A SEARCH FOR DIRECT AND RADIATIVE DECAYS OF THE BO I\!IESON TO INVISIBLE FINAL STATES USING A HADRONIC TAGGING METHOD AT THE BABAR DETECTOR by NICHOLAS L. BLOUNT 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 December 2008 11 University of Oregon Graduate School Confirmation of Approval and Acceptance of Dissertation prepared by: Nicholas Blount Title: "A search for direct and radiative decays of the BO meson to invisible final states using a hadronic tagging method at the BaBar detector" This dissertation has been accepted and approved in partial fulfillment of the requirements for the Doctor of Philosophy degree in the Department of Physics by: Eric Torrence, Chairperson, Physics David Strom, Advisor, Physics Nilendra Deshpande, Member, Physics Dietrich Belitz, 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. December 13,2008 Original approval signatures are on file with the Graduate School and the University of Oregon Libraries. @December 2008 Nicholas L. Blount III IV An Abstract of the Dissertation of Nicholas L. Blount for the degree of in the Department of Physics to be taken Doctor of Philosophy December 2008 Title: A SEARCH FOR DIRECT AND RADIATIVE DECAYS OF THE BO MESON TO INVISIBLE FINAL STATES USING A HADRONIC TAGGING lVIETHOD AT THE BABAR DETECTOR Approved: Dr. David Strom This dissertation describes a search for the decays BO -----+ invisible and B°-----+ invisible+" where invisible refers to a final state consisting of long lived particles with a low cross-section for interaction with matter, leading to a low probability of detection in typical particle detectors. While the branching fractions for these decays predicted by the Standard Model are far below what could be feasably measured by current experiments, new physics such as right-handed neutrinos propagating in large extra space-time dimensions or light R-parity violating neutralinos in supersymmetry could greatly enhance the branching fractions. The decays are searched for in data· corresponding to 423.5 fb -1 integrated luminosity produced at the Y(48) resonance collected with the BAEAR detector at the PEP-II B factory, corresponding to v2.30 X 108 BOliO pairs. Using those events that contain a hadronically reconstructed neutral B meson, evidence for the signal decays is sought in the remainder of the event. In (5.00 ± 0.02) x 105 events with a fully reconstructed neutral B meson, a total of 39 events consistent with the BO -----7 invisible decay mode are seen in data with an expected background of 28.5 ± 7.8(stat.)±9.2(syst.) events, and 8 events consistent with the BO -----7 invisible+)' decay mode are seen in data mode with an expected background of 14.1 ± 5.5(stat.)±8.1(syst.) events, from which upper limits of B(B°-----7 invisible) < 11.7 x 10-5 and of B(B°-----7 invisible+i) < 4.3 x 10-5 at the 90% confidence level are obtained. CURRICULUM VITAE NAME OF AUTHOR: Nicholas L. Blount PLACE OF BIRTH: El Paso, TX DATE OF BIRTH: September 28, 1979 GRADUATE AND UNDERGRADUATE SCHOOLS ATTENDED: University of Oregon, Eugene, Oregon Reed College, Portland, Oregon DEGREES AWARDED: Doctor of Philosophy in Physics, 2008, University of Oregon Bachelor of Arts in Physics, 2002, Reed College AREAS OF SPECIAL INTEREST: Dark matter, Quantum mechanics, Neutrino physics Teaching PROFESSIONAL EXPERIENCE: Graduate Research Assistant, University of Oregon, 2002 - 2008 Graduate Teaching Fellow, University of Oregon, 2002 - 2004 VI VB TABLE OF CONTENTS Chapter Page I. THEORY AND PREVIOUS EXPERIMENT , . . . . . . . . . 1 Introduction 1 Standard Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 New Physics 7 Previous Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13 II. DETECTOR AND EXPERIMENT 15 Experiment Overview 15 The Detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19 MC Simulation 26 III. ANALySIS 29 Overview 29 Dataset 30 Event Reconstruction 31 Event Tagging 33 Signal Cuts 43 Systematic Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58 IV. CONCLUSIONS AND FURTHER RESEARCH 74 Branching Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78 Further Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79 APPENDICES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81 A. CUT OPTIMIZATION 81 B°-----+ invisible 81 B°-----+ invisible + '"Y •••••.....••••••••..•..••••••••.........••••••••....••• , 87 Chapter viii Page B. BACKGROUND SCALING 94 C. PID LISTS 112 Track Lists 112 Neutrals Lists 113 PID Lists 113 Composite Particles 115 BIBLIOGRAPHy 117 IX LIST OF FIGURES Figure Page 1.1 Diagrams for B°-----+ vv in the Standard Model. . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 1.2 Diagrams for B°-----+ vv, in the Standard Model. . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 B°-----+ invisible Enhancing Feynman Diagrams with Supersymmetry 10 1.4 Mass Limit on the Neutralino LSP 11 1.5 Limits on Neutralino Versus Stop and Sbottom Masses 12 1.6 Number of Events in the NuTeV Detector 13 2.1 PEP-II Rings 16 2.2 Integrated Luminosity at the BABAR Detector .. . . . . . . . . . . . . . . . . . . . . . . . . .. 18 2.3 The BABAR Detector 20 2.4 Silicon Vertex Tracker. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21 2.5 Resolution in the Transverse Momentum PT 24 2.6 Electromagnetic Calorimeter 25 2.7 Resistive Plate Capacitor Cross Section 27 3.1 !:1E Plot after Preselection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34 3.2 Plot of mES after Preselection 35 3.3 Integrated Purity Plot after Preselection 36 3.4 eP * and Ni,Y f 40 3.5 mES Plot for Data and Combinatoric MC Simulation 41 3.6 mES Plot for MC and combinatoric MC Simulation 42 3.7 Eneu in B°-----+ invisible and Background 48 3.8 NCT in B°-----+ invisible and background 49 3.9 N 7r0 in B°-----+ invisible and Background 49 3.10 R2 in B°-----+ invisible and Background 50 3.11 Eneu in B°-----+ invisible +, and Background 52 3.12 E hi in B°-----+ invisible +, and Background 52 3.13 N 7r0 in B°-----+ invisible +, and background 53 3.14 NCT in B°-----+ invisible +, and Background 53 3.15 R2 in B°-----+ invisible +, and Background 54 3.16 Tag BO Yield with Combinatoric Contributions Floated 59 3.17 Tag BO Yield with ee, uds, and T+ T- Scaled to Offpeak Data 60 3.18 Eneu for the K s Control Sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62 3.19 Eneu for the p- .