron (see Section 3).
• The number of entries in the ChargedTracks list is less than eleven.
• The thrust is defined as the vector which minimizes the transverse momentum
for all entries in the ChargedTracks and CalorClusterNeutral lists. The thrust
axis is used to divide the event into hemispheres in the CM frame. The
number of EMC clusters with energy greater that 50 MeV in each hemisphere
must be less than or equal to six.
• Using tracks from the GoodTracksVeryLoose list, one hemisphere must
contain one track, while the other must contain at least three.
61
CHAPTER III
DATA ANALYSIS
1 Introduction to Analysis
Measurements made with the BABAR data can be classified by the expected
statistical significance of the signal. BABAR is generally considered a precision
experiment, meaning that one expects to find many events corresponding to the
measurement that one wishes to make. In some cases, such as the measurement of a
branching fraction, it is simply the number of these signal events which one wishes
to measure. In other cases, the measurement is derived from information contained
in the signal events. In either case, the large number of these events allows the
physicist to make a measurement with relatively little statistical uncertainty. Many
BABAR analyses are of this type, where systematic uncertainties dominate the total
uncertainty.
The T --- fff search is one of a complimentary sort of analyses in which the
statistical significance of the expected number of signal events is small. In many
cases the observed number of signal events is small enough that the experiment can
be said to have a null result. In this case, rather than making a measurement, a
limit is placed on the quantity in question. For the T --- fff searches, the goal is to
place an upper limit on the branching fractions.
A few BABAR analyses are of a hybrid sort. These measurements yield
statistically insignificant numbers of signal events based on data from the early
years of running, but are expected to result in statistically significant measurements
with most or all of the final BABAR data set. The search for the leptonic B meson
decay B --- n'T is one of these experiments. The T --- iff processes are not predicted
by the SM, but they are predicted at varying levels by untested extensions of the
SM. Therefore, the search must be conducted in such a was as to naturally
62
incorporate the observation of a statistically significant number of signal events. In
other words, the analysis should not be biased toward a null result, and the choice
to quote a measurement of the branching fraction or an upper limit on the
branching fraction must be well-justified.
1.1 Branching Fractions
Even though we expect not to measure a branching fraction for T ~ eee, the
essential elements of a branching fraction must be measured before an upper limit
can be calculated. Theoretically, the branching fraction for T ~ X is defined by the
ratio of the T partial width for final state X to the total width,
f xB(T ~ X) =-.
f tot
A measurement of the branching fraction is given by
NxB(T~X) = N'
T
(IIL1 )
(IIL2)
where Nx is the measured number of T ~ X decays and NT is the total number of T
decays.
From Equation IIL2, we can now see the quantities necessary for a measurement
of the branching fraction. The total number of T decays can be calculated from the
cross section cr(e+e- ~ T+T~) and the time-integrated luminosity £ of the data set.
The number of decays T ~ X is estimated by the ratio
N
x
= N meas = Nabs - N bk9 ,
E E
(IIL3)
where the number of decays measured N meas is given by the number of decays
observed Nabs minus the number of background events N bgd . A background event is
an e+ e- collision with decay products that look like T ~ X, but in fact are a
different process. The quantity E is an estimate of the signal efficiency, the
probability that a real T ~ X decay is identified as such. This quantity incorporates
detector, trigger, and software reconstruction inefficiencies, as well as the effects of
event selection criteria in the analysis itself. In summary, five quantities must be
measured or estimated to calculate the branching fraction: the number of events
observed (Nabs), the number of expected background events N bgd , the signal
63
efficiency (c), the luminosity £, and the cross section (Jr~r' Uncertainties must be
estimated as well for all quantities (except Nabs)'
With the five quantities previously mentioned (and the associated errors), one
can calculate the branching fraction for T -----+ X. Because the decays T -----+ £££ have
never been observed, we approach the analysis with the expectation of a null result,
where Nabs is statistically consistent with a Poisson fluctuation around N bgd .
Therefore, we must define a procedure to calculate an upper limit on the branching
fraction.
1.2 Upper Limits
Before we discuss upper limits, we must first introduce some basic tools for
describing the uncertainty associated with a measurement. These methods could be
applied to statistically significant measurements, as well as upper or lower limits on
unmeasured quantities. Much of the material in this section can be found in greater
detail in Cowan [60].
Confidence Intervals for a Continuous Variable
In the classical (or frequentist) interpretation of statistics, the uncertainty of a
measurement can be expressed through the construction of Neyman confidence
intervals [61]. In this method, one defines the estimator e, which is the outcome (or
a function of the outcome) of the experiment, and an estimate of the true value B.
Furthermore, one knows the probability density function G (e; B) as a function of e,
with the true (but unknown) value B as a parameter. In many practical cases, this
PDF is a Gaussian function or a Poisson function. From this PDF, one can define a
value U Q such that there is a fixed probability a to observe B 2': U Q • Similarly, one
can define a value U(3 such that there is a fixed probability (3 to observe B :::; U(3.
Thus, UQand u(3 can be determined from
a = p(e :::; uQ(B)) = 100 G(e; B)de,
uc«(I)
j U/3((I)(3 = p(e :::; u(3(B)) = -00 G(e; B)de.
(IlIA)
(IlI.5)
64
The functions ua(B) and u{3(B) can be plotted in the BliJ plane and the bounded
region is called the confidence belt. For a true value B and PDF G( iJ; B), the
probability for the experiment to yield an estimator iJ that is in the interval
[ua(B),u{3(B)] is 1 - {3 - Q.
A line corresponding to a given measurement Bobs intersects the curves U a and
u{3' Call the corresponding values of B a and b, respectively. The interval [a, b] is
called the confidence interval at a confidence level 1 - {3 - Q. If the experiment were
repeated n times, yielding n values of Band n confidence intervals, the resulting
intervals would include the true value B in a fraction 1- (3 - Q of the experiments.
For a specific value of iJ that leads to an interval [a, b],
(III.6)
Equations IlIA and III.5 then become
j (JObS{3= -00 G(iJ;b)diJ.
(III.7)
(III.8)
In addition to the two-sided interval [a, b], the values a and b alone correspond to
one-sided confidence intervals, or upper and lower limits. The value a is the
hypothetical value of the unknown parameter B for which a fraction Q of repeated
estimates for iJ would be higher than the current value iJobs' Similarly, the value b is
the hypothetical value of B for which a fraction {3 of repeated estimates for B would
be lower that the current value Bobs' Therefore, b represents an upper limit on B
given the observation Bobs at the 1 - {3 confidence level. In many high-energy physics
experiments, {3 is chosen to be 0.1, so that upper limits are reported at 90%
confidence levels.
A physicist must choose to report a one-sided or two-sided confidence interval,
but this choice can introduce some complications. As noted by Feldman and
Cousins [62], it is undesirable for this choice to be made on the basis of the outcome
of the experiment. For example, a physicist may decide to quote a two-sided
interval if the number of signal events observed is greater than some number, and
otherwise quote a limit (or one-sided interval). Under closer scrutiny, this procedure
can lead to intervals which do not satisfy Equations IlIA, III.5 , III.7, or III.8. The
65
procedure also fails by producing empty confidence intervals for certain values of e.
This failure often occurs in counting experiments for which there is an expected
background such that eabs = Nabs - N bgd . The Feldman and Cousins prescription for
the construction of confidence intervals involves an ordering principle by which
individual values of eare added to the interval until the confidence level reaches or
exceeds the desired value. Such intervals naturally shift from one- to two-sided
intervals as the observed number of events increases. For the case where the
observed number of events is significantly lower than the background, these intervals
also have the desirable behavior of remaining non-zero. Feldman and Cousins also
suggest that the experimenters should quote the sensitivity, or the average upper
limit that would be obtained for an ensemble of experiments with the quoted
background and no true signal. This quantity is discussed in more detail in
Section 1.5. In the case of the' T -----+ en analysis, the values for Nabs are consistent
with the background expectations. Therefore, we make use of the sensitivity to give
a sense of the most probable outcome of the experiment, but the upper limits can be
accurately calculated without constructing the full Feldman and Cousins intervals.
Confidence Intervals for Discrete Variables
When searching for rare or unobserved processes such as T -----+ ue, the outcome of
the analysis is an observation of a small number of events which pass all selection
criteria. For any rare reaction which leads to a small number of expected events
N exp , the number of observed events Nabs is sampled from a Poisson distribution in
the variable n with mean v = N exp ,
(III.9)
Next, we rewrite Equations III.7, IIL8 for the Poisson variable n = e, with
Nabs = eabs and v = e,
(III.10)
(III. 11 )
66
The Poisson distribution is a function of the discrete variable n, so the integrals in
Equations III.7 and IlLS have been replaced by sums in Equations III. 10 and III.11.
With Equation III.ll and the outcome of the experiment Nabs, one can calculate an
upper limit b at the 1 - 13 confidence level.
Now that we have defined the upper limit on the number of signal events
observed in terms of a one-sided classical confidence interval, it is important to
clarify what this upper limit actually means. The upper limit at the 1 - 13
confidence level on the number of events observed seL = b is the hypothetical value
of the number of signal events for which the probability of observing Nabs events or
less is 13. This is an important point: the calculated upper limit is nothing more
than the hypothetical value of the true signal strength for which the experimental
observation is unlikely to a particular degree.
1.3 Incorporating Uncertainties into Upper Limits
All measured quantities come with associated uncertainties and it is important to
take these into account in a consistent manner. As listed in Section 1.1, there are
five quantities needed for the calculation of a branching fraction or upper limit, and
four of these quantities can have significant uncertainties. It is helpful to define a
quantity known as the sensitivity S = 2E:£aTT • The uncertainties on the cross
section, the luminosity, and the signal efficiency can be combined into the
uncertainty on the sensitivity, effectively leaving two uncertainties in the problem.
We'll start with the simplest case of a 90% confidence level upper limit on the signal
observed, with no background and no uncertainty. We will then generalize to the
case of an upper limit on the branching fraction, with uncertainties on all measured
quantities.
In the absence of background events,
N obs
0.1 = L P (n; S90) ,
n=O
(III.12)
defines the upper limit on the number of signal events observed (s90) at the 90%
confidence level, where Nabs is the number of events observed in the experiment,
and P (n; s) is the Poisson function of n with expectation value s. Equation (III.12)
is typically solved numerically.
67
To add an expected background, we introduce the constant background
parameter b, which must be estimated from the experiment. Now the outcome of
the experiment is assumed to be drawn from a Poisson distribution with mean 8 + b.
Then, the upper limit on the number of signal events observed (890) is given by
N obs N obs ( 90 + b)n
0.1 = L P(n; 890, b) = L 8 I exp [_(890 + b)J .
n.
n=O n=O
(IILI3)
To include the effect of an uncertainty on the number of expected background
events, we follow the Cousins and Highland [63] procedure and "smear" the
expected background over a range about the central value. The width of the
smearing is given by the uncertainty on the background. Under the assumption of a
Gaussian distribution for the background, the upper limit on the number of signal
events is given by
Nobs fJ
0.1 = L 1G (b'; b, O"b) P (n; 890, b') db',
n=O (X
(III.14)
(III.15)
where G(b'; b, O"b) is a Gaussian function of b' with mean b and width O"b. The limits
of integration f3 and a can be set to +00 and -00, respectively, in the case of an
analytical solution, or to the desired precision in the case of a numerical solution.
When the upper limit is to be set on a branching fraction, uncertainties in the
signal efficiency E can be accounted for in a similar way [64]. Recall that the
branching fraction 8 is the ratio of the number of signal events to the total number
of events,
8- 8 _p-b
- N
tot
- -------S-'
where S = ENtot = 2ELO" , and p = S8 + b is the mean number of events expected to
be observed for a signal with branching fraction B, sensitivity S, and background b.
Thus, in the case of significant uncertainty on both the expected background and on
the sensitivity to the signal, the upper limit on the branching fraction (890) is
defined by the following:
Nobs
0.1 = L JJG (S/; S, O"s) G (b'; b, O"b) P (n; b', S, 890) db'dS',
n=O
(III.16)
68
where
P(n; b, S, B90 ) = (SB 90 +br exp [- (S~90 + b)]
n.
(IIL17)
As mentioned at the beginning of this section, the total uncertainty on S may need
to take into account the uncertainty on the total number of events Ntat = 2£0-, as
well as the uncertainty on the signal efficiency.
A numerical solution to equation (IIL16) is implemented in the
TCousinsHighland C++ class. The basic strategy is to find the zero of the function
1(B) = (Prob(Nabs ,B)) - 0.1, (IIL18)
where (Prob(Nabs ,B)) is the average Poisson probability as defined below. The
average is taken over a distribution of values for Prob(Nabs ,B), where each value is
calculated with a sample background count b and a sample sensitivity S, both
drawn from Gaussian distributions. Here, S is defined as before and is proportional
to the signal efficiency.
The root of equation (IIL18) is estimated with the Bisection method, in which
two values of 1 (Jo,h) are varied until they differ from zero by no more than the
desired precision, and the conditions 10 < 0 and h > 0 remain true. Values for 1
are calculated from values for B via the following method:
1. Chose a value for B.
2. Draw a value for the background bi from a Gaussian distribution with mean b
and width o-b.
3. Draw a value for the sensitivity Si from a Gaussian distribution with mean S
and width O-s.
4. Calculate the expected number of events f1i for this point: f1i = BSi + bi ·
5. Calculate the i-th Poisson probability Probi (Nabs , f1i) for n :s Nabs:
N Ob8
Probi (Nabs , f1i) = L P(n, f1i)
71=0
6. Repeat steps 2-5 j times.
(IlLIg)
69
7. The Poisson probability for B is the average over the values Probi(n, fJi), and
1 is given by
(III.20)
The value for the upper limit is given by
(III.21 )
where 10(Bo) and h (B1 ) fulfill the conditions for the Bisection method listed above.
1.4 Overview of Analysis Steps
.
In the previous section, we discussed the ingredients necessary for placing upper
limits on B(T ~ eee). Now, we outline the major steps in the analysis which lead to
these final ingredients. These steps are nothing more than a very carefully chosen
set of selection criteria by which the set of all the events in the BABAR dataset is
filtered down to a few final events. Each of the six T ~ eee searches employs a
different set of selection criteria, although the variables used are generally the same.
Data events, as well as signal and background NIC events, are all run through the
same selection procedure. Unqualified references to "events" should be assumed to
refer to both data and NIC events.
In the first step, we select events which pass a very broad selection called a skim
(see Section 6.2). The selected events are then required to pass a set of preselection
cuts, which reject poorly reconstructed events and other events which look very
little like the T ~ eee signal. \Ve next ensure that the preselected events contain the
three leptons appropriate to the particular search channel. vVe define two important
variables, a mass variable and an energy variable, which provide some of the most
precise separation of signal and background events. Rather than immediately using
cuts in these variables to reject background events, the distributions of the MC and
data events in the plane of the mass and energy variables is used to estimate the
final background contribution in the region where the signal is expected. Lastly, a
final set of selection criteria is applied to further reduce backgrounds. These criteria
are chosen separately for each search channel, and tuned to address channel-specific
backgrounds.
70
A signal region which contains most of the signal MC events is defined in terms
of the mass and energy variables. This analysis is conducted in a blinded fashion,
meaning that the number of data events in this region is left unknown until all
selection criteria are fixed and all systematic uncertainties are studied. This
technique avoids bias by ensuring that the selection criteria are not tuned to a
statistical fluctuation in the number of data events in the signal region. The
distribution of the remaining background MC events in the mass and energy plane
provides the final estimate of the background contribution in the signal region.
Systematic uncertainties are studied and errors are assigned to the background
estimate and the signal efficiency. Finally, the methods described in Section 1.3 are
used to calculate the upper limits on the six T ---. UP branching fractions.
1.5 Analysis Optimization and Expected Upper Limits
The choice of selection criteria in this analysis should be based on an optimization
of the result. One would typically choose. the upper limit for this figure of merit,
and optimize for the lowest limit. Because we are blind to the number of data
events in the signal region Nabs, we need to optimize some other quantity which
does not depend on Nabs' vVe choose to optimize the analysis to produce the lowest
expected upper limit, as suggested by Feldman and Cousins [62]. This expected
upper limit is defined as the mean upper limit expected in the background-only
hypothesis for a given sensitivity 5 = 2E£r5TT and background contribution N bgd .
This expected upper limit on the branching fraction is calculated as
B;~p = L P(n; Nbgd)B90(n, N bgd , 5),
n=O
(III.22)
where B90(n, N bgd ) is the upper limit on the branching fraction based on the
observation of n events with background contribution N bgd and sensitivity 5, and
P(n; N bgd ) is the probability of observing n events from a Poisson distribution with
mean N bgd . The upper limit B is calculated by the method described in Section 1.3,
which incorporates all uncertainties.
71
2 Selection of the Data
This analysis is performed using data recorded from June 1999 through August
2006. The BABAR Collaboration divides the data-taking period of the experiment
into Run Cycles, or simply Runs. The data used in the analysis comprise the full
dataset for Runs 1-5, with a total luminosity of 376 fb-l. These data include
339 fb- 1 recorded at the 1'(43) resonance with a CM system energy of 10.58 GeV.
The rest of the data, 36.6 fb- 1, were recorded off-resonance at a CrvI energy of 10.54
GeV. To speed up the data processing, only data included in the TaulN skim
(described in Section 6.2) were used for the initial data and Monte Carlo samples.
The signal MC explicitly includes one (signal) tau lepton decaying to three
lighter leptons, while the second tau decays according to the standard (generic) tau
decay tables. These decay tables include the latest values of the tau branching
fractions from the Particle Data Group [65]. The signal sample is divided into 6
subsamples according the LFV mode (inclusion of charge conjugates is implied):
Each subsample contains a total of 286k events with equal numbers of T+ and
T- LFV decays. The signal events are generated with the KK2f generator [50] which
simulates the initial state radiation and final state photon production. The LFV
decays in the signal modes are produced using a flat phase-space distribution in the
decay products, while the generic tau decays are simulated with TAUOLA[55].
Radiation from the final-state leptons has been simulated with PHOTOS[57].
Background estimations are made using large MC samples which simulate the
types of background events expected to be seen in the analysis. These backgrounds
can be grouped into three broad classes: bb, ce, uu/dd/ ss (qq background); Bhabha,
/1+ /1- (QED background); and generic T+ T- events with no LFV decays (T+ T-
background) .
72
Due to an insufficient quantity of Bhabha and /1+/1- MC events, these MC
samples have been ignored and the QED contribution is estimated with data
samples. Exact process names, MC statistics used and cross sections assumed for
the processes are given in Table III.1. The cross sections used are taken from [66]
except for 7+7-, which is calculated with KK2f [67] As described in Section 7, the
overall background normalization for each background type is determined from the
data, so the absolute cross sections are not actually used in this analysis. Generic
7+7- events have been generated with KK2f.
Table IIL1: Background .MC samples used in the analysis.
Sample
bb
cc
uds
7+7--bkgr
MC Process Name (J (nb) Nfte~ts' 106 LMC/Ldata
half B+B-, half BOBObar 1.05 1025 2.60
e+e- ----+ ccbar 1.30 275.2 0.56
e+e- ----+ uubar/ddbar/ssbar 2.09 398.8 0.51
e+e- ----+ tau+ tau- (KK2f) 0.89 184.4 0.55
3 Event Preselection
The LFV tau decay to three leptons produces three charged track. To reduce the
background contribution of high multiplicity qq events, we require the other tau in
the event to decay to one charged track. Therefore, the first step of the analysis is
to select events with a 1-3 topology that is characteristic of the signal tau events.
The Tau1N skim is used for all data and MC samples. The criteria for the
Tau1N selection are described in Chapter II, Section 6.2. The further preselection
requirements are listed below. Efficiencies for each cut are shown in Table III.2 .
• Event has BGFMultiHadron filter bit set.
This bit is set true for events with more that two tracks in the
ChargedTracks (see Appendix 2) list and with R2 < 0.98. R2 is the ratio of
the 2nd to the Oth Fox-vVolfram moment .
• Exactly 4 'good tracks' are required in the event.
For this analysis, we acquire our good tracks from the
GoodTracksVeryLoose list (see Appendix 3). These good tracks are
additionally required to point to the collision region (docaXY< 1 cm,
73
docaZ< 5 cm) and have a momentum in the range PT > 0.1 GeVIc, P < 10
GeVIc in the Lab frame. Good tracks must have value of the polar angle e
which allows for good particle identification (0.41 < e< 2.46, driven by the
range of the PidTables for lepton selectors, and by the EMC acceptance). The
tracks identified as a part of a converted photon candidate (found in
gammaConversionDefault list, described in Appendix 4) are not counted
as good tracks. No attempt has been made to reconstruct K s decays .
• The total charge of the good tracks in the event is equal to O.
• The event has a 'reconstructed 1-3 topology'.
The event is divided on two hemispheres using the plane perpendicular to the
thrust l axis of the event. The sign of scalar product of the given track
momentum with the thrust direction determines the hemisphere to which this
track belongs. The thrust of the event is calculated using charged and neutral
(with energy greater than 50 MeV) particle candidates in the CM frame. One
hemisphere must have exactly one good track, while other 3 must belong to
the second hemisphere. This defines a reconstructed 1-8 topology.
4 Particle Identification
After events with a 1-3 topology have been selected, particle identification (PID)
criteria are applied to the tracks in the 3-prong hemisphere. Except for a few cases
to be addressed is Section 6, tracks and neutral clusters in the I-prong hemisphere
are not subject to particle identification. Like the pre-selection criteria described in
Section 3 and the more specific selection cuts described in Section 6, the particle
identification step is designed to reject background events, while maintaining a high
efficiency for signal events.
To identify tracks and neutrals as specific types of long-lived particles, analysts
at BABAR have developed a set algorithms called PID selectors. These selectors take
input information from many components of the BABAR detector. Typical inputs
are dEldx energy loss in the drift chamber, energy loss and shower shape in the
calorimeter, and hits in the IFR. The output of a selector which is run on a
particular track or neutral cluster is always a true or false signal. Appendix B lists
IThe thrust axis is defined as the axis which minimizes the transverse momentum in the event.
74
Table III.2: Preselection efficiencies in percent for signal MC, background MC, and
data samples. Cuts are appli~d sequentially and the marginal efficiencies are quoted.
For the signal samples, the loss in efficiency due to the one-prong branching fraction
is included in these numbers. 'Trigger' means that L30utDch or L30utEmc tagbit
is set. The bb efficiencies include both B OEO and B+ B- samples. Uncertainties on
the total efficiency numbers are from ~ilC statistics.
Sample Tau1N BGFMH 4 tracks Zero Charge 1-3 topology Total
Signal MC
EEE 43.0 99.5 89.6 98.5 99.5 37.6 ±0.1
EE.Mr 42.0 99.5 89.9 98.8 99.5 38.6 ±0.1
EEMw 44.1 99.5 89.7 98.7 99.5 38.7 ±0.1
EMMr 45.6 99.5 91.1 98.9 99.5 40.7 ±0.1
EMMw 45.6 99.6 90.9 99.0 99.5 40.6 ±0.1
MMM 47.2 99.7 92.3 99.0 99.6 42.7 ±0.1
Background MC
bb 0.41 98.5 39.2 65.1 83.7 0.18
cc 4.49 97.8 46.0 72.6 89.1 1.28
uds 6.06 97.9 52.2 80.2 90.7 2.11
T+T- 16.0 95.1 77.1 98.4 99.5 11.5
Run 1-5 Data
DATA On-peak 3.63 93.5 51.9 85.5 93.3 1.51
DATA Off-peak 4.13 93.8 52.4 86.1 93.4 1.72
75
the specific criteria for the selectors used in this analysis. No modifications have
been made to these standard BABAR particle identification algorithms.
Information about particle identification is stored in lists called PID lists. The
PID list is a list of all the tracks or neutrals in the event which meet the criteria for
a particular PID selector. In this analysis, we do not directly identify any neutral
particles, so all particles mentioned in this section will be charged tracks. A given
track is said to be identified as a particular particle type when the track is included
in the list for the selector of that particle type. The PID lists are not exclusive, and
a track which meets the criteria for more than one particle type will appear in both
lists.
Analysts often need flexibility and control over the certainty of the identification
of a given track or neutral cluster. Therefore, multiple lists are generated for each
particle type, with each list corresponding to a different level of certainty. "Tighter"
selectors have lower efficiencies to identify a particle of the correct type. They also
have lower probabilities to incorrectly select a particle of a different type. The
selector names generally reflect three properties of the selector: the particle being
selected, the type of algorithm used, and the tightness or looseness of the selector.
For instance, this analysis make use of the muNNLoose selector, which selects
muons based on a neural network (NN) algorithm, using a loose selection which has
a relatively high efficiency to identify real muons. Because different T -----+ £U search
channels are populated by different background types, it is helpful to apply looser
particle identification criteria to some search channels, and tighter criteria to others.
The choice of PID selector is that which, when applied along with a set of nominal
selection cuts (Section 6), provides the best expected upper limit on the branching
fraction (see Section 1). The PID selectors used for the analysis are listed in
Table III.3.
Table III.3: Particle ID selectors used to identify the 3-prong tracks.
Search channel Electron selector Muon selector
e-e+e- eMicroTight N/A
fL- e+e- eMicroTight muNNLoose
e- fL+e- eMicroTight muNNLoose
e- fL+fL- eMicroTight muNNLoose
fL- e+ fL- eMicroLoose muNNLoose
fL-fL+fL- N/ A muNNLoose
76
The BABAR PID group generates PID tables which reflect the performance of the
PID selectors for tracks with a wide range of kinematic properties. The group starts
with high purity samples by selecting data events with a very high probability of
containing a particular set of particles. For instance, the muon sample comes from
the easily-identified process e+ e- -------- /-l+ /-l-'. The group then runs all selectors on
these samples and calculates the selection efficiency for each particle type as a
function of e, cP, and p = 1P1. The PID tables allow one to calculate the efficiency to
pass any selector for any particle type with any value for e, cP, and p. Because
selectors for all particles are run over all the samples, these tables include not only
efficiencies but also mis-identification rates.
To ensure that the MC samples accurately reproduce the particle identification
performance observed in data, most BABAR analyses apply a correction factor to
compensate for the observed difference between the MC and data PID efficiencies
and mis-identification rates. In this analysis, we avoid this correction by ignoring
MC PID information all together. Instead, we make use of the fact each MC track
was generated as a specific particle type. Each MC track is re-weighted by a PID
probability for a particle of its type and values of e, cP, and p. This PID probability
is given by the efficiency or mis-identification probability for data as obtained from
the PID tables. Take, for example, a MC particle generated as a muon with
(e, cP,p)MC, which is being identified as a loose muon with the muNNLoose
selector. This MC particle is re-weighted by the efficiency obtained from the entry
for (e, cP,p)MC in the muNNLoose PID table, which was created from real muons
in data. The original information regarding which MC tracks are in which PID lists
is completely ignored. This procedure makes much more efficient use of the available
MC statistics by not explicitly rejecting any MC tracks or events. It also avoids the
need to correct for the differences between data and MC PID selector efficiencies.
The final ]\IIC event weight is given by the product of the MC track probabilities
in the 3-prong hemisphere of the event. The I-prong track PID information does
not contribute to the event weight. Data events are accepted or rejected in the
traditional manner by requiring that all tracks in the 3-prong hemisphere are found
in the appropriate PID lists.
One potential deficiency in such a PID weight scheme for MC is that only tracks
with a MC truth match are assigned a PID efficiency. All MC particles are
generated with a definite particle type, but the MC truth match, which associates a
generated MC track with a reconstructed MC track in the detector simulation, does
77
not always exist. The remaining tracks without definite particles types (usually
pions or ghosts2 , but could also be leptons) are not assigned a PID efficiency at all.