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63 3.20 Eneu in e- 64 Figure x Page 4.1 mES vs. Eneu 76 4.2 Data and MC Simulation, after All Cuts, for mES 76 4.3 Data and MC Simulation, after All Cuts, for Eneu 77 A.l NaTL high statistics comparison in B°-----+ invisible 82 A.2 Eneu high statistics comparison in B°-----+ invisible 83 A.3 NCT high statistics comparison in B°-----+ invisible 84 AA N,ro high statistics comparison in BO-----+ invisible 85 A.5 R2 high statistics comparison in B°-----+ invisible 86 A.6 NaTL high statistics comparison in B°-----+ invisible + r' 88 A.7 Eneu high statistics comparison in B°-----+ invisible + r' , 89 A.8 E hi high statistics comparison in B°-----+ invisible + r 90 A.9 NCT high statistics comparison in B°-----+ invisible + r 91 A.I0 N1r0 high statistics comparison in B°-----+ invisible + r 92 A.ll R2 high statistics comparison in B°-----+ invisible + r 93 xi LIST OF TABLES Table Page 2.1 PEP-II Beam Parameters 16 2.2 Production Cross Sections 17 2.3 Properties of Helium-isobutane Gas Mixture. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23 3.1 Data Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 30 3.2 Off-peak Data Samples 31 3.3 Background Monte Carlo Samples 32 3.4 Signal Monte Carlo Samples 32 3.5 Signal Event Tag Efficiency Corrections 43 3.6 B°-----t invisible Combinatoric Background Cutfiow Table 56 3.7 B°-----t invisible Cutfiow Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 56 3.8 B°-----t invisible +, Combinatoric Background Cutfiow Table 57 3.9 B°-----t invisible +, Cutfiow Table 57 3.10 B°-----t invisible e- Control Cutfiow Table 66 3.11 B°-----t invisible /1- Control Cutfiow Table 67 3.12 B°-----t invisible K2 Control Cutfiow Table 68 3.13 BO -----t invisible +, e- Control Cutfiow Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69 3.14 B°-----t invisible +, /1- Control Cutfiow Table 70 3.15 B°-----t invisible +, K2 Control Cutfiow Table 71 3.16 Systematic Errors on the Background Estimates 73 3.17 Systematic Errors on Signal Efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 73 3.18 Systematic Errors on the Tag BO Yield 73 4.1 Upper Limits for BO-----t invisible(+,) at the 90% Confidence Level. . . . . . . .. 78 B.1 B°-----t invisible Cutfiow Table. Background luminosity weighted 95 B.2 B°-----t invisible +, Cutfiow Table. Background Luminosity Weighted 95 B.3 B°-----t invisible Eneu Sideband 98 B.4 B°-----t invisible mES Sideband 99 B.5 B°-----t invisible Eneu Sideband e- ControL 100 B.6 B°-----t invisible mES Sideband e- Control 101 B.7 B°-----t invisible Eneu Sideband /1- Control 102 B.8 B°-----t invisible mES Sideband /1- Control. 103 B.9 B°-----t invisible +, Eneu Sideband 104 B.lO B°-----t invisible +, mES Sideband 105 B.11 B°-----t invisible +, Eneu Sideband e- Control 106 B.12 B°-----t invisible +, mES Sideband e- Control 107 B.13 B°-----t invisible +, Eneu Sideband /1- Control 108 Table xu Page B.14 B°-t invisible + "y mES Sideband /1- Control. 109 B.15 B°-t invisible Peaking Ratio 110 B.16 B°-t invisible Peaking Ratio e- Control 110 B.17 B°-t invisible Peaking Ratio /1- Control 110 B.18 B°-t invisible + "y Peaking Ratio 111 B.19 B°-t invisible + "y Peaking Ratio e- Control 111 B.20 B°-t invisible + "y Peaking Ratio /1- Control 111 C.1 Reconstructed Composite Particles Used in the SemiExcl Skim 115 C.2 Masses of Particles Used in Making the Seed in the SemiExcl Skim 116 1CHAPTER I THEORY AND PREVIOUS EXPERIMENT Introduction This dissertation describes a search for the decays EO -----+ invisible and EO -----+ invisible +1 with a hadronically tagged 13° using a data sample containing 2.35 x 108 E0130 pairs collected by the BABAR detector at the PEP-II B Factory. Invisible is defined as particles with a low probability to decay in or measurably interact with the BABAR detector. The charge conjugate modes EO -----+hadrons, f3 0 -----+ invisible (+1) are also searched for: throughout this dissertation the inclusion of charge conjugate modes is implied. This chapter presents the decays in the context of the Standard Model and considers two theories that could enhance such decays, large extra dimensions and supersymmetry, as well as summarizing the previous search at BABAH for the decays. Chapter 2 describes the PEP-II accelerator and BABAR detector, as well as the simulation used in the analyses. Chapter 3 presents the EO -----+ invisible (+1) analyses, including the hadronic tag reconstruction, the cuts applied for background rejection, and determi-nation of systematic errors. Chapter 4 gives the resulting branching fractions and limits, conclusions, and ideas for future research. Appendix 21 details the cut optimi-zation used in Chapter 3, Appendix 2 details the background scaling, and Appendix 3 describes the particle definitions used in the analysis. Standard Model The Standard Model of particle physics (SM) is a theoretical framework that describes the fundamental particles so far discovered and their interactions. All matter visible in the universe, and every force that acts on it other than gravity, is composed from 18 quarks, 6 leptons, 12 bosons, and anti-particles corresponding to each of the quarks and leptons. Each of three generations of quark pairs consists of an up type quark with charge +2/3 and a down type with charge -1/3, while each of three generations of lepton pairs consists of a charged lepton and a neutrino. The three generations of quarks are the up u and down d quarks, the charm c and strange s quarks, and the top t and bottom b quarks. Each quark also comes in three colors, where color is a quantum number affecting how the quark interacts via the strong force. The quarks are never found individually in nature, instead combining to form various charged and neutral hadrons, either as mesons consisting of a quark and an anti-quark, or baryons consisting of three quarks or of three anti-quarks. The three generations of leptons