Secondly, PID efficiencies can only be assigned to tracks with parameters that fall
within the range of the PID table bins. Thirdly, some low momentum bins in the
PID tables have no entries, in which case the low momentum MC track would be
assigned zero weight by default. The truth-matching problem affects about 0.3% of
the pre-selected uds lVIC tracks, primarily low momentum tracks in the range
100 - 300 MeVIc. The difference between assigning these tracks zero weight and
assigning them the average track weight has been studied, and the impact is
negligible. The requirements on the polar angle 8 in the pre-selection (see
Section 3) ensure that all tracks lie within the range of the PidTables. The effect of
low momentum tracks (for which the corresponding PID table bin is empty) is more
significant, as 35.3% of the T- -----+ /1- /1+ /1- events have at least one slow muon below
500 lVleVI c. These tracks account for the low PID efficiency for channels with
muons. The average PID efficiency for muons is 65%, which includes the effect of
zero-weight slow muons. Figure IlL 1 shows the muon efficiency as a function of
momentum, over a wide range of polar angles. The average PID efficiency for
electrons is 91 %, including the small effect of electron tracks which have no truth
match. Figure IlL2 show the electron identification efficiency. The corresponding
electron (muon) mis-identification rate for pions in 3-prong SM T+T- decays is
2.7(2.9)%, Figures IlL3 and IlIA show the pion fake rates as a function of
momentum. The mis-identification rates for kaons in 3-prong uds events are 4.6%
and 2.3% for electron selection and muon selection, respectively. The kaon fake
rates are shown in Figures IIL5 and IIL6.
As described in Section 7, the Bhabha and di-muon backgrounds are modeled
with data control samples. For channels T-- -----+ e-e+e- and T- -----+ e-/1+/1-, the PID
efficiency for these samples is the same as that for data. For all other channels,
QED control samples of sufficient statistics are obtained through a procedure that
does not involve particle identification. The rejection factors for different sources of
the background are given in Table IlIA.
2 A ghost is a second track reconstructed from the same physical track.
78
17.00 S; 8 < 147,00 17.005 e< 147.00
.t~·-tt*:t*~ .. =
;
;;
ut 0.9o
I I' fl ' Dara I
o J,l', MC
lV
G 0.8
c
<l)
'S
L::
<-
u
17.0058 < 147.00
II' fl+, Dma I'
,I " J,l+. MC 1
lV
G 0.8
c
u
OJ
L::
4-
Q)
0.6 0.6
o
2 345
p [GeV/cJ
2 345
P [GeV/c]
0.8 I 2 345
p [GeV/c]
Sdct:l<)f :'\\:[_f1(I.'c~ill('"So.:lcl'llnll r.lblc~ aL'al~'clllll I 'ljl II2U(17 (1).11:'11 17/112u07 (\le)
Figure II!.l: The efficiency for mllon identification in dat.a and ~IC by the
muNNLoose selector, as 8. function of Illuon Illomentulll for (::\) positively charged
muons, and (h) negatively charged llluons. Plot (c) t>hows the ratio of the data
efiiciency t.o t.he i\'IC efti.ciency.
3 4 5
P rGeV/c]
2
22.18 S; e < 141.72
I:: ,jjl.~~ll~I!I~1
0.96
I
22.18 s; 8 < 141.72
..di.,q,'l-.. •.;.. 0
0.7"---'-.w........~2~73~.......4~-'-'.S
P [Gcv/c]
"
, ,'e', Datu 1lV 0 9 ~ 0 c', MCG '.,
c
OJ
'u
L::
'Q:; 0.8
22.18 s; 8 < 141,72
~. I' e+. Data I~ 0.9 ~ 0 e+, MC
OJ
c
Q)
'0
t: 08Q) .
0.7"---'-.w........~2~73~.......4~-'-'.S
P [GeV/c]
\elcl'lOf ·llf!.hll:k·L'lrtlll~licr(l.'ck~·lIIIJl IhLI.~CI ,ill-fiSh
Figure III.2: The efficiency for e+ / e- identification in datCl and ~\'IC by the
eMicroTight selector, 8S a function of particle momenturn for (8) positrons. and
(b) electrons. Plot (c) shows the ratio of the data efficiency to the :\'IC' efficiency.
22.18 $ e < 137.38
4
2 ........ •_ .....--=t=:::::~=*1 =1
: --
O,L.....f~...L.-...~~I~.2 3
p [GeV/cl
0.02 o~
~-+-
2 3
P [GcV/c]
22.18s;8 < 137,38
lV
GO.06
c
Q.l
20.04
<-
OJ
o
0.02
2 3
P lGeV/cJ
I, 7[+,Dala I0.08 01• C' 7[+, MC
lV
GO.06 •
c
u
OJ
:=: 0.04
Q)
J );Il;l~, I :Ill-r JXb
Figure III.3: The lllis-ID rate for pions in data and MC' by the eMicroTight selector,
as a function of particle momentum for (a) positively cha.rged pions, and (b) llegMively
charged pions. Plot (c) shovvs the ratio of the clat::\ l1lis-ID wte to the Me mis-ID
rate.
79
17.00 s: 8 < 147.00 17.00! 8 < 147.00
UJ 0.081-'---~~---'
;>.,
u
~ 0.06
~ 0.04 + .- ......1+~t
.":<><><r<>"'~+
0.02 <> <><>
J 234 5
P [GeV/cl
1.4 t
G 1.2
·CIJ
+
:>-
UJ • 11'
t ---- I"
"'0UJ O.~
0.6
2 3 4 5
P lGeV/c]
S..:Ic~I(ll ~~I.ll(l~..:\ltl<lIlSck..:tl'lll ]);Il;I~CI ;i1I·rl Xh Tahk.... t·rl··Ik'11 Oil JSII121)07 (1);)1:1) J7/1/2nll7 (;'1.'1('1
Figlll'C III.4: The mis-IO late for pions ill data and MC by the muNNLoose selector,
as a functioll of particle llIomentum fOl' (a) positively charged pions, and (b) negatively
charged piolls. Plot (c) shows the rntio of the data mis-IO rate to the :,VIC lllis-iO
rate.
22.18S:8<137.38
·1.lb)~',nl.::llcdnl1l:-:1l/2007fl);lla) 17/1/2()()7C...lC)
UJ
;>., 0.2
u
c "o
u 0
l;:; •
'0 0.1
22.18 s: 8 < 137.38
o
~-.0l....-...~~:Ii:::=I~2""""""~-13
P [GeV/c]
0.3", I• K. Data
" K'>. Me
UJ
G' 0.2 ~
c "
"G • ~
t: 0 Jo .
Figlll'e III.5: The mis-IO rate for kaolls in data and MC hy the eMicroTight
selectoL as a fUllction of particle momentum for (a) positively charged kaons. and
(b) negatively charged Imol15. Plot (c) shows the ratio of the dHta mis-IO rate to the
i\IC mi::;-IO rate.
Table rlI.4: Efficiellc.y fOl' preselected f'vents to pass the rrD requirements.
Signal bb (·c uris T+T DATA
(' e+ (' 0.775 9.2·10 7 6.9·10 9 1.9 . to 6.4· 10--' 9.9· 10 <I
- + -- 0.531 1.2 . 10-6 9.0· 10-8 3.2 . 10-7 5.8. 10- 7 5.0· 10-:>I_I e e
e- p+e- 0.533 2.2· 10-6 2.0 . 10--6 1.6 . 10-(; 1.1 ·1O-(i 2.1·lO-(;
~l-e+p- 0.368 8.7.10-7 2.0 . 1O-() 5.9 . lO- G 7.2 . 10-6 8.0· 10-(j
e-Il+11- 0.359 1. 7 . 10--6 9.G·1O- 7 2.5 . 10-7 1.4.10-7 1.4 ' 10-/1
-- + -- 0.235 2.4· 1O-() 1.2 . 10-6 2.1 . 10- 6 3.4 . 10-b 1.0 . 10-5I' P P
80
-J--
I-~
2 3 4:"'-""'5
p [GeV/c]
20.05 ::; 8 < 146.10
0.6
.g
UJ 0.8
2 3 4 5
p [GeV/c]
20.05::;8 < 146.10
UJ O. I Sf- L-~'-'--'-'=--.J
g 0 I j~o.OS ~l
_0", -0- T
3 4 5
p [GeV/cj
2
20.05::; e < 146.W
0.2:
1
K- 0 ~• • at.a
o K+. Me
UJ 0.15
>..
u
c
.~ 0.1
u
<=
'-
(00.05
1):\1.I;;l.:I.lll-rI8b TJbk., C!'::ll\:d Ilil IKIJ/2007 m.Il,I) J 71J/2U07 (\1('1
FigurE' 111.6: The mis-IO rate for lmons in data and MC by the muNNLoose
selector. 8S R function of ]Huticle momentum for (8) positively charged hans, and
(b) neg8tivcly charged lmons. Plot (c) shows the ratio of the data llIis-IO r8te to tile
l\JC mis-ID rate.
5 :Mass and Energy Determination
Sillce llO lleutrino is present in the LFV decay mode .. the sigllrd events are expected
to bave the smne total ellergy and invarin.nt mass as the parent tau lepton. The
total energy difference
!\E E' E*u ~ == Tee - !Jearn (111.23)
and the invariant mass difference
61\1 = ml'ec - m r (IIl.24)
are calculated from the mC)1nentulll of the three observed tracks in the 3-prong
hemisphere. ,>,,'ith the track llUiSS hypotheses corresponding to t he search channel. In
the study of B meson dccclyS, the energy substituted mass (?TIES = Jrnt - ITJI'2.
where ?TI [J is the B ll1CSOil lllass) provides better resolution by taking illto aCCoullt
the low CM lllomentum of the D mesons For T events. the decayillg particles arC'
not nearly n.t rest: and the reconstructed 1l18SS ntl'CC prO\'idcs better resolution. Tll('
energy-constrained mass ?Tl ec , W bile having slightly better resolut ion: is not used dlle
to t.echnicCl.l difficulties. It is also expected that t.he lise of Tr/,ec would not decreflse
the expected upper limit by l!lore than 10%, fillet that only for t lie channels wit h
expected I)(tc-kgrounds 8bove one event.
The search for LFV dee-fly modes proceeds by considering t.he two-dimensional
distribu tiOll in the (61\1, 6£) plane where the signal events shonld peak around the
81
ongm. The quantities £lE and £lM tend to be smeared out somewhat due to
tracking resolution and radiative effects from initial-state, final-state, or
bremsstrahlung photon emission. As the initial tau energy is unobservable and must
be inferred from the beam energy, energy lost to these radiative effects tends to
preferentially push events toward lower values of both £lE and £lM.
Since electrons have larger radiative losses than muons, the radiative tail in the
(£lAi, £lE) distribution depends upon the decay channel considered (see
Figure III.7). For this reason, the optimal signal region is defined separately for
each signal channel. The selected signal region, as well as the borders of the Large
Box (LB) used for background studies, are shown in Table III.5. The Grand
Sideband region (GS) is defined as the large box minus the signal region. The
choice of a box for the signal region over something more complicated (like an
ellipse) is primarily for technical convenience, as it is easier to perform a 2D
integration over a rectangular region. The signal efficiencies to pass SB and LB cuts
are given in Table III.6.
Table III.5: Signal region boundaries 1'11 < £lA1 < Nh, E l < £lE < E 2 for each
decay mode. The boundaries of the large box (LB) used in the background fits is
also shown in the last column. The last row shows the signal efficiencies in percent
for these signal regions (for the events passed preselection and PID requirements).
Sample e-e+e~ e-p+e- p-e+e- p-e+p- e-p+p- p-p+p- LB
M l , GeV/c2 -0.07 -0.10 -0.05 -0.05 -0.05 -0.02 -0.6
M 2 , GeV /c2 0.02 0.02 0.02 0.02 0.02 0.02 0.4
E l , GeV/c2 -0.20 -0.35 -0.20 -0.20 -0.20 -0.20 -0.7
E2 , GeV/ c2 0.05 0.05 0.05 0.05 0.05 0.05 0.4
81.2 %
86.6 %
86.6 %
90.4 %
91.0 %
94.5 %
LB efficiency [%]
Ce+e- 52.0 %
p-e+e- 59.5%
cp+e- 69.8 %
e-p+p- 67.3 %
p-e+p- 70.6 %
p--p+p- 82.3 %
Table III.6: Signal efficiency for events passing preselection and PID to be in the
signal box or in the large box.
=::::::===:==::::=======::::===~:o=;==:::=:::::::==~====;;~
Sample SB efficiency [%]
~0.4
~
w
<0.2
.'
•
0.2 0.4
t,\ M (GeVlcA 2)
~O.4
~
w
<»0.2
•
..
82
~O.4
~
w
--:j 0.2
lau+ -:> e- J1+ 11+
•
>O.4,-r;,..,-.--r~"-'-"""""'1CI',",""r-r-.-r'I' ...
e. tau+ -:> 11+ p- 11+
W
-10.2
a
0.2 0.4
~ M (GeV/c"2)
Figure III. 7: The (6.1\1, 6.E) distriblltions for the signal channels after preselection
and particle identification. The box shows the borders of the signal region. The
histognun borders correspond to the large box. The 't-axis is logarithmically-scaled.
6 Event Selection
After 1. he preselection etud part ide ID reC[uircments, there is still R significant
contribl1t.ion of backgroLlnd events expected in the signal region. A final set of
selection cuts arc applied separately for each signal hypothesis to further reduce the
remaining background (l,lld improve the sensit.ivit.y of the analysis.
Since T---7 tie events have never been observeu and the best limits [36. 37]
previous to t.his analysis are of the order of 10--7 , it is expected that this analysis
\\'ill find a null rc~mlt. For this reason. the cuts bave been optimi:wd to minimize the
expected l1pper limit. on the brauching fractiou. This expected upper limit on 1. he
number of signal events is defined as the meal! upper limit expected for the
background-only hypothesis for a given background contribution lYbgd and sign(l,l
efhciency f: (see Sectioll 1.5).
83
As described more fully in Section 7, the background estimates are extracted
from the data itself in the sideband region. There is a danger that statistical
fluctuations in the data will favor a particular cut value and the background
estimates will be biased toward a value which is too low. To avoid being sensitive to
this kind of bias, the background normalizations forthe optimization procedure are
estimated and fixed with a nominal set of cuts applied. The data are not refit as the
cuts are moved, but rather the MC and control samples are used to predict the
relative background change as a function of a particular cut value. Cut optimization
is considered for each channel separately. In some cases the optimal cut value does
not change significantly for different channels, or there is a wide range of optimal
cut values. In these cases, a single cut value is chosen for all channels.