are the electron e~ and electron neutrino Ve , the muon f-L- and muon neutrino vI" and the tau T- and tau neutrino VT • The bosons mediate the fundamental forces that govern interactions between the particles of the SM. The photon is a massless particle that mediates the electro- 3magnetic force and couples to charged particles. Eight types of gluons correspond to the strong nuclear force and couple to quarks and other gluons. They differ by their color composition. Each carries a unit of color and a unit of anti-color. The weak bosons Vl/T± and ZO, unlike the photon and gluons, are massive, correspond to the weak nuclear force, and only couple to left-handed particles. Particles with positive chirality are referred to as right-handed, while those with negative chirality are referred to as left-handed, where chirality is a fundamental property of a particle that describes how it behaves under parity transformations. Gravity theoretically also has a boson, the graviton, but as of yet it has not been experimentally verified, and is not included in the 8M. The last 8M boson, the Higgs boson, has not been detected experimentally. The Higgs mechanism explains the masses of the massive 8M particles, using a scalar field with a non-zero vacuum expectation value. This field corresponds to 4 particles, including the Higgs boson. Experimental searches in e+e- data from the LEP experiment constrain the Higgs boson to have a mass greater than 114.4 GeV at the 95% confidence level [1]. Precision electroweak measurements constrain the 8M Higgs boson to a mass less than 285 GeV at the 95% confidence level [2]. For the decays EO ----> invisible (+,), invisible refers to particles that are long lived and have a small cross section, making them unlikely to leave a signature in the BABAR detector at a significant rate. In the 8M, the only particles that meet the definition of invisibility are neutrinos. Neutrinos are neutral and colorless, and 4therefore do not interact via the strong or electromagnetic forces. Since the weak nuclear force has small couplings GF/(17,C)3 = 1.166 X 10-5 GeV- 2 , they are highly unlikely to measurably interact with the BABAR, detector. At energies of a few GeV, typical of particles produced in BABAR, neutrinos have a cross section of order (5// = 10-38 cm2 [3]. The average detector density is less than the density of steel, p = 8 g/ cm3 : given a nucleon mass of u = 1.66 X 10-24 g, and a detector radius of r = 350 em this gives a probability for a neutrino produced at the interaction point to interact in the detector of P < (5//pr /u ~ 2 X 10-11 . d 3 D .. w. -)- .u,c, .... .7'1 W·~ ~ d I Figure 1.1. Diagrams for B°-----t lJV in the Standard Model. The BO meson is composed of a b and a d quark. Since neutrinos do not interact via the strong or electromagnetic forces, in the SM BO -----t lJV must be mediated by w± or ZO bosons. The prohibition on flavor changing neutral currents prohibits the B°-----t lJv(+,) decays at the tree level by ZO production through the annihilation of 5the b quark and J quark, so to highest order B O--7 vv must occur through a loop or penguin diagram (Figure 1.1). For B O--7 vvry, the photon can radiate from any charged particle in the decay tree, resulting in decay trees like those in Figure 1.2. Figure 1.2. Diagrams for B°--7 vvry in the Standard Model. Helicity Suppression and B to Neutrino Anti-neutrino Gamma The decay B°--7 vv is helicity suppressed. The helicity h refers to the component of a particle's spin S in its direction of momentum p, h = S· p. For spin 1/2 particles, the possible values for helicity are h = ±n/2. For massless particles or for massive particles in the relativistic limit, the particle's helicity has the same value as its chirality. For charged leptons, which are left-handed, this leads to the helicity of leptons produced in weak decays to be dominantly negative, with the average helicity proportional to the lepton's velocity v, h = -v/ c· n/2, for their anti-particles h = v / c . n/2. Since BO particles are scalar, the daughters in a 2 body decay must have opposite spins and momenta, and therefore identical helicity. As the weak force 6only couples to left-hande? particles, this leads the decays to be helicity suppressed, with a branching fraction proportional to m 2 , where m is the daughter particle mass. Under the SM, with the assumption of massless neutrinos, neutrinos can only be left- handed, and anti neutrinos can only be right-handed, and therefore the decay B°----+ vv is forbidden due to helicity conservation. In 1998, Super-Kamiokande measured neutrino oscillation, showing that neutrinos are not massless [4]. Neutrino oscillation between two types of neutrinos is given by Pa -->{3 = sin22esin2 ((lim2L)/(4E)) ,where ex and (3 are two neutrino types, e is the mixing angle between them, lim is their difference in mass, L is the distance the neutrino has travelled, and E is the neutrino energy. If neutrinos were massless, lim2 and therefore Pa -->{3 would be zero. More recent neutrino oscillation measurements give lim~l = 7.58~g:ij(stat.)~~:i~(syst.) x 10-5 ey2 (KamLAND [5]), and lim~3 = O.00243±O.00013 ey2 (MINOS [6]). The WMAP experiment measured the distribution of light from the early universe, called the cosmic microwave background, and com- pared the distribution with that predicted under various assumptions about the composition and development of the universe. WMAP put a limit on the total mass of the 3 neutrinos, with a current combined limit of mTOT < 2 eY [7]. Therefore, while neutrinos are not massless, their masses are small, and so the decay B°----+ vv is allowed but strongly helicity suppressed, with a branching fraction to be proportional to the neutrino mass squared. Assuming the branching fraction for BO ----+ vv is otherwise the same as for the other dilepton decays, this leads to a branching fraction 7of at most 10-20 , many orders of magnitude lower than EO decays to heavier dileptons such as E°----7 T+ T-, and far below BABAR's ability to measure. The addition of an emitted photon from one of the charged particles in EO ----7 l/V breaks the helicity suppression, giving a branching fraction for EO ----7 l/V, of order 10-9 , calculated from the partial width given in Equation 1.1-Equation 1.3 [8]: 0 2 f2 5r = a BdmBd (1441T)2m~ , o = V2GFa 11; 11:* ~ (x + 2 3x - 6 In x) . 