The selection cuts applied to all channels are the following:
• Mass of the one-prong hemisphere (mlpr ) is calculated as the invariant mass of
the charged candidates and neutrals in the the I-prong hemisphere and the
total missing momentum in the event. The charged track is assigned the
most-likely mass hypothesis. This one-prong mass is required to be
mlpr E (0.3,3.0) GeV/c2 for all channels except e-e+e- and jJ-e+e-, for
which the requirement is mlpr E (0.5,2.5) GeV/c2 .
• Momentum of one-prong track (pims )is less than 4.8 GeV/c.
• No tracks on the 3-prong side may pass tight kaon criteria (see Appendix B
for definition of the KLHTight selector).
The following selections cuts are not effective in all search channels, and are
applied to individual channels as noted:
• Total transverse momentum in the CM frame (Pr S ) is greater than 0.4 GeV/c
for channels e-e+e- and e-jJ+jJ- and greater than 0.2 Gev/C for p-e+e-.
• The invariant mass is calculated for the two possible pairs of opposite-sign
tracks on the 3-prong side. The smallest of these values (m~~~n) must be
greater that 0.25 GeV/c2 . Applied to channels e-e+e- and jJ-e+e- as a cut
against conversions in Bhabha and di-muon events. This cut is tighter than
the conversion cut in the preselection criteria.
• One-prong track must not be identified as a loose electron (eMicroLoose)
(see Appendix B for definition of the eMicroLoose selector). To ensure that
84
the veto works, the track is additionally required to have non-zero EMC
information 3. Applied as a cut against Bhabha events in channels e- e+e- and
e-/J-+/J--.
• One-prong track must not be identified as a loose muon (muNNLoose). (see
Appendix B for definition of the muNNLoose selector). Applied as a cut
against di-muon events in channels /J--e+e- and /J--/J-+/J--
The efficiency of the selection is given in Table III. 7. Optimization plots, showing
the expected upper limit on the branching fraction for different cut values, are show
in Figures C.1- C.6 in Appendix 1. Other cuts which have been considered include:
• polar angle of missing momentum in LAB frame.
• # of photon candidates on I-prong and 3-prong hemispheres.
• minimum track momentum in the 3-prong hemisphere.
• the acollinearity angle between the I-prong and 3-prong momentum vectors in
the CM frame.
The distributions of the MC and data events in the selection variables are shown in
Figures C.7-C.12 in Appendix 2. The events are plotted with all selection criteria
applied except the cut in the plotted variable.
Table III. 7: Efficiency for events after PID and LB requirements to pass the selection
cuts. As described in Section 7, the Bhabha and dinmon contributions are modeled
with data control samples. The corresponding selection efficiencies are not shown.
Signal[%] bb[%] cc[%] 'uds[%] T+T- [%] DATA [%]
e-e+e-
/J--e+e-
e- /J-+e-
/J--e+/J--
e-/J-+/J--
/J--/J-+/J--
68.6 48.6 13.8 9.21 0.130 0.215
72.3 60.3 38.1 35.7 8.12 1.7
94.3 79.2 23.7 50.9 90.1 40.0
93.7 56.8 27.7 51.1 87.1 63.2
71.7 57.8 21.6 45.4 65.5 0.700
77.2 50.0 21.8 50.7 71.7 18.3
3We mean that the software object BtaCalQual exists. This object will not exist if the prompt
reconstruction found no EMC energy deposit associated with the track. This requirement ensures
that events with electrons which hit cracks in the EIVIC do not pass the I-prong electron veto.
85
7 Estimation of Background
To estimate the expected background contribution in the signal region, a
background fitting procedure has been developed which uses the data directly to
estimate the background levels in the two-dimensional (flJvI, flE) plane. For ee,
v,ds, and generic 7+7- backgrounds, Monte Carlo samples are used to construct an
analytic two-dimensional PDF as a function of flJvI and flE. Due to lack of
suitable MC events, the QED (Bhabha and di-muon) background is estimated
directly from the data using the procedure described in Section 7.3.
The final background rates are estimated by performing an unbinned likelihood
fit over the large box region excluding the signal region (also known as the grand
sideband). Each of the background classes (QED, ee, uds, and 7+7-) has a single
analytic PDF which describes the shape of that background in the (flJvI, flE) plane
for each signal hypotheses. The normalization of each PDF is determined from the
fit to the grand sideband data, and the final background estimate is then made by
integrating the normalized PDFs over the signal box region.
Systematic uncertainties due to the background estimation, including
dependence upon the exact PDF functions used and variations of the shape
parameters, are discussed in Section 8.
7.1 Backgrounds from cc and uds
The shapes of the ee and uds backgrounds in the signal region are estimated using
MC samples. These two backgrounds have very similar distributions in flA1 and
flE. Since the overall rate is determined in a fit to the data sidebands, the uds MC
sample is used to simulate both uds and ee backgrounds. Background estimates
which include fits to the ee sample differ negligibly from background estimates
which use only the uds MC sample.
An unbinned likelihood fit with weights is used to constrain the parameters of
an analytic two-dimensional PDF to the observed MC distributions of (flM, flE).
The weight of the events corresponds to the probability of the Particle Identification
(taken from the PID tables). As one can see from the Figure IlL8, the average
PID-weight is not constant across the fl1\1 and flE distributions and the usage of
the average weight is unacceptable.
c:
:c
~ 35~
'i
c
a: 30
Q)
Cl
~
Q)
10 25
20
15
10
5
-+-
-+-
-+-
-+-
25
20
15
10
5
-
- -
tt
+
86
-0.6 -0.4 -0.2 o 0.2 0.4
AM (GeV/c h 2)
-0.6 -0.4 -0.2 o 0.2 0.4
A E (GeV)
Figure III.8: T- ~ f-L-f-L+ f-L-: uds background. The histograms show the average
PID-weight per bin as a function of tllvI (left) and tl£ (right).
87
The two-dimensional (t1M, t1E) PDF for the ttds sample is constructed as the
product of two one-dimensional PDFs (PMf, PEl)' Since we observe a correlation
between t1M and t1E distribution for '/l,ds background, the rotated variables
t1A1' = eos(a)t1M + sin(a)t1E; t1E' = -sin(a)t1M + eos(a)t1E (III.25)
(III.26)
are used as dependents of each one-dimensional PDF. The angle a is included into
2-dimensional fit as a free parameter. PM' is a bifurcated Gaussian and PEl is given
by
( X 2 3PEl = I - ) . (I + a.T + bx + ex ),VI +x2
where .T = (t1E' - t1Eb)jfJ(E'). The values t1Eo and fJ(E) are free parameters to be
determined from the fit. Therefore fit minimizes the function
(III.27)
where sum is taken over all points in corresponding sample, 'Wi is PID weight of
event, PM' and PEl are the parameters of the corresponding PDFs. There are in
total nine parameters describing the shape of the uds PDF. The results of fits to the
MC distribution are shown in Figure C.13 in Appendix 3. Although the PDF
contains many parameters, the MC statistics are sufficient to constrain all of them.
High PID-weight Events
The uds background MC sample contains a small number of high PID-weight events
which pass the LB criteria and selection cuts. These high-weight events have
particle identification weights which are much greater than the average PID weight
for the sample (2-3 orders of magnitude greater). These rare events contain
signal-side tracks which are real leptons and thus are have PID efficiencies close to
unity. Fits have been done with and without the inclusion of these events, and the
resulting background estimations are negligibly different. For plotting purposes,
these events have been removed. For actual background estimations, the events have
been kept as part of the data sample.
88
7.2 Background from T+T-
The two-dimensional PDF for T+T- is a product of the two one-dimensional PDFs
(PMII, PEII) for I:!..JvJ'l and I:!..E" dependents, respectively. The variables I:!..JvJ'l and
I:!..E" are functions of I:!..M and I:!..E
I:!..JvI" = cos(/3I)I:!..M + sin(/31)I:!..E; I:!..E" = -sin(/32)1:!..111 + cos(/32)I:!..E, (III.28)
but unlike the uds PDF, they are not required to be perpendicular. Angles /31 and
/32 are included in the fit as free parameters. The PM" PDF is a sum of two
Gaussian PDFs with common mean, while PE" is described by Equation III.26 with
x = (I:!..E" -I:!..E~)/(J(E"). Therefore fit minimizes the function
(III.29)
where sum is taken over all points in the corresponding sample, Wi is PID weight of
event, PM" and PE" are the parameters of the corresponding PDFs. There are in
total eleven parameters describing the shape of T+T- PDF. The results of the fits to
the T+T- distributions are shown in Figure C.14 in Appendix 3.
7.3 QED Background
Since the number of Bhabha and J-L+ J-L- MC events is smaller than the number of
events expected in the data sample, a procedure has been developed to use data
control samples to estimate the shape of the QED background in the (I:!..M, I:!..E)
plane. The shapes of the Bhabha and J-L+ J-L- backgrounds are actually very similar,
and a single PDF is used in each signal channel to parameterize both components.
For the final background fit, the PDF extracted from the Bhabha control sample is
used in channels where the Bhabha background is dominant (e-e+e- ,e- J-L+/.C) ,
while the PDF extracted from the J-L+ J-L- control sample is used for J-L- e+e-. The
remaining search channels, e-J-L+e-, J-L-e+J-L-, and J-L-J-L+J-L-, have negligible QED
backgrounds in the GS.
89
Reverse PID Sample
In two of the channels where the data include significant QED background
(e- e+ e- and e- p,+p,-), it is possible to construct an adequate QED control sample
by simply looking at events in the grand sideband region that pass all selection cuts
except the cut on the I-prong particle ID (reverse PID data sample). In other
words, we select events in which the I-prong track is identified as either
eMicroLoose or muNNLoose but otherwise pass the selection cuts.
An analytic PDF for the QED background is then constructed for each signal
hypothesis by performing a maximum likelihood fit to the control sample. The QED
PDF function PQED defined by a product of 1 dimensional distributions p;.,,/, and p~,
over lvI' = cos({3)!::..M + sin({3)!::..E and E' = -sin({3)!::..l\!£ + cos({3)!::..E parameters.
p;.,,/, is a third order polynomial in 11,1' and p~, is the Crystal Ball function (PCB):
{
exp( - X2
2
) X > Q:
PCB = (n/a)n' exp(-a2 /2) x < Q:
n/a-a-x -
(III.30)
where x = (E' - Eb)I(JE', while Eb and (JE' are fit parameters which describe the
shape of the peak. The rotation angle {3 is used to account for the observed
correlation between !::..iv! and !::..E for the QED events. In total, there are six free
parameters to describe this unit-normalized 2D PDF.
Fits of this PDF to the Bhabha and di-muon control samples are shown in
Figure C.I5 in Appendix 3. As can be seen, the control samples have adequate
statistics to determine the PDF parameters.
Alternate QED Sample
For the p,-e+ e- channel, the reverse PID sample does not have adequate statistics
to determine the background shape. An alternate control sample (alternate QED
sample) is defined by taking preselected data events with a identified muon on the
I-prong side, 0.5 < mlpr < 2.5, p~ms > 4.8GeVIe, and no PID requirements on the
3-prong side. The I-prong PID requirement guarantees that this alternate Bhabha
sample is independent from any candidate signal events in the p,- e+e- data sample.
The alternate QED sample is fit with the same PDF as the reverse QED sample.
90
7.4 Final Background Fit
Using the analytic PDFs for the uds, Bhabha/di-muon, and generic T+T-
backgrounds determined as described above, a final unbinned likelihood fit is
performed to the data found in the grand sideband region for each of the signal
hypotheses, with the number of sideband events for each of the background classes
(yields) as the fit parameters. The results of these fits are shown in
Figures IIL9-IlL14. For some search channels, one of the three background classes
has a negligible contribution in the LB. Only background classes with significant
contributions are actually included in the final background fit. Table IlL8 lists the
background contributions to each search channel.
Table IlL8: Expected number of background events in the grand sideband (GS) and
signal box (SB) after the background fits. By construction, the total number of
expected background events in the GS is equal to the number of data events in the
GS. The luminosity is 376 fb-l.
e-e+e- f-L+ e- e- f-L- e+e- e+ f-L- f-L- e- f-L+ f-L- f-L-f-L+f-L-
GS SB GS SB GS SB GS SB GS SB GS SB
uds 30.5 0.41 18.1 0.25 33.6 0.53 29.2 0.49 28.9 0.41 24 0.29
QED 28.5 0.92 0 0 16.9 0.33 0 0 11.1 0.38 0 0
T+T- 0 0 20.9 0.05 15.5 0.03 122.8 0.05 38.0 0.02 92 0.04
Total 59 1.33 39 0.30 66 0.89 152 0.54 78 0.81 116 0.33
91
7
6
5
4
3
2
o -0.6 -0.4 0.4
5
4
3 .
2 I
0.1 0.2 0.3 0.4
-0.2
-0.4
-0.6 -
( ",
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
0.2
o
-0.2
-0.4
-0.6-
_I I, ,.I .. I ,I .. J •
-0.6 --0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Figure II1.9: T- -) e-e+e- channel: PDFs 'with Me-fitted shapes a.re scaled t.o dat.a:
a) t::.E projection of the dat.a (points) and t.he sum of the ba,ckgrouncl PDFs (curve):
b) t::.JI1 projection of t.he data (points) and the sum of the backgrouud PDFs (curve);
c) PDF (t::.JI1. t::.E) distribution: d) data (t::.JI1. t::.E) distribution. The filled black
boxes and open red box show the signal region (blinded for data).
92
8
7
6
5
4'
3.
j, , I
o 0.1 0.2 0.3 0.4
x.l0· 3 0.4 ~. I~
If
0.2f- II''''
Of- I - -- - -
-0.2-
-0.4- -
-
-0.6- '-:1'--
··0.6 -0.5 -0.4 -0.3 ··0.2 -0.1 0 0.1 0.2 0.3 0.4
F'igmc IlI.IG: T- -) p-C+C- clwnnel: PDF's \vith :\lC-fitted shapes are scaled to
data: a) 6£ projection of the data (points) and the sum of the background PDFs
(cmve): b) 6.1\1 proj ection of the data (points) and the sum of the background PDFs
(curve): c) PDF (61\1: 6£) distribution: d) data (6.1\1,6£) distribution. The filled
hlack boxes and open red box shmy t he signal region (blinded for data).
93
rr-rr-,..,..,...,..,CT"T"T""""""I"""" iii Iii I • i • i I • t, I I • .,.-rrrr.....,....-..-.-.,._
10
-t8
6
4
2 --
0.4
,,10. 3 0.4
0.20.2
0.2 0.3 0.4
o
--
-0.2
-0.4
. .
" -.
-0.6
~l~'! I" ,1.",1 I
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
Figure III.ll: T-- ---t I-t+ e- e- chaullel: PDFs with \IC-fitted shapes are scaled to
data: a) 6£ projectioll of the datH (points) and the SUlll of the background PDFs
(cUl've): b) 61'\1 projection of the data (points) and the SUlll of the background PDFs
(cUl've); c) PDF (61\1. 6£) (listribution: d) data (6111.6£) distribution. The filled
black boxes and open red box show the signal region (blinded for dati'l).
94
0.2 0.4
0.4
0.2
D
o 0.1
0.2
o
-0.2
-0.4
-0.6-
-"-.LILt. ,I , ,I "."., I'LLLJ~
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
FigLll'C'III.12: T -) e+/Fp- channel: PDFs with lVIC-fittcd shapes are scaled to
data; a) 6.£ projection of the data (points) and the sum of the background PDFs
(curve): b) 6.111 projection of the dat8 (points) and the sum of the background PDFs
(curv('): c) PDF (6.M. 6.£) distribution; d) data (6.111,6.£) distribution. The filled
black boxes and open red box show the signal region (blinded for data).
95
10
o -0.6 0.4
0.2
o
-0.2 -
-0.4
-0.6
~~~~~~;~I",' "~
-0.6 -0.5 -0.4 -0.3 -0.2 ..0.1 0 0.1 0.2 0.3 0.4
Figure III.13: T -) c-//+ /1- channel: PDFs vvith Me-fitted shapes are scaled t.o
data: a) /'::"E projection of the dnta (points) nnd the sum of the background PDFs
(curve); b) /'::"JI1 projection of the dn t.a (points) and the sum of the ba,ckgroulld PDFs
(curve); c) PDF (/'::"JI1, /'::"E) distribution: cl) data (/'::,,111, /'::"E) distribution, The filled
black boxes anel open red box show the signal region (blinded for cla ta),
96
25
0.4
L...l...i....J.,. I, ,.1" !,! I,. I", I. ,.I,!
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
-16.6 -0.5 -0.4 -0.3 -0.2 -0.10 '0.1
20
-0.6
o 0.1 0.2 0.3 0.4
xlO·1 0.4 ~
0.2
0 0
-0.2
-0.4
18
16
14
12
10
8
6
4
2
0
0.4 ~
0.2
Figure III.14: T ~ /./-/1+p- cllallllel: PDFs with Me-fitted shapes are scaled to
data: 8) 6.£ projection of the data (points) and tl1C' sum of the background PDFs
(curve): b) 6.J11 projection of the data (poiuts) and the sum of the background PDFs
(curve): c) PDF (6.111.,6.£) distributioll: cl) data (6.J\1, 6.£) distributioll. The filled
black boxes and opell red box show the signal region (blinded for cla ta).
97
8 Systematic Uncertainties
The systematic uncertainties in this analysis can be divided into three parts:
uncertainties related to the signal efficiency, uncertainties related to the background
estimate, and uncertainties related to computing the branching fraction (luminosity
and 7+7- cross section).
In principle, some sources of uncertainty effect the signal efficiency and
background estimate in a correlated way (like tracking efficiency), however these
uncertainties have been found to be negligible.
8.1 Signal Efficiency
The signal efficiencies are determined from signal MC samples, and hence the
efficiency systematics are driven by understanding the deficiencies and uncertainties
in the MC modeling.
Limited lVIC Statistics
The absolute uncertainty due to the limited signal MC statistics is calculated using
O"MC =
E(l - E)
N MC '
(IIL31)
where N MC is the number of events in the initial signal MC samples and E is the
total signal selection efficiency. The relative uncertainties range from 0.5-0.8%
(depending on selection channel) and are shown in Table lILIO. This number does
not include the uncertainty due to PID efficiency which is considered separately.
Production Model
The signal samples have been produced assuming a flat 3-body phase space decay of
the tau lepton. The decision has been made to state this assumption explicitly and
assign no additional uncertainty for possible model-dependent structure in the decay.
A Dalitz plot of the selection efficiency for the J.C J.l+ J.l- channel is shown in
Figure III.15. The selection efficiency in the Dalitz plane4 looks fairly flat. However,
4The Dalitz plane is defined for sets of three energy-momentum four-vectors, PI,P2,P3. On one
axis is plotted the invariant mass of PI and P2, and on the other the invariant mass of PI and P3.
98
there are notable variations in the efficiency when projected on to each invariant
mass spectrum. This is due to the large number of soft muons in the signal MC
which get zero weight in the PID selection. Upon removing particle identification
from the selection procedure, the signal efficiency is uniform across both of the
invariant mass spectra.
Radiation Modeling
Deficiencies in the description of initial-state (ISR) and final-state (FSR) radiation
in the lVIC can lead directly to errors in the predicted (t::.AI, t::.E) distributions.
Generator level studies with KK2f ISR weights are used to estimate the size of this
effect due to missing higher-order corrections. The number of events with 3 signal
tracks within the detector acceptance and with invariant mass and energy
corresponding to the signal box are compared with and without the 0(0:3 ) diagrams,
as recommended by the KK2f authors. The relative efficiency difference of 0.06% is
taken as an estimate of the uncertainty related to the missing higher-order diagrams
in the calculation. This negligible uncertainty on the signal efficiency is ignored.
A similar study is done to estimate the uncertainty due to FSR from the
outgoing leptons in the decay (generated by PHOTOS). The associated systematic
uncertainty is also negligible.
Generic T Branching Fraction
The generic decays of the second T in the signal MC are simulated by TAUOLA with
PDG 2004[65] branching fractions with an additional unitary constraint imposed.
The systematic uncertainty related to the branching fraction errors is evaluated as a
quadrature sum of the individual branching fraction uncertainties weighted by the
relative fraction of selected events in a given signal channel with this generic tau
decay mode. The relative systematic uncertainty is 0.9%.
PID Efficiency
The uncertainty due to particle identification performance for the 3-prong tracks is
estimated from the statistical uncertainty of the PID table efficiencies. As a
conservative estimate, the relative uncertainty for the event weight is taken to be
99
I. Dalitz plane lor signal ill I Elficiency in Dalilz plane I
0.9
0.8
0.7
0.6
0.5
-0.4
- 0.3
0.2
0.1
L
400 :f 2
N' 3
-'"~
500 S 2.5
100
200
- -300
2.5 3 0
M(I'!") (GeVlc'l
ir'~l-~'_ I j I I i I i I ,~-
~ v~1
\~ 0.10.080.060.040.02-L 001.5 2 2.5 3 0.5 1.5 2.5 3
MilT) (GeV/C') M(I'f) (GeV/C'j
0.5
1.5
N' 3
~
~
e. 2.5 -
>-
u
~ 0.2
u
~0.18
0.16
0.14
0.12 :-
0.1
0.08
0.06
0.04
0.02
00 0.5
[ Efficiency in 1+1+ (no pi5[J I Efficiency in 1+1- (no PID) I
~
.~ 0.7
u
:;:
UJ 0.6
0.5
0.4
0.3
0.2
0.1
>-
u
~ 0.7
'u
:;:
UJ 0.6-
0.5
0.4
0.3
0.2 ::..
Figure III.15: T'- ----0 /1.-,,1+ /,-' a) gcncrated i\IC Dahtz distribution after preselection;
b) efficiency to pas" all selection exccpt SB as ['unction of Dalitz distribution; c)
selection efficiency as a function of invariant Illass squared of the pair of same-sign
leptons: d) "election efficiency CIS a fUllctioll of invaricwt mass squared of the pair of
opposite-sign leptons: e) efficiency for all selection cuts except PID as C1 function of
invariant lllRSS squared of the pair of same-sign leptons; e) efficiency for all selection
cuts except PID as a fUllction of illvariallt Illass squared of tile pair of opposite-sigll
leptons;
100
the quadrature sum of the relative uncertainties of the three-prong track weights.
The resulting distribution of event weight uncertainties is significantly asymmetric
and has a large tail at high uncertainties. The distribution is integrated from zero
up to the value where 68% of the distribution is included. This value is taken as the
uncertainty due to particle ID on the 3-prong tracks.
The kaon veto on the 3-prong tracks affects less that 1% of the signal events
passing all other selection criteria. It has a negligible effect on the signal efficiency
and no uncertainty is assigned. The uncertainty due to the lepton veto on the
one-prong track is estimated from the spread around unity of the ratio of MC and
data efficiencies, about 1.5% for the electron veto and 6.5% for the muon veto. This
uncertainty is added in quadrature with the uncertainty from the 3-prong track
PID. Total PID uncertainties for each channel are shown in Table IlL10 and range
from 1.7% (e-e+e-) to 10.7% (p-fJ+J-C).
Tracking Efficiency
Any mismatch between the data and MC tracking efficiency will lead to a bias in
the signal efficiency estimate. Internal BABAR studies show that the modeling of the
single track efficiency in the MC is good to 0.23% per track in low multiplicity
events for track momenta PT > 180 MeVIc. For the few tracks with momentum
PT < 180 MeVIc we conservatively assign a 1.2% uncertainty per track. Using the
individual track PT values observed, a tracking uncertainty for each event is
calculated by simple addition of the individual track uncertainties. This implicitly
assumes that the tracking efficiency uncertainties are correlated for all tracks. The
total uncertainty is taken to be the mean event uncertainty observed for each signal
mode.
The fraction of tracks with PT < 0.18 GeVIc is approximately 0.4% for all
channels. The relative uncertainty on the selection efficiency ranges from 0.99% to
1.01% depending upon the specific channeL Exact values are shown in Table IlL10.
In principle, this uncertainty is correlated to the background estimate, although due
to the way the backgrounds rates are fit directly from the data, this correlation is
assumed to be negligible.
101
Tracking Resolution
If the MC tracking resolution does not match that found in the data, the signal
distributions in the (6.111, 6.E) plane wi11 be incorrect. This affects the number of
signal events falling in the signal box and hence the overall signal efficiency. Most
studies done of tracking resolution have found that the width of the invariant mass
spectra of various control samples are reproduced by the MC simulations to within
5% relative.
To evaluate the efficiency uncertainty due to this level of agreement, an
additional smearing of the track momentum was added such that the track
resolution was increased by 5%. Assuming that the average track momentum
resolution is 0.5%, an additional Gaussian smearing of 0.16% wi11 increase the
resolution by 5% relative. This procedure is implemented by adding a random value
bp to the momentum magnitude of each track Po drawn from a Gaussian with width
equal to (JfJp = 0.0016po.
The effect of this additional smearing is to migrate some fraction of the signal
events out of the signal box and reduce the efficiency. This effect varies for the
different signal channels, giving a reduction ranging from 0.01 % to 0.30% relative.
Therefore, no uncertainty is assigned for tracking resolution.
Dependence on Selection Cuts
Most of the uncertainties related to the modeling of the selection cut variables are
already accounted for by other systematic uncertainties.
Uncertainties due to PID requirements in the selection are evaluated from the
stated PID selector uncertainties.
The uncertainty on the transverse momentum and on the I-prong momentum
and mass distributions are mostly due to the errors in the tracking model, which
has also been accounted for explicitly.
8.2 Background Estimation
Fit Uncertainties
Since the data are used directly to evaluate the background level, a primary source
of uncertainty in the background estimation comes from the statistical precision of
102
the background fit to GS data and varies from about 10% for channels with a lot of
data in the GS to 36% for channels with only few data events in the GS. These
uncertainties are estimated by varying the background yields within their fit errors
and refitting for the expected background contribution in the SB. The ratio of the
width to the mean of the resulting distribution of SB background contributions is
taken as the relative uncertainty due to background yield errors.
Additional systematics come from the choice of background PDF used for the
fits. Estimations for this uncertainty are obtained in one of two ways. For channels
where the full covariance matrix can be obtained from the fits to all MC and control
samples (e- e+ e- , /-c e+e-, e- M+e-), the parameters of the background PDFs have
been varied according to the error matrix. For each variation, the GS data are refit
and a new estimation of the background in the SB is calculated. The relative
systematic uncertainty on the background estimate is taken to be the ratio of the
width to the mean of the background distribution. For channels where the full
covariance matrix for the background fits are not all available (M-e+M-, CM+M-,
M- M+M-), the (6M,6E) background distributions are parameterized by the
product of a line in 6E and a line in 6111, and are fit to the MC and control sample
distributions. In the same method as before, the sum of these background PDFs is
fit to the sideband data events and the expected background in the SB is
recalculated. The difference between the expected background from this simplistic
model and the expected background from the full parameterization is taken as a
conservative estimate of the systematic error due to IVIC shape modeling.
The uncertainty due to statistical fluctuations in the number of data events in
the GS ranges from 8.2% (M+e-e-) to 17.7% (e+M-M-). The errors on the
background estimate are summarized in Table IlL10.
To verify that the PDF used fits data, the number of expected and observed
events is compared for the boxes neighboring SB as described below.
Fit Crosscheck
As a cross check we calculate the background level in a set of neighbor boxes and
make a comparison with number of events observed there in the data. The neighbor
boxes have the twice the size of the signal area. In total 4 boxes are considered: left,
bottom, right and top with respect to the signal box. The data events in the
neighbor box under consideration are excluded from the background fit in this
103
cross-check. With a few exceptions, the expected and observed numbers of events
agree within the statistical uncertainties (see Table III.9).