2 e tb td 8 1 + ( 1)2 '1TSln w X - x- 2/ 2X = m t m w , (1.1 ) (1.2) (1.3) where a is the electromagnetic coupling constant, fBd is the pseudo-scalar decay constant for B decays, mBd is the mass of the EO meson, md is the mass of the d quark, GF is the Fermi coupling constant, ew is the weak-mixing angle, vtb and vtd are components of the CKM matrix, mt is the top quark mass, and mw is the W boson mass New Physics While in the 8M EO ----7 invisible (+,) are not predicted to occur at measurable rates, there are strong reasons to expect particles and processes beyond those of the 8M that could greatly enhance the branching fractions. Dark matter, first detected using galaxy rotation measurements, composes much of the matter in the universe and is not explained by the 8M. Currently the best estimates of the total dark matter 8composition of the universe come from WMAP. The best fitting parameters to the WMAP measurements predict the cold dark matter content of the universe to be Dch2 = 0.1099 ± 0.0062, with baryonic matter as Dbh2 = 0.02265 ± 0.00059 [9]. While most theoretical models that explain dark matter do not predict an enhanced rate of BO -----+ invisible (+"y), the possibility of decays of BO to dark matter is not expressly prohibited. New physics might enhance the rate of BO -----+ vv(+"y). One theory that could do so is with large extra dimensions, which neutrinos and gravitons could propagate in, with the other 8M particles confined to the standard 4 dimensional spacetime. 8upersymmetry is an extension to the 8M that proposes a set of additional particles, one partner to each 8M particle. It may be possible for invisible super- symmetric particles to be produced in BO decays. In this section, large extra dimen- sions and supersymmetry are examined in more detail. Large Extra Dimensions Large Extra Dimensions is one theory that resolves the hierarchy problem. It explains why the Higgs mass, less than 285 GeV at the 95% confidence level, is not of the same scale as the Planck mass mp = V8:~ = 2.43 x 1018 GeV/ c2 , where G is the gravitational constant. In calculating the Higgs mass, fine tuning is needed to avoid quantum corrections leading to terms that are of the order of the Planck mass. One possible alternative is the existence of dimensions beyond the standard 4 spacetime dimensions. If gravitons propagated in these dimensions while most the 8M particles were confined to 4 dimensions, the result would be that the observed Planck mass 9would follow from a much smaller fundamental Planck mass: M~l ~ ROM~+2 where .A1Pl is the 4 dimensional Planck mass, 0 is the number of extra dimensions, R is the size of the extra dimensions, and M* is the fundamental Planck scale. If, further, right handed neutrinos are allowed to propagate in the extra dimensions, left handed .\ M neutrino masses would be suppressed to m ~ f() M * l/, where .\ is a dimensionless v 2 Pi 5 dimensional coupling and l/ is the Higgs vacuum energy of 246 GeV [10]. In this scenario, the rate for E°---+ invisible would be enhanced by additional contributions from Higgs exchange. This effect is large when all the Kaluza Klein modes of the right handed neutrino lighter than the EO meson are taken into account, resulting in an enhancement in the E°---+ invisible branching fraction up to 10~12 [11]. While a large enhancement over the 8M, branching ratios of this order are still below what is measureable by BABAR. 8upersymmetry 8upersymmetry posits that for every 8M particle there is a corresponding super- particle, a fermion for each 8M boson and a boson for each 8M fermion. In calculating the Higgs mass, fine tuning is needed to avoid quantum corrections leading to terms that are of the order of the Planck mass. With supersymmetry the contributions to these terms by each 8M particle are cancelled by the contribution of its super- symmetric partner. While searches for supersymmetric particles have so far been unsuccessful, it is still possible that there are such particles light enough for a EO to decay into, but experimentally invisible and therefore undetected (Figure 1.3). 10 d 0 __~) ----, Xl d ( I) ( d ) < V - V b R i --.....(E--------'------_O ii Xl Figure 1.3. E°--+ invisible enhancing Feynman diagrams with supersymmetry [12]. As with neutrinos, invisible supersymmetric particles would be long lived neutral fermions. As super-symmetric particles have the same charge as their SM partners, the candidates in supersymmetry that meet these criteria are the neutralinos, the superpartners to the neutral gauge bosons. Searches for supersymmetric particles at LEP and Tevatron found no significant evidence of light supersymmetric particles, and place limits on supersymmetry parameters that heavily restrict light supersymmetric particles [13][14] (Figure 1.4 and Figure 1.5). NuTeV Experimentally, neutralinos produced in EO decays could have resulted in the excess of dimuon events seen in the NuTeV experiment [12]. NuTeV was the neutrino detector for a neutrino beam produced by fixed target collisions of 800 GeV protons from Fermilab's Tevatron. The detector consisted of a section of alternating layers of iron, scintillators for energy measurements, and drift chambers for position measure- 11 : : : : (intl1\1 ~ 17~ f1~·V.l~·-~;; ···1···· r" .-" C··~ .~ .. _. ';": {..r'-'f -.~-.~..~.~ -.., .........; .... ,..-... ~·I U -.> 54 (\j o 50 . . . .. , I • , .. . ; i : ; 4H ........ · ...... ......... . .. :. ;~~ ... ,-.- .. :..... ' .. ....-..... ..- .... . . ...,. 46 - L : L t tin4hb..(~dtTidor . Excluded ;It 95%[ C.U .; : : . . . 