Table III.9: The number of expected (left) and observed (right) events in the boxes
neighbor to the signal box. Uncertainties on the sum of the expected background for
all four boxes are estimated from the uncertainty on the expected background in the
SB. Poisson errors are assigned to the sum of the data for all four boxes.
neighbor left top right bottom all four together
e-e+e- 3.78 3 1.40 4 3.17 1 3.03 0 11.4±2.2 8 ± 2.8
f.L- e+e- 2.45 1 1.50 2 1.71 6 2.02 1 7.68 ± 2.3 10 ± 3.2
e- f.L+ e- 0.47 3 0.11 0 0.34 0 0.58 2 1.50 ± 2.8 5 ± 2.2
f.L- e+ f.L- 2.31 1 0.02 0 0.79 3 1.75 0 4.85 ± 1.9 4± 2.0
e- f.L+ f.L- 2.17 2 0.93 1 1.87 1 2.10 3 7.07 ± 2.7 7± 2.7
f.L-f.L+f.L- 1.07 0 0.17 0 0.56 1 1.01 2 2.81 ± 1.6 3 ± 1.7
Sum 12.25 10 4.11 7 8.44 12 10.49 8 35.31 37
Two-photon Contribution
Two-photon fusion events can lead to four-fermion final states. These events are
characterized by small net transverse momentum in the event (Prms ) and initial
leptons flying close to the beam line after scattering. To separate two-photon events
from radiative Bhabha and di-muon events, the dependence of the momentum of
the I-prong track (pf~n on pyms is studied. From Figure III.16 one can see a large
diagonal band due to radiative QED events, as well as a small band at low Prms
values due to the two-photon contribution. This contribution is observed in three
channels: e- e+e-, /L- e+ e-, and e- f.L+ f.L-. A data control sample with two-photon
events is selected from data events passing preselection and PID by making the cuts
pf~.s < 4 and p¥ns < 0.2 GeVIe. The later cut ensures that the sample is disjoint
from the final data sets in the affected channels.
For search channels e- e+e- and e- f.L+ f.L-, we find that no events from this
control sample pass all other selection cuts. For f.L - e+ e-, two events are passed.
Most are rejected by the one-prong lepton veto, which passes less than 10% of the
two-photon events for all channels. If selection cuts are released, the (6M,6E)
distribution for two-photon data sample looks similar to the qq distribution as one
can see from the Figure III.16. Therefore, even if we inappropriately neglect this
104
4.5
3.5
- 3
2.,
_ 2
1.5
0.5
0.2 0.4
~ M (GeV/c2)
Figure III.1G: Ft) The distri butioll of r)~ms versus pf,ms for the T- -----7 e- e+ e- c:hFtllnel
after preselection and PID. The :0-Ftxis is logmitlnnic. The red line shows t.lle cuts
applied t.o select the two-photon control sample. b) The (6.j\1, 6.£) distribution of
these eveuts plotted without the cut on P!:j1Jl8.
type of background: the fit of data willn8t.urally coned for the difference. TIlliS. vve
neglect the background uncert.ainty rdnted t.o t.vvo-photon contribution.
Tracking Efficiency
Uncertainties in the overall tracking efficiency CiUl be neglected because of the
datH-drivell fmckground estimation which fits the background rates directly from
the data observed in the grand sideband region.
Tracking Resolution
The same smearing study is applied to t.he wls and T+ T- background samples as
was performed for the signal Me. The relative difference in the accepted
bRckground rate in the signal box clmnges by less than O.5o/c for all signal channels.
Other UnknOlvn Backgrounds
Ullknown backgrounds are ['8 ther difficult to estimatp. Since the backgrollmls arc
already being fit from the data, our ]Jl'Ocedmp probably accomlllodates any
H.dclitional unknown background already. I-Iere we assume thFtt none of tIle
backgrounds pea.k in the signal region and (wy signatme for the peak is due to LFV
telU decays. This is true for the otandard lllodel tau decays which is verifled with
gencric: T+T- Me sample.
105
Some backgrounds which are not simulated which we should be able to estimate,
however, are the tau decays T- ---t £-£'+£'-vTv/" which have a measured branching
fractions of (2.8 ± 1.5) x 10-5 (e-e+e-vevT) and < 3.6 x 10-5 (p-e+e-vj.lvT) [68]. For
other possible T- -----+ £-£'+£'- VTV/' modes, the expected branching fraction is close to
10-7 .
\iVith 376 fb- l of data, we expect a maximum of 0(103 ) of each of these decays
in the data set. The signal total efficiency for pre-selection, PID, and event selection
is 12.5% and 10.7% for channels e-- e+ e- and p- e+ e-, respectively. This potentially
leaves around 100 events per channel distributed about the LB. However, the SM
Feynman diagram for the process includes a virtual photon; therefore the
electron-positron pair of the final state have a small invariant mass. The
preselection includes at rejection of gamma conversion candidates. Furthermore,
channels e-e+e- and p-e+e-also have tighter cuts on the electron-positron
invariant mass (see section 6). Given these cuts, and the fact that such SM decays
would be distributed similarly to the generic T pair background in the LB, we can
safely neglect this background.
8.3 Other Systelnatics
Luminosity and TT Cross Section
The best estimate of the T pair production cross section is 0.919 ± 0.003 nb [69].
Given the 0.9% uncertainty on the luminosity which takes into account the
run-by-run variations and the cancellation of the theoretical uncertainty in the
product (J£, the combined uncertainty on the luminosity and the cross section is
taken to be 1%.
Signal Bias
Since some of the signal events are found outside of the signal box in the grand
sideband region, in the case where a signal is found, the background rates predicted
by the grand sideband fit will actually be overestimated. If evidence for a signal had
been found, a small correction would have been applied to account for this bias.
Table IlLI0: Systematic uncertainties expressed in relative percent.
106
e~e+e- fce+e- e- /1+e- /1- e+ /1- e-/1+/1- /1-/1+/1-
Uncertainties on the Signal Selection Efficiency
NIC Statistics 0.69 0.73 0.52 0.59 0.73 0.76
Tau BF 0.9 0.9 0.9 0.9 0.9 0.9
PIO (3-prong) 1.7 4.1 6.1 8.6 7.1 10.7
PID (I-prong) 1.5 6.5 0 0 1.5 6.5
Tracking Efficiency 1.0 1.0 1.0 1.0 1.0 0.99
Total Uncertainty [%] 2.7 7.9 6.3 8.7 7.4 12.6
Uncertainties on the Expected Background
GS fluctuations 12.7 12.4 17.7 8.2 11.1 9.4
Fit to MC 10.6 23.7 179 20.0 12.2 48.1
Fit to data 9.85 13.2 36.2 24.4 20.2 27.1
Total Uncertainty [%] 19.1 29.8 183 39.5 37.8 56.0
107
CHAPTER IV
RESULTS AND CONCLUSIONS
1 Results
All that remains in the T ----7 UR search is to compare the number of observed events
in the signal region to the background expectation. This step is referred to as
unblinding and can only occur after the selection criteria are finalized and all
uncertainties are estimated. Let us first recall quantities necessary to place an upper
limit.
First, the background expectation in the signal region must be estimated, along
with an uncertainty on that estimate. This quantity is calculated separately for
each search channel and makes use of both MC and data samples (see Section 7).
MC events provide an estimate of the shape of the data distribution in the Large
Box, and data events outside the signal region provide an overall normalization.
Second, the signal efficiency for each search channel must be calculated. This
efficiency takes into account the effects of skimming (Section 6.2), preselection cuts
(Section 3), particle identification (Section 4), channel-specific selection criteria
(Section 6), and the signal box size (Section 5). Finally, the number of T+T- pairs
produced must be estimated from the luminosity of the data sample, and the T+T-
production cross section for e+e- collisions at 10.58 GeV CM energy. The
uncertainties for all three of these quantities are estimated in Section 8.
After unblinding, the observed number of events in the signal region Nabs is
compared to the background expectation N bgd to test the signal hypothesis in the 6
signal channels. Under the assumption that no evidence for a signal is found, a 90%
CL upper limit on each branching fraction can be calculated following the technique
detailed in Section 1.3. Table IV.1 shows the final results for each search channel,
including the signal efficiency, the expected number of background events in the
108
signal box, the Feldman-Cousins expected upper limit described in Section 1.5, the
number of observed events Nabs, and the upper limit. Figure IV.1 shows the
unblinded data distributions in the (!:lM, !:lE) plane, along with regions including
50% and 90% of the signal MC events.
4.3 . 1O~8
8.0.10-8
5.8.10-8
5.6.10-8
3.7. 10-8
5.3.10-8
1
2
2
1
o
o
NabsBULexp
4.9. 10-8
5.0.10-8
2.7. 10-8
4.6.10-8
6.6.10-8
6.7.10-8
1.33 ± 0.25
0.89 ± 0.27
0.30 ± 0.55
0.54 ± 0.21
0.81 ± 0.31
0.33 ± 0.19
c,[%]
8.9 ± 0.2
8.3 ± 0.6
12.4 ± 0.8
8.8 ± 0.8
6.2 ± 0.5
5.5 ± 0.7
e-e+e-
I-Ce+e~
e- f-L+ e-
f-L- e+ f-L-
e-f-L+f-L-
f-L-f-L+f-L-
Table IV.1: The total efficiency c, estimated background level in the signal region,
expected upper limit, observed number of events in the SB and 90% CL upper limit
on B(T ~ UP}
===;:;;:;=='==;=====~~==~===~rr==:::::;:=;===~rr==Channel
2 Discussion of Results
In all six search channels, the number of events observed is compatible with the
expected background. As expected, the values for Nabs are fluctuations around N bgd ,
with the largest upward fluctuation seen in T- ~ f-L+ e- e- where N bgd = 0.3 ± 0.55
and Nabs = 2, and the largest downward fluctuation seen in T- ~ e- f-L+ f-L-, where
N bgd = 0.81 ± 0.31 and Nabs = O. Combining all six search channels, we observe a
total of 6 events in data, while expecting at total of 4.2 background event. Ignoring
the uncertainty on the total background, this observation of 6 events while
expecting 4.2 has a Poisson probability of 0.11. Taking into account the uncertainty
on the N bgd values would widen the distribution and mildly increase this probability.
Thus, the result can be characterized as somewhat "unlucky" but not suspiciously
anomalous.
2.1 Implications for Theory
In the absence of Higgs-like couplings, the assumption of lepton universality leads to
essentially equal rates for the four lepton-number conserving T ~ 12££ decays. \iVhile
models do exist which predict rates for the other two decays modes [70, 71], they
109
-
- e+ e- - ----j J.!+e- -'t ----je 't e •0.2 ••
• • ••
-
•
• 1] • ••0.0 • • •~• • • • • ~'•• • 4 • •• • •• •• • •-0.2 • • • • • ••• •• • •
-0.4 • • • •• • • ••• • , .,• • • •
-0.6 • •
• •• • •• • • •
-
- e+ e- 't- ----j e+ J.!- J.!-
>' 0.2 't ----jJ.! • •
.)
~
• • •
80.0 • • •• • n•~ • •• • ,y• • • t· • •r.r:l •• • • •<]-0.2 • • •• •I ... • •
• • •
-0.4
•• • •• •• • • • •
-0.6 •• • ••
't- ----j e- J.!+J.!- 't- ----j J.!- J.!+ J.!-0.2 •
•• •
•
• •0.0 • ~ • • ~I!>j ••• • • • ••• • • I·• •• • •
-0.2 •... ,. • • •• •
• • ••• • •
-0.4 •• • • •)e. ,.
• • • •.. •
-0.6 • • • ••
•
-0.4 -0.2 0.0 0.2 -0.4 -0.2 0.0 0.2
~ M (GeV/c2)
Figure IV.l: Observed data shown as dots in the (6.JvJ, 6.E) plane and the boundaries
of the signal region for each decay mode. The dark and light shading indicates
contours containing 50% and 90% of the selected Me signal events, respectively.
110
are generally much lower than the lepton-number conserving modes. Furthermore,
since most models include at least some Higgs contribution, is makes sense to focus
on the decay mode most sensitive to these contributions, T~ -----> /-l- /-l+ /-l-. The
ability to directly constrain new physics models with the T- -----> /-l- /-l+ /-l- result is
hampered by the fact that most models predict much higher rates for T- -----> /-l-,
than for T- -----> /-l- /-l+ /-l- in most areas of parameter space [72, 5, 73]. The situation
is remedied slightly by the higher experimental sensitivity to the three body decay
(a factor of rv 10).
Two-Higgs Doublet models (2HDM), including minimal supersymmetric models
(MSSM), generally have two types of contributions to T- -----> /-l- /-l+ /-l-. The first type
is a subset of T- -----> /-l-, in which the photon is off-shell and produces a lepton pair
(muons, in our case; rates are similar for electron pairs). This contribution to
T- -----> /-l- /-l+ /-l- is naturally suppressed by a factor of rv 100 relative to
T- -----> /-l-i [74],
a (rn; 11)B(T -----> 3/-l) = - In- - - B(T -----> /-li)
'Y 27f rn2 4
IJ
(IV.I)
except in special cases of fine tuning. The second type of contribution occurs via
Higgs-like couplings, as shown in Figure IV.2. In models where the super-particle
masses lie above the TeV scale [75], a sizable contribution from the Higgs-mediated
channel can lead to ratios like
(IV.2)
'With the experimental sensitivity difference noted previously, this means that this
sort of new physics could be seen in T- -----> /-l- p,+ /-l- before T- -----> p,-,. MSSM
models where the Higgs contribution is sizable [75, 76, 77] predict the rate for
T- -----> /-l- /-l+ /-l- to be
(IV.3)
where tan,6 is the ratio of the two Higgs doublet VEVs, and rnA is the mass of the
neutral pseudoscalar Higgs particle. In the case of large (rv 50) tan,6, the results for
T- -----> p,- p,+ /-l- presented in this work constraint rnA to be greater that 100 GeV.
Furthermore, no fine-tuned cancellations are required at this point in parameter
space to keep the rate for T- -----> /-l- i below the experimental limit of 4.5 x 10-8 [78].
111
I-l
illp tan;3
Figure IV.2: Feynman diagram of the leading Higgs-induced contribution to T- ->
P, - p,+P, - in the MSSM.
3 Conclusion
We have used a sample of approximately 350 million T+T- pair events recorded at
the BABAR detector to search for the six lepton flavor violating decays T -> Uf. In
the absence of statistically significant signals for these decays, we have placed upper
limits on the branching fractions at the 90% confidence level, using a procedure
which takes into account the systematic uncertainties on the signal efficiency, on the
number of expected background events, and on the number of T+T- pairs produced.
The limits on the branching fractions are in the range (4 - 8) X 10-8 , and improve
on the previously published limits by a factor of (2 - 5) [36, 37].
In Chapter I, we discussed the structure of flavor violation in the interactions of
the quarks and leptons. We showed that lepton flavor is essentially conserved in the
Standard Model, but that models of new physics provide many options for LFV. We
also presented a history of experimental searches for neutrinoless lepton decays. In
Chapter II, we presented the BABAR experiment. Starting with an overview of the
accelerator facilities, we continued with a more detailed look at each of the detector
subsystems. The chapter concluded with a discussion of data simulation, triggering,
and data processing. In Chapter III, we presented the method by which we actually
make the search for T -> fU and the statistical procedure that we use to set upper
limits on the branching fractions. Chapter IV starts with a presentation of the final
results and continues with a discussion of their theoretical implications.
While we were unable to observe the decays T -> fU, the limits on the branching
fractions that we set with this analysis still constrain theories of physics beyond the
Standard Model. And our ability to further constrain these model increases
dramatically as limits are pushed into the 10-9 range. The PEP-II/BABAR facility is
112
in many ways an ideal 7 factory. Consequently, the prospects for a Super-B-factory
are very exciting. Such an experiment would retain many of the desirable features of
BABAR, such as the relatively high 7+7- production rate and good separation of the
decay products in the detector. With a luminosity 100 times that of BABAR and
relatively little increase in backgrounds, we can reasonably expect sensitivity to the
7 --+ fee decays down to the 10-10 range. But the question of what physics we might
actually observe at such tiny rates must remain unanswered until such a facility is
built.
113
APPENDIX A
TRACK LISTS
1 The CalorClusterNeutral List
The CalorClusterNeutrallist contains all multi-bump neutral clusters in the
EMC, as well as single bumps which are not associated with a charged track.
2 The ChargedTracks List
The ChargedTracks list contains all reconstructed tracks with non-zero charge. A
pion mass hypothesis is assigned.
3 The GoodTracksVeryLoose List
The GoodTracksVeryLoose list contains tracks from the ChargedTracks list for
which the following criteria also apply:
• Lab momentum is less than 10 GeVIe.
• Max DOCA (distance of closest approach) in X-Yplane is 1.5 em.
• Min DOCA in Z is -10 em,
• Max DOCA in Z is 10 em.
4 The gammaConversionDefault List
The gammaConversionDefault list contains pairs of oppositely-charged tracks
from the ChargedTracks list for which the following criteria also apply:
• Max DOCA in X-Y plane is 0.5 em.
• Max DOCA in Z is 1.0 em.
• Invariant mass of the two tracks is less than 30 MeV.
114
115
APPENDIX B
PARTICLE IDENTIFICATION ALGORITHMS
1 The eJ\!IicroTight Selector
The tight, cut-based electron selector is called eMicroTight. The corresponding
PID list contains particle candidates which meet the following criteria:
• dE/dx is in the range [500,1000].
• Minimum of 3 EMC crystals hit.
• The ratio of the EMC energy to the track momentum (E/p) is in the range
[0.75,1.3].
• The lateral energy distribution (LAT) is in the range [0,0.6].
(B.1)
where the sum is over all crystals in a shower, TO = 5cm (the average distance
between two crystal frontfaces), and Ti is the distance between crystal i and
the shower center.
• The shower shape (A 42 ) is in the range [-10,10].
with Ro = 15 cm and
(B.2)
s!((n + m)/2 - s)!((n - m)/2 - s)! (B.3)
116
with n, m ~ 0, n - m even, and m :::; n.
2 The muNNLoose Selector
The loose, neural-net-based muon selector is called muNNLoose. The neural net
(NN) consists of:
• One input layer with 8 nodes,
• One hidden layer with 16 nodes,
• One output layer with one node.
The transfer function used in the NN is
1
f(x) = 1 +e-x' (B.4)
with the total input x = 2.= VVijA i , for weight Wij and incoming activity A.
The 8 inputs to the NN are the following detector variables normalized to fall in
the range [0,1]:
1. Energy released in the EMC (Ecaz )
2. The number of interaction lengths traversed by the track in the detector
(Ameas ). This is estimated from the last layer hit by the extrapolated track in
the IFR.
3. D.A = Aexp - Ameas , where Aexp is the expected number of interaction length to
be traversed for the track with a muon mass hypothesis.
4. The X2 jdegree of freedom of the IFR hit strips with respect to a third-order
polynomial fit of the cluster (XJit).
5. The X2 jdegree of freedom of the IFR hit strips in the cluster with respect to
the track extrapolation from the DCH (X~at).
6. The continuity of the track in the IFR (Te).
7. The average multiplicity of hit strips per layer (in).
8. Standard deviation of the average multiplicity of hit strips per layer (O'm).
117
The muNNLoose selector uses multiple kernels for different ranges of
momentum, polar angle, and time. The kernels are tuned to provided relatively
constant muon identification efficiency.
3 The KLHTight Selector
The tight likelihood-ratio-based kaon selector is called KLHTight. For each
particle candidate, a likelihood is calculated for each particle type. The KLHTight
list contains particle candidates which fulfill the following conditions on the ratios of
the likelihoods:
• LK/(LK + Lrr ) > 0.9
• LK/(LK + Lp ) > 0.2
Furthermore, particles must not pass the electron likelihood selector to be included
in the KLHTight list. The likelihoods are calculated from measurements of dE/dx
in the SVT and DCB, and from the Cherenkov angle, the number of Cherenkov
photons, and the track quality in the DIRe.
1 Optimization Plots
APPENDIX C
AUXILIARY PLOTS
118
119
5
p~ms max (GeV/c)
5
p~ms max (GeV/c)
4
4
I EEMw I
,.:-
b 0.4
...
~
-~
~0.35
Q.
Q.
:::J
0.3
3
I EMMr I
,.:-
b
...
~
-~ 0.8
...
Cll
Q.
Q.
:::J
0.7
3
5
p~ms max (GeV/c)
5
p~ms max (GeV/c)
4
4
4 5
p~ms max (GeV/c)
3
~
f- -
f- -0.5
...
Cll
Q.
Q.
:::J 0.55
,.:-
:= 0.65
~
-
._.§ 06
.
I EMMw I
~ 0.6
...
~
-~0.55
...
Cll
Q.
Q. 0.5:::J
0.45
3
I MMM I
,.:- 0.9b
...
~
-~ 0.8
...
Cll
Q.
Q.
:::J
0.7
3
Figure C.l: Expected upper limit on branching fraction as a function of p~ms. /-l- e+e-
channel is excluded because the dimuon control sample does not have a requirement
on the maximum value of p~ms (see section 7). Arrows indicate optimized value for
the selection cut.
120
rC'"
b
... 0 65~.
-'E
:: 0.6
CIl
Q.
Q.
:::l
0.55
::-0.55
~
"- t -
I--
0.4 0.6
Pims min (GeV/c)
0.2o
0.5
..
CIl
Q.
Q.
:::lWlL--"-0~----~-0'""'.2L-..-----'L-· 0.4 0.6
Pims min (GeV/c)
0.5
0.4 0.6
Pims min (GeV/c)
0.2o
0.451-
0.4 0.6
Pims min (GeV/c)
0.2o
~ -
I-- -
I-- -
-0.28
~
... 0.34
~
-'E
:: 0.32
CIl
Q.
Q.
:::l
0.3
-
-
-
8. 0.7"-
go.,," W
lL- L-..-_ .----,,------,,---,,,------,---,'---iJ
o 0.2 0.4 0.6
Pims min (GeV/c)
0.4 0.6
Pims min (GeV/c)
0.2o
I- -
l- t -
I- -
I- -0.65
-'E
:: 0.75
CIl
Q.
Q.
:::l 0.7
~
:; 0.8
Figure C.2: Expected upper limit on branching fraction as a function of the minimum
total transverse momentum FTms. Arrows indicate optimized value for the selection
cut.
121
f- ~ -
f- I0.5
~ 0.6
t
8:0.55
::I
I EEMr I
.:-0.65
b
...f- -
f-
~
f-
I0.5
...
~ 0.6
t
Q.
Q.
::I 0.55
~
:;.0.65
-0.1 -0.05
t> M min (GeV/c2)
-0.1 -0.05
t> M min (GeV/c2)
~ 0.4
...
~
t
~°.lLL
-0.1 "---'---~_--=O'"'.0-=C5~~----"
t> M min (GeV/c2)
~ 0.55f-
t
Q.
.g- 0.5f-
-0.1
-
-
-
-0.05
t> M min (GeV/c2)
f- -
f-
f- ~ -
f- -
f- -
-
f-
{t
f- I-
.:-
~0.85
~
~ 0.8
!0.75
Q.
::I
0.7
0.65
-0.1 -0.05
t> M min (GeV/c2)
~b
... 0.9
~
...
~t 0.8
Q.
Q.
::I
0.7
-0.1 -0.05
t> M min (GeV/c2)
Figure C.3: Expected upper limit on branching fraction as a function of !::l.M~fn.
Arrows indicate optimized value for the selection cut.
~
-
-
f- -
f- ~ -
f- -
f- ~ -
f- -
f- -
f- ~ -
t
-
f- -
I EEE I
,c'0.65
b
...
~
-~ 0.6
...
CIl
Co
Co
::;) 0.55
0.5
I EEMw I
'b0.34
...
~
-'E
=0.32
...
CIl
Co
Co
::;)
0.3
0.28
'b
... 0.8
~
-~0.75
...
CIl
Co
Co
::;) 0.7
0.65
0.02
0.02
0.02
0.04 0.06
/I, M max (GeV/c2)
0.04 0.06
/I, M max (GeV/c2)
0.04 0.06
/I, M max (GeV/c2)
'b
:; 0.6
-~8.0.55
Co
::;)
0.5
'b
...
~
-~ 0.5
0.45
'b
...
><
:;0.75
,§
...
CIl
~ 0.7
::;)
0.65
0.02
0.02
0.02
0.04 0.06
/I, M max (GeV/c2)
0.04 0.06
/I, M max (GeV/c2)
0.04 0.06
/I, M max (GeV/c2)
122
S'BFigure C.4: Expected upper limit on branching fraction as a function of flMmax '
Arrows indicate optimized value for the selection cut.
'b
,....
..
ell
liO.55
::l
0.5
~ -
t
L.
-
'b
,....
~
-~0.55
..
ell
0.
0.
::l
0.5
L. ~
-
123
-0.4 -0.3 -0.2 -0.1
~ E min (GeV/c)
-0.4 -0.3 -0.2 -0.1
~ E min (GeV/c)
b 0.4
,....
~
-~
Qi 0.35
0.
:3" ~
0.3r- I I
'b
,....
~
-'E
= 0.5
8.
0.
::l
0.45
~
f-
-0.4 -0.3 -0.2 -0.1
~ E min (GeV/c)
-0.4 -0.3 -0.2 -0.1
~ E min (GeV/c)
~0.75
Qi
0.
:3" 0.7
0.65
r- t -
-
-
'b
:;0.75
..
~ 0.7
0.
::l
0.65
f- t
r-
r-
-0.4 -0.3 -0.2 -0.1
~ E min (GeV/c)
-0.4 -0.3 -0.2 -0.1
~ E min (GeV/c)
Figure C.5: Expected upper limit on branching fraction as a function of 6Efnfn.
Arrows indicate optimized value for the selection cut.
124
-~8.0.55
Q.
;:)
~0.55
""'b 0.6
....
0.5
f- -
t
I- -
-
...
Gl
Q.
Q.
;:)
0.5
t
I-
0.04 0.06 0.08
,A,. E max (GeV/c)
0.04 0.06 0.08
,A,. E max (GeV/c)
f- t
'- -0.45
-~ 0.5
...
GlQ.
Q.
;:)
t
f-
-~
~0.32
Q.
Q.
;:)
0.3
~0.34
0.28
0.04 0.06 0.08
,A,. E max (GeV/c)
0.04 0.06 0.08
,A,. E max (GeV/c)
t
-
I- -0.65
~0.75
~
8: 0.7
;:)
IMMM I
.::-- 0.8
b
....
f- t
-0.65
I EMMr I
.::-- 0.8
b
....
~
~0.75
...
Gl
Q.g- 0.7
0.04 0.06 0.08
,A,. E max (GeV/c)
0.04 0.06 0.08
,A,. E max (GeV/c)
Figure C.6: Expected upper limit on branching fraction as a function of !1E~~x'
Arrows indicate optimized value for the selection cut.
2 N-l Plots
125
126
5 6
p~m. (GeV/c)
~ ]
~
~+IJ3.5 4 4.5 5
l-prong mass (GeV/c"2)
..,
..
e. 301-
~
c
f·
~ 25
20
15
10
00
10
00 0.1
m ...........,-.-,..,..,.,-. l' ~"T"'"'"""T""I'I'I li~
~ 16-
!?
:; 14 -
c
~~ 12
~ I i ., ~-0t- I
O- j I
\11 I
0
._---
OC-
0
0 0.2 OA 0.6 0.6 1 1.2 1.4 1.6 1.8 2
I-prong track has EMC energy (true = 1)
'"c
~ 0
g
~10
FiguI'f-' C 7: T-- -> e- e+e- clmnncl a) total transverse 1ll0lnent"lllll: b) i-prong
llloment·UIll: c) min 2-track mass: d) 1-Pl'Ollg lllass: e) (bool) 0118-prong track has
£1\IC energy. The points show the data distributions for evcnts in the grand sideba.nd
region with all other cuts applied. The bllle llistograll1 SllOWS the expected T+T-
background level.. the green histogram sllO'wS the expected BhahhC\ background level,
and the yellow histogram shcw,'s the expected uds background level. all normali6ccl
by the background fit.s with all selection cuts applied. Arrow(s) indicate the chosen
cut value(s). For cOlllparison, the red curve shows the \'IC signal distribution for the
large box 'with arbitrary normalization.