5 In tanp Figure 1.4. Mass limit on the neutralino L8P as function of tanJ1 [13]. ments, followed by a section with alternating toroids and drift chambers, for tracking and measuring the momentum of muons produced in the first section. The NuTeV experiment saw 3 J..l+ J..l- events, with an expected 8M background of 0.069 ± 0.010 events, which when combined with the other dilepton channels corresponds to a 30' fluctuation. One explanation for the excess events seen is that B mesons produced at NuTeV decayed into Rp violating neutralinos, with the neutralinos subsequently LEP constraints prevent pair production of such neutralinos, with subsequent dimuon decays from producing enough 12 00 Run2 ; Theoretical uncertainty incl. renormalization and . factorizalion scale~b~"r::'"'''''''''''' 1-.:' :.... I,· "~--:. ,..: :t -Observed ..... Expected limit -00 Run2 COF Run 1 ·LEP ~~-"-':'::'-"-'::'::'-~B'::':~~1~~O'1JO '1~O '160 180 200 220 M(61) (GeV/c 2) 40 60 o~ l~ :E BO Figure 1.5. Limits on neutralino versus stop (left) and sbottom (right) masses from the CDF search in the heavy flavor + missing transverse energy channel [14]. events to explain the excess of dimuon events in NuTeV. However, if the neutralino is dominantly Bino, the superpartner to the gauge field that forms the 3rd component of weak isospin, it could be produced in B decays while not being pair produced in s channel decays of the ZO boson. This would suppress neutralino pair production from Z boson decays and avoid the LEP constraints. The neutralinos would have a lifetime in the range T = 10-78 to 10-58, corresponding to a decay length of 30m to 3000m, and would thus be invisible to the BABAR detector(Figure 1.6). The neutralino mass would be between 4.5 and 5.5 GeV. Such B°----'> invisible decays could have branching ratios up to order 10-5 , calculated from the width given in Equation 1.4 (1.4) where '\~13 are dimensionless R-parity violating coupling constants of supersymmetric 13 BR(BO~xv)=10-5 -------- =10-" =5x10-7 --- --- ----- =10-" I , I " ..~ . i Tis Figure 1.6. Number of events in the NuTeV detector for neutralino production in B-meson decays as a function of the neutralino lifetime and rate of BO- invisible. particles, g' is a supersymmetric gauge coupling, IE is the pseudo-scalar decay constant for B decays, mEO is the mass of the BO meson, Pcm is the momentum of the daughter particles, md is the mass of the d quark, mb is the mass of the b quark, Mj is the sfermion mass, and Mx~ is the mass of the lightest neutralino. Previous Experiment While the 8M branching ratio for BO - invisible is far below what is currently measurable, experimentally the branching ratio is not well constrained. The decay BO- invisible was searched for in a previous analysis at BABAR [15] using 81fb-1 data, and obtained upper limits of B(Bo _ invisible) = 22 x 10-5 and B(Bo- 14 invisible + I) = 4.7 X 10-5, using a reconstructed EO -----+ D(*) lv decay to tag the other EO in the event. It obtained these limits from a fitted signal of Nsig(E°-----+ invisible) = 17 ± 9 on top of a background of NBkgrnd(E°-----+ invisible) = 19!~O, and a fitted signal of Nsig(EO -----+ invisible + I) = -1.1!~:~ on top of a background of N Bkgrnd(EO -----+ invisible + I) = 28!~. The analysis in this dissertation instead uses an entirely hadronic tagging method, as well as a much larger dataset. 15 CHAPTER II DETECTOR AND EXPERIMENT Experiment Overview The search for B O-----+ invisible (+,) with hadronic tag analysis was run on data produced at the PEP-II asymmetric e+ e- collider and B factory at the Stanford Linear Accelerator Center. The PEP-II experiment was designed for precision measurements of B meson decays at high luminosities. The PEP-II collider consists of a 3.2km long particle accelerator, which leads to two storage rings of 2.2km in circumference [16]. The storage rings share a tunnel, with the Low Energy Ring (LER), which contains the positron bunches, mounted 0.89 m above High Energy Ring (HER) carrying the electron bunches. Permanent bending magnets bring the LER beam to collide head on with the HER beam at the IP. The BABAR detector is located where the two beams intersect (Figure 2.1). Luminosity The performance of the PEP-II collider is characterized by the luminosity delivered to the BABAR detector. The rate dN/ dt of interaction is determined by the physical process that produces the interaction, given by the cross section (J", and by the 16 SLAC......... ~ 1inac ' PEP-II ~ i n.e,~ ...-... 1'0 ... i1 rOll~ II i~h Erwrgy Rin~ Figure 2.1. PEP-II rings Table 2.1. PEP-II beam paramet.ers. Values are given for the design, for typical colliding beam operation in the first year, and the best. values obt.ained as of April 2008. HER and LER refer to t.he high energy e- and low energy e+ ring, respectively. (h~" (JLy' and (JLz refer to the hori7.0ntal, vertica.l, and longitudinal rms size of the luminous region [17][18]. Parameters Design Typical Best Energy HER/LER ( GeV) 9.0/3.1 9.0/3.1 9.0/3.1 Current. HER/LER (A) 0.75/2.15 0.7/1.3 2.07/3.21 # of bunches 1658 553-829 1732 Bunch spacing (ns) 4.2 6.3-10.5 (JLx ( lIm) 110 120 (J Ly (j.l.lll) 3.3 5.6 (JLz (mm) 9 9 Luminosity (1033 cm- 2s- 1) 3 2.5 12 Luminosity (pb -1 / d) 135 120 911 17 Table 2.2. Production cross sections at VS = M(Y(4S)). The e+e- cross section is the effective cross section, expected within the experimental acceptance [19]. I e+e ---+ I Cross section (nb) I bb 1.05 cc 1.30 S8 0.35 ui], 1.39 dd 0.35 I T+T 0.94 f.1+f.1- 1.16 e+e- 40 mechanics producing the interaction, given by the luminosity 12: dN/ dt = £ . ()". The cross sections are determined by what particles are involved in the interaction and the center of mass (CMS) energy of the interaction. Cross sections of some processes for e+ e- at 10.58 GeV are given in table (Table 2.2). NN Luminosity is given by the equation £ = tnT where L is the luminosity, t is the revolution frequency, n is the number of bunches in one beam of the storage ring, N i is the number of particles in each bunch from beam i, and A is the cross section of each beam. Parameters for the PEP-II beams are given in Table 2.1. Over the lifetime of the BABAR experiment, the detector collected an integrated luminosity of 531.43 fb-r, with a peak luminosity of 12.069 x 1033cm-2see1 (Figure 2.2). This corresponds to 227.3 million BOl3o pairs, assuming B(Y(4S) ---+ B0l30) = 0.5. 