127
M
"'C 18
e
~ 16
~ 14
12
10
8 - •.
~ 12fa .
e.
~ 10
~
~
6
,.
.'. '1" , 1: '" 22F"'-.........,;-rrT-rrr....,~..,,-,.,.....,~"'.~-...,...,......-~"~ 20~ 10.~ 16
14 .
12
g 90
~ 00
E 70
~
'" 60
50
40
30
20
10
- I .;,
E- I
:-
t
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.0 2
l-prong track has EMC energy (lrue = 1)
Figure C.8: T- -) IJ.-c+p- duulllel a) total tra.nsvcrsc momentum; b) I-prong
mOlncnt.um: c) min 2-track nUlSS: d) I-proug IWl.')S: c) (bool) one-prong track lias
E\IC euergy. The poiuts sllO'w t.he data distriblltiom; for event.s in the grand sideband
regiou with all other cuts applied. The blue histogram shovvs the expect.ed T+T-
backgrouud level, t llC' greeu histogra.lll SllOl,.VS the expected dill1110n backgrouud level,
and the yellow histognun shows the expcdrduds background level. all uormalized
hy the ba.ckground fits with all selectiou cuts npplied. Anow(s) iudicat.e the choseu
cut valuc(s). For cOlllpa.rison. t.he red C\ll've shows t.he 1\IC sigual dist.rilmtiou for the
large box with arbitrarv uonnali7,atiou.
128
U~~~~5: 6
p~ms (GeV/c)
12-
00 0.5 1.5
'" rrn~~,..,...,...,........~r...-.-",-- t , I "I I • 1 ' i • ',-,-r
;': 7
S
i 10
"
r , .... , r I ~Ir"i....."T~iI.......,.~.,-il~',~,.,-,I~"TI~I1~'''TI~''Tlrr'~i
~ 70:
":- 60-
~
c
~ 50
40
30
20
F===.............~
10
00 0.2 0.4 0.6 0.0 1 1.2 1.4 1.6 1.0 2
1-prong track has EMC energy (true;:: 1)
Figure e,g: T- -) p+c-e- channel a) tota.l transverse momentum: b) i-prong
momentum: c) mill2-track mass: d) I-prong l1lass: e) (bool) onf-prong track has EMC
energy, The points show the data distributions for events in the grand sideband
regioll with all other cuts applied. The blue histognun shov\'s the expected T+T-
ha.ckground leveL the green histogram shows the expected Blwbha background level,
and the yella'w histogram shO\-\'s the expectedu.cls background leveL all normalized
by t.he backgroullCl fits with all selection cuts applied. Arrow(s) indicate the chosen
cut value(s). For comparison. the red curve SllOWS HlC l\IC signal distribution for the
large box with arbitrary normalization.
129
°O~""""'~-~~-'+-~.n.I--'":'5""""'-'--!6
p~nl$ (GeV/c)
22 'I ~ <- 3020 810 ~ 25016
'">
'"14 20
15
10
~ 24g::
£ 22.Eg 20
~ 10
16
14
12
10 .
o
6
2
°O~O'K-:.l~;;-:t--':;-';;~;o:;--;;-;;,...-:~~~~-::'::~ °0~-=----::--*4:----::-;'~S~3.5~""!4t·~~4.5...-i5
I-prong nmss (GeV/c"2)
~200
'">
'"
150
Figure C'.10: T- ~ ('+ Ji- p-- channel a) total t"ransver0e momentum: b) I-prong
momentum; c) min 2-track mass: cl) I-prong mass: e) (bool) one-prong track bas
El\JC energy. The points slww the dFttCl distribut.ions for (-'wnts in the grand sidehand
regioll with all other cuts applied. The blue histogram shows the expected T+T-
background le\'E~I, the' green histogrmn shows the expecteel Bhabha background level,
and I'lw yellovY histogram shows the expected luis background level. all normalized
by the background fits wit.h all selectioll cuts applied. Anow(s) indicate the dlOsen
cut value(s). For comparison. the red C'lu\'e shows the ?dC signal distribution for the
large box wit h arbitrary normaliha.tion.
130
- 10=-'~"""""""""'---1.---·..--.--.--,·.---.---,....,r-.--.-;rr~~;:::
8
6
°0l--'---:-----::---:..~-.....I..:!....I.......Jw..:~5d.k--... 6
p~oni (GeV/c)
00! .....~~:--~---:~~~~~3.,.;O.:t...4~..,..4.5,........:j5
l-prong mass (GeV/c .... 2)
/"0',,fi 25
8
'"c
~ 8
'"No
e.. 10
8 '10CT_ ,....,,~"'T"'""'~II~r·'""11r.-'..,....,..,oIrr'~''1'I~'~''1'I~'~I' ~~,'1'Ir.-'~'"':]~
~ IOOE-
~ 90r- I
~
Q,l 00-
70E-
60 .
50
40 -
30 I
20b .. I , ! I, I
o 0.2 0.4 0.6 0.6 I 1.2 1.4 1.6 I.e 2
1.prong track has EMC energy (Hue = 1)
Figme C.ll: T- -7 e- fJ+ /1- channel n) total transverse momcntum: b) I-prong
momentum: c) lllinilllllm 2- track tllass: d) I-prong mass: e) (bool) onc-prong t.rack has
EMC energy. The POillt.S show the data distributions for events in the grand sideballd
region with all 01"11er cuts applied. The green histogram shows the expected Dhabha
background level and the yellow histogram shows tbe expected vds background level.
all llonnali;;ed bv the backgronm] fits 'witb all sclection cuts applied. Arrow(s)
indicFlte lhe chosen cut value(s). For comparison. the red cur\'(' shu\\'s the l\IC signal
distribution for t.be large box 'with arbitrary normalization.
131
;: 24
~ 22-
; 20
~ 18
>
'" 16
14 :.
12
10
!£
l?) 18
'"~ 16
~ 111
~ 12
10
I I
80
GO
40
20~~~~~00 0.2 0.4 0.6 0.0 1 1.2 1.4 I.G 1.8 2
l-prol1g track has EMC energy (true = 1)
Figure C.12: T- ----l /L- f-l+ fJ-- Cha.llll<~! (I) tot.a! transverse momentum; b) 1-prong
mOlllclltUln: c) minimum 2-track mass: d) I-prong mass: e) (boo!) one-prong t.rack
has Ei\lC energy. The point.s show tll(' data clistrib11 tiOllS for events in t.he gralld
sideband region \\·it.h a.1I other cuts applied. Thr blue histogram shows the expected
1+1- backgnllllld level alld the yellow histogram shows t.he expect.eel ucls L)(\.ckgwUlld
level. all llormali:0ed by t.he background fits \:vitll all selection cut.s applied. Arrow(::;)
indicat.e the dlOsen cut valuc(s). For colllparison, t.he red curve show:-> t.he :\IC signal
distribution for tl18 large box with arbitrary normalization.
3 Plots of Background Fits
132
133
O.4~·· ·-·,.,···~.-__-:I..
r
o.~;
.0.11
0'>;
O~
O.4~·· ~T··""""""·-....-r-l··~-"-
'O.2~
-0.4:,
IO::~oi~To.2~O~1~·~ooT~010T·O:4
0..25,'
r0.",
I
0.15:-
o:L.. "~'--:;I,--,~_,
0.6 -0.4·
'! O.4~--'-"~" •••··'·f···....~·~~
·06:-
.........J....~.,.~...__ .'-__~..,-......Lo.~ __
-0.6 -0.5 -0,4 -0.3 .0.2 ·0.1 0 0.1 0.2 0.3 0.4
J
. 1
oj ~2-O:4
,(I I
'11 'J I
J--fT;-I' ., ; T
•. ; .' +1+.1 I
-,·1 IO"f ' . "
:1-
O~O.6- -0.4 -0.
0.4;--"---····_-1..-,- ... ·
r
0.2'
i0:-,
.O.'2't.-
I
O,~ • 1
.o·.:~~~5-i·~.3··~~-·.·o~,- '·itj-~~i-i!r~l
:i~f,~., I.>+r~':~:'~·,•.;:+~ ,
~~ ~;
...1-
0.1&[
O.lf
O.O.~t.-:Oh;':O'.i"·_o.2·J'-OoJ..-o.rO~2·oh~4
1.U·' .,.-...... .---n-. .......-.---
E • ...l<i:!.:.. ! I
:::r.:t+.o:t :j "l-I •...'.......
O.4 ..-~·-~---~···_··-
O.4~·__,--~_.oJ:~~-:+:t.a:.t: • -..!.,
0.' .
0,'
{:.-rr t _•.-._. N~ ~.:·-"'l
O'f ; ,.! I
°T, ; ~.~
O'l
0.2;
O:--:-o~-:t·f--·~j- -O~2 0:"
0,':----
0.2..
o~
,o"~
0'1
·OA1-
..l1""o.&-:o.,'..O:-.,'."'o.,'."'o.,:-*"o..":.
Figlll'C' C.13: wls ]mckgroulld: Fit of the 'lids (6111.6£) rdC distributioll wit.h PDF
cle~cribed in the text. COhUllll 1) 6Af projection of tile !\lC di::>tribut.ioll (points) and
the PDF (cllI've): COlUlllll 2) 6£ projection of the !\K' distributioll (points) and the
PDF (ClllVC): colullln ~3) \lC (6;11,6£) distributioll: COlUlllll 4) MC PDF (61~1, 6£)
distributioll: row 1) c-e+e-; row 2) {l--e+('-: 1'O'W 3) p-/l+e-: ww 4) /j-e+{l,-: 1'o'W 5)
e--fl+fl-: row 6) /[/1+/1-.61\1 is plotted in (GeVjc2) alld 6£ is plotted ill (GcV).
134
[ I
1
~ 1
'0.' .. __.~_~._._o.._~ I
·CUI o.~ 0.4 ·0.3 ·0.2 ·0.1 0 0.1 0.2 0,3 0.4
.
_ "_~__.~_" .._.....~..1 j
-0.6-0.&·0.".0.3-0."·0.' 0 0.' 0.2 0.3 0."
O'''i~''~'' .. _,_.- -~~-,"'-"'''''''''''~~'-'-
0.2:
0.4,..,_~~~_~~_
0.2~
°c
::t
r
.D.6~_ • '
-0.6 ·0.5 -G.' -0.3 ·D.2 ·D.l 0
I
:-OtL~4
f' .•-- .......,....-.,- .....-1'1-... -
22;
~:~Ill-
14:-
li-
laf-·
L
t \.' ,
.t6 -0.5"'4.4'\{3 .;;~~;-o 6.1 3.2 d.5 lot
l
0.',
I
:::t'-" ,
................~~~.....l-..
·0-6 ·0.5 ·0.4 ·0.3 '0.2 '0.\ 0
0.4t~··'''''''''''"''T·v-r--'~I--------''''
01o
i
·0.2
._ ~. __ ...o.-_ ~. _
·0.6 ·0.5 -0.4 -0.3 ·0.2 ·0.1 0 0.1 0.2 0.3 o.~
;
·0.2:",
I.Sr
Ii
ior· ---,n;;--:t.-----"1i"--.;:-;--i
-G--:6 0.2
[I
O.4-----r-·'---,·-,· ......
I
o.z:-
I
0-
I
i I
.J
___ -~_~_.. ',1
.0.6 ·0.5 -0.4 '0,3 ·0.2 ·0.' 0 0.1 0.2 0.3 0.4
0.2~'
"
lD~~~ '--""-'fT""~"'-- t· • .....1
r'\,
Figure C'.14: T+T- backgroLllld: Fit of the T+T- (6.U,6E) :'odC di:st.ribution "vith
PDF desc:ribed in t he text. colullln 1) 6 j\1 projectioll of the :\Ie distribution (points)
aml the PDF (curve); colullln 2) 6E projection of the rllC distribut.ion (points)
and the PDF (curve): colullln 3) .\IC (6J\1,6E) distribut.ion: colullln 4) \IC PDF
(6J\1,6£) distribution: roy\' 1) p-e-1e'-; row 2) e-fJ+c-: row 3) IFe+/(-; row 4)
e-fJ+/c: row 5) fJ-fJ+fJ'-. 6Al is plotteel in (GeV/c2 ) and 6E i:-; plotted in (GeV).
Only dHtllnels with significant T+T- cOlltributions in the LB arc showlI.
135
~:f:-
160f-
140;--
120~
l00~
sot i. j'
'~ .'.:~t:;:rl-h'-!- -0.2
'l~
.',i l~[\ I
, ! 1
! "t~
0.2 0.4
0.2~
Of
.o.?~·
i
0 ......, -
.0.". _...~..~~"_'" __.__~1
-0.6-o.S-<I.4.().3·0.2·0.10 0.10.20.30.4
·0.6:
·0:6·.0.6·0,:r~.'3 .0.2-:'0.1 0 0.10.20.3 '0:4-
O.4F
O""t.i-~~~1
,1
;
-<1.4:-
.
,o::i~ -<1.5 .0.4 .0.'3 .0.2 .0.1 0 ltlO:2-o.3·~4
:r 'I -.--"~~
.O} .'..,
f ~
-0.,[
_0.61...
l .•~..... , ...-1._...._.. , , _
·0.6-O.5-O.4.0.3·0.2.0.t 00.10.20.30.·1
Figure C.15: Bhabha and eli-lllI.IOll backgrounds: Fit of the Bhabha and eli-muon
(/~J\1: 6.£) Me distributiollS \-vith PDF described in the text, column 1) 6.J\1
projection of the control sample distribution (points) awl the PDF (curve): colulIln
2) 6.£ projection of the control salllplf' distribution (points) and the PDF (curve);
column 3) control sample (6.J\l,6.£) distribution: C01Ulllll 4) PDF (6.J\l,6.£)
distribution: row 1) c-cTe-; row 2) /l--c+e-; row 3) C-f.J+~/'-. 6.J\1 is plotted
in (GcV/(2 ) and 6.£ is plotted in (GeV). Only c:hmllleis with significant QED
contributions ill the LD are shown.
136
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