18 As 01 2008104/11 00:00 >- -'iii 500o c: 'E ~ ....J "0$ 400 III ... g' - .E 300 200 100 PEP II Delivered Luminosity: 553,4fJ/fb SaSar Recorded Luminosity 531,43/tb SaSar Recorded Y(4s): 432.89/fb SaSar Recorded Y(3s): 30.23/fb SaSar Recorded Y(2s): 14.45/fb Off Peak Luminosity: 53.85/fb __ Delivefed LUm"nOSlry __ R~QI'di~d luminOSIty R6""...orded lllmulC5lly Y(4s) __ Reocordcd lummoslty Y(3s) R orc!cd lummoslty Y(2s) au Penk 1~IJJillillillmJlU11I111l1111111 ~ 1111111111111111111111~ Figure 2.2. Integrated luminosity at the BAEAR detector, 19 The Detector The BABAR detector consists of a series of subsystems designed to detect and characterize particles produced at the interaction point (IP). From innermost to outermost, it consists of the silicon vertex tracker (SVT) , drift chamber (DCH), detector of internally reflected Cherenkov light (DRC), and electromagnetic calorim- eter (ElVIC) contained in a superconducting solenoid producing a 1.5T magnetic field, surrounded by the instrumented flux return (IFR)· (Figure 2.3). The SVT and DCH measure the trajectories of charged particles as they emerge from the interaction point (IP). Combined with curvature of the trajectories due to the solenoid field, the momenta and energy loss of the tracks can also be measured. The DRC uses Cherenkov radiation to measure charged track velocities, enabling improved differen- tiation between types of charged particles. The ElVIC uses electromagnetic showers to detect and measure the energy of photons and electrons produced at the IP. The IFR detects showers produced in the steel surrounding the solenoid, detecting neutral hadrons undetected by the other subsystems and allowing improved differentiation between muons and charged kaons. This section describes the subsystems in greater detail [17]. In describing these subsytems, I will use the following coordinate system: with +z along beampipe in direction of electron travel, +x in direction away from the center of the ring, and y in the upward direction. For angles, () is the angle from +z axis and ¢ is the angle around the z axis from +x. The center of the detector is 20 e+ 3·2001 8583A5t I 3500 i -- DCH ··DIRC IZ Superconducting - Coil --~- Electromagnetic Calorimeter (EMC) __ Drift Chamber (DCH) _... Silicon Yertex Trackar (SYT) I 3500 I - I L 3·2001 8583A50 -:-r-~' --+----1 o Scale 4m BABAR Coordinate System I y Instrumented _.- Flux Return (IFR» Barrel --+-----.-1149.) i Cutaway Sec~ion Dete~tor 500 mrad with an efficiency of 98 ± 1%. Lower energy charged tracks rely on the SVT for 23 Table 2.3. Properties of helium-isobutane gas mixture at atmospheric pressure and 20°C. The drift velocity is given for operation without magnetic field, while the Lorentz angle is stated for a lo5T magnetic field. Parameter Mixture He : C4 HlO Radiation Length Primary Ions Drift Velocity Lorentz Angle dE/dx Resolution Values 80:20 807m 2lo2/cm 22 !Jm/ ns 32° 6.9% detection: the SVT can detect tracks with a transverse momentum greater than 50 MeV with greater than 80% efficiency. Combined, the track resolution for the DCH and SVT is (Jdo = 23!Jm, (Jzo = 29!Jm, (J¢;o = 0.43mrad, and (Jtan.>- = 0.53.10-3 , where do and Zo are the distance of closest approach of the trajectory of the charged track to the IP in the x - y plane and along the z axis, respectively, and A is the dip angle of the charged track relative to the transverse plane. In transverse momentum, the resolution is (JPt/Pt = (0.13 ± 0.01)%· Pt + (0.45 ± 0.03)% (Figure 2.5). DRC The DRC, located outside the DCH, is designed to measure the velocity of high energy charged particles. Combined with the momentum information from the DCH, this allows for a calculation of the mass of the particle producing the track. A primary motivation for this is for pion/kaon separation. The DRC consists of synthetic fused silica, which causes high energy charged particles passing through to emit a cone of Cherenkov radiation. The cone is produced 24 2.0 •~~ ci' ...... ~ 1.0 '0 1-2001 8583A23 o 048 Transverse Momentum (GeV/c) Figure 2.5. Resolution in the transverse momentum PT determined from cosmic ray muons traversing the DCH and SVT [17]. with an opening angle of cos e= 1/(nfJ) , where n is the refractive index of the medium. The Cherenkov is transmitted by total internal reflection and is subsequently detected by photomultiplier tubes. From the location and time of arrival of photons to the photomultiplier tubes, the angle of emission of the light cone is reconstructed. The DRC measures the Cherenkov angle with a resolution of 2.5 mrad, which leads to a 7f / K separation of greater than 40- for tracks between 700 MeV and 4.2 GeV. EMC The EMC serves to cause photons, electrons, and positrons to produce electro- magnetic showers, depositing their energy into the material of the EMC, allowing the energy of the particle to be measured (Figure 2.6). The EMC consists ofthallium doped cesium-iodide (Cs-I(TI)) crystals that collect electromagnetic showers. The energy deposited and location of a shower are read out 25 I~------- 2359---1 r1555---I.~----2295---~ ----1979--- Figure 2.6. Electromagnetic Calorimeter [17]. External Support 1·2001 8572A03 by silicon PIN diodes glued to the outside of each crystal. The EMC consists of 16- 17.5 radiation lengths of material. The EMC is able to obtain an energy resolution of CJEIE = (1.9 ± 0.07)% at 7.5 GeV, and (5.0 ± 0.8)% at 6.13 MeV. The angular resolution ranges from 12 mrad for low energy photons to 30 mrad at high energies. IFR Because of their similar masses, muons (105.7 MeV) and charged pions (139.6 MeV) are difficult to distinguish by mass, and both pass through the SVT, DCH, DRC, and EMC with little momentum loss or chance of interaction. The steel of the IFR increases the chance of interactions, allowing for improved muon ID. By the time they hit the IFR, muons and hadrons have traveled through 0.3-2.0 radiation lengths of material. Neutral hadrons rarely interact before the IFR, so the IFR also serves as a detector of K L mesons and other neutral hadrons. The IFR consists of resistive plate capacitors (RPCs) and limited streamer tubes 26 (LSTs) in between layers of flux return steel, which is used as a muon filter and hadron absorber. The RPCs consist of an argon, freon, and isobutane gas mixture sandwitched between layers of bakelite. Layers of graphite on the backelite are held at OV and 8kV. External layers of aluminum serve as capacitive conductors to measure streamers produced in the gas mixture (Figure 2.7). In 2006-2007, the barrel RPCs were replaced with LSTs, which consist of groups of PVC tubes oriented in the z direction [20]. Each has a gold plated anode signal wire running down the middle. The inside wall of each tube is painted with graphite, which is grounded. Streamers in the CO2 , argon, and isobutane gas mixture that fill the LSTs are collected by the sense wires. A layer of copper strips runs perpendicular to the LST tubes to provide z coordinates for hits in the LSTs. Showers in the iron ionize gas in the detector. The electrons from the ionization are collected on the wire or plate. The RPCs achieved a muon identification rate of 90% with a charged pion fake rate of 6 - 8% for tracks in the range 1.5 - 3 GeV, and a neutral hadron detection efficiency of 20 - 40% over the range 1 - 4 GeV. MC Simulation The BABAR experiment uses detailed Monte Carlo (MC) simulation to simulate the production of particles in an underlying physics event, transport the particles through the material of the detector, calculate the idealized energy deposits in the detector, overlay backgrounds and digitize the energy deposits, and reconstruct the event. 27 Figure 2.7. Resistive plate capacitor cross section [17]. The program Bogus, consisting of a detailed simulation model of the material and electromagnetic fields of the detector used with Geant4 [21], combined with various event generators depending on the physics of the event performs the generation, transport, and energy deposit calculations. The event generators model initial decay at or near the IP, using predicted branching ratios, angles, and momentum distri- butions to give the daughter particles propagated by Geant4. Geant4 is a toolkit produced by CERN to simulate the passage of particles through matter, to model the behavior of the particles as they traverse the detector. The detector simulation defines non-overlapping regions, each giving the space occupied by a section of uniform material in the detector. Particles are transported in steps of the smaller of 1 cm and the distance to a region boundary, for each step calculating energy deposited and any changes to the particle's location and momentum due to interactions and electromagnetic fields. The program SimApp converts the idealized energy deposits 28 into simulated detector signals, using measured responses of the BABAR detector to events in data, and uses background mixing to add effects of cosmic radiation and detector noise, using cosmic ray data measured in the BABAR detector. The program Bear performs the Me reconstruction, using the same methods as are used in data. 29 CHAPTER III ANALYSIS Overview For a given event registered in the BABAR detector, particles are reconstructed into charged tracks and neutral clusters. Momentum, energy, charge, and velocity measurements from the various detectors are used to identify possible particle identifi- cation (PID) for each track and cluster. Combinations oftracks and neutrals are then combined to form reconstructed particle candidates. This analysis searches for signal events of the topology e+e- ~ Y(4S) ~ BOlJo (BO ~hadrons,lJo ~Invisible(+,)), The analysis strategy follows. First, events are found that contain a hadronically decaying B O• Cuts are applied to reduce the number of background events in the tagged sample. MC simulation is used to determine the efficiency of signal events to pass these cuts, as well as predict the number of background events remaining. The number of events in the tagged sample, signal efficiency, background estimate, and data events remaining after applying cuts are used to obtain a branching fraction calculation and upper limit. 30 Dataset The events used in this analysis are divided into data and MC collections. A collection is a file containing the reconstructed events in a data or MC sample, along with any composite particle information and calculated variables associated with the events. The data used in this analysis are summed up in Table 3.1. The luminosity and number of events in the table were determined from the BbkLumi script, which uses bhabha events in the data to calculate the luminosity. Off-peak data is used to study continuum backgrounds (See Table 3.2). Off-peak data is data taken 40 MeV below the Y(48) resonance. Table 3.1. Data samples used in this analysis. Run I £( fb 1) I BDBDEvents (x 106) I Run 1 20.403 11.173 Run 2 61.076 33.697 Run 3 32.278 17.784 Run 4 100.28 55.255 Run 5 133.26 73.595 Run 6 76.156 41.018 Total or Average 423.5 fb -1 2.325 X 101) To help understand the behavior of signal and background in the data while keeping the analysis unbiassed, Monte Carlo(MC) simulated events were used. The MC events used in this analysis are given in Table 3.3 for background MC, and Table 3.4 for signal MC. The MC events are normalized to the data luminosity using 31 Table 3.2. Off-peak data samples used in this analysis I Run I £( fb 1) I Run 1 2.165 Run 2 6.923 Run 3 2.486 Run 4 10.121 Run 5 14.485 Run 6 7.275 Total 43.437 the luminosities in Table 3.1 with the luminosity determined by the number of events produced and the known cross sections at the Y(4S) resonance. The BD-t invisible+r MC uses phase space to model the photon energy distribution. The B DJ3D Cocktail MC sample consists of events where one BO decays into one of a set of modes (Bo -t D(*)- X,X = 7]"+ ,p+ , or a1+) that are easily reconstructed using the hadronic method used in this analysis with the other neutral B in the event decaying freely, and is used when greater statistics of peaking B DJ3D background is needed. Peaking events refers to events with a correctly reconstructed B meson. When used, the BOJ3o Cocktail MC sample is compared to the BOJ3o generic sample to ensure the two are in agreement. Event Reconstruction Recorded signals in SVT and DCH are reconstructed into charged tracks. Tracks are found using hits in the DCH using a Kalman filter algorithm. They are further refined by performing a helix fit to the hits found by the Kalman filter algorithm, 32 Table 3.3. Background Monte Carlo samples used in this analysis I Background Simulation Sample I 0-( nb) I £( fb 1] Events (x 106 ) I BOBO generic 0.549 1274 699.68 B0J30 Cocktail 0.0209 3758 78.537 B+B- generic 0.549 1303 715.3 cc generic 1.30 841 1093.288 udsgeneric 2.09 435 906.386 T+T- generic 0.94 413 387.884 Table 3.4. Signal Monte Carlo samples used in this analysis. Cocktail samples have one BO decay to a B°-----'t D(*)-X with X = 7f+ ,p+, or a1+, representing 3.99% of BO decays. I Signal Simulation Sample I Events (x 106) I I BU-----'t VV I 5.828 I B°-----'t VV, 5.828 and searching for hits in the DCH that may be associated with the track but were not identified by the Kalman filter fit, followed by refitting using the Kalman filter algorithm. The tracks are then extrapolated to the SVT, and hits in the SVT consistent with the tracks are identified. The tracks are then refit using the combined DCH and SVT hits. Hits in the SVT that are not associated to tracks are then passed to another track finding algorithm, to look for tracks that only register in the SVT. The tracks are then extrapolated to the EMC, and clusters (energy deposits in single EMC crystals) consistent with the tracks are merged with them. Clusters not merged with tracks are used to fill the EMC neutrals list: CalorNeutral. The extrapolation is then continued to the IFR, and hits not associated with the tracks or neutral EMC lists are then used to create a neutral hadron list: NeutralHad. These track and 33 neutral candidates are then used to create sublists for track quality, based on number of hits in the detectors, distance from the IP. Those that fit certain mass/momentum requirements are used to fill particle identification (PID) lists. Combinations of track and neutral particles are used to fill composite particle lists. The track, neutral, PID, and composite particle lists used this analysis are described in Appendix C. Composite particles are defined using desired daughter particle lists, vertexing, and mass requirements. For each event, particles and composites are checked for consistency with these composite particle definitions, and used to fill composite particle lists. The composite particles used in this analysis are detailed in Appendix C. Event Tagging Since the daughter particles of B O-+ invisible are invisible to the detector, the first step in the analysis is to fully reconstruct the other neutral B meson in the event, referred to as the "tag B O". The particles in the event not associated with the tag B O are the "signal side," which is checked for consistency with the expected noise, lost particles, and background of B°-+ invisible events. This section details the reconstruction of the tag B O• 34 j.024 ~.022 uds ::, Dec I 0.02 +_ ~ BB §0.018 onO a: '-0,016 III ~.014 > UJO.012 0.01 0.008 0.006 0.004 0.002 GeV Figure 3.1. ~E plot aft.er preselect.ion. The uneven cut.offs are due t,o t.he mode dependent ~E cuts. Tag Side V;uiables A reconstruct.ed nO candidate is considered a good nO candidate if it has 5.2 GeV < 'm'ES < 5.3 GeN, and I~EI < 0.04 GoV. The variables rilES and ~E arc defined in equat.ions Equ3 han III. 1 and Equation III. 2: (III. 1) (III. 2) where E"eam is half t.hc beam energy in the center of rnomcntllDl system (eMS), the inertial reference frame where t.he average electron mornenturn of an electron in t.he 35 - "~ «J (J II) II) ~ 0.06 >W 0.04 0.021__~__--"""----'-'__ Figure 3.2. Plot of mES after preselection. electron beam is opposite the average momentum of a. positron in the positron beam, En and Pr-J are the reconstructed energy and momentum of the tag nO in the C:vIS frame, and the purity is defined as the fraction of the events in the peak of amES plot. for a given mode. The value m'ES is the reconstructed EO mass, using the beam energy for better resolution, and for a correctly reconstructed EO meson peaks at the true n° mass of 5.28 GeV, and 6.E is the difference of the reconstructed EO energy with half the C:vIS beam energy, which for correctly reconstructcd EO mesons peaks at I:ero, as each daughter nO particle in the two body decay e+ e- -----* Y( 45) -----* BOlJo has half t.he CrvIS encrgy. Combinatoric ba.ckgrounds, where combinatoric events a.re 36 lint grated Purity I x103 s B -0 ~,~. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 O.B -, I I I rrn -n I I Dud - Dec DB+ - ORal r- f- I r- J f- I I" I mI~~ ~ 3 0.5 1.5 =0- ~ C'Cl U (/) CD I ,.. 2.5 (/) 2 -c:Q) > w intpurity Figure 3.3. Int.cgrated Pmit.y plot (l,ftcr prci:iclcction. The cutoff at 0.2 in int.egrated purity is due t.o t.he 0.1 purity cut in preselection. events where a tag nO is found but. the particles composing t,he t.ag nO do not. come from (l single n meson, arc Argus in shape in mES (l,nd peak more broadly in 6.E t,han correctly reconstructed n° mesons, where the Argus distribution is defined in Equation III.3, f(x) =.1" VI - (x/c)2 cxp{ -X' (1 - (X/C)2)} for x> 0 (III.3) where c is t.he cutoff and X t.he curvature of the dist.ribution [22]. The variables 1?7ES and 6.E function a.s mass and momentum constraints on the nO candidates, using the precisely known beam parameters t.o improve resolut.ion, and integrated purity serves t.o eliminate reconstruction modes dominat.ed by combinat.oric backgrounds. 37 Semi-Exclusive Skim The tag EO is reconstructed using the Semi-Exclusive hadronic method [23], which works as follows. Hadrons (7f+, K O, K+, and K s candidates) are added to an initial D(*)+ candidate to form a EO candidate. Charged tracks are required to pass the requirements of the GoodTracksVeryLoose list and fail eMicroTight and muMicroTight (see Appendix C for particle ID information). The D*+ is reconstructed in the modes given in Table C.1. The masses of the charm particles used in making the seed are in Table C.2. The EO candidate is considered a tag EO if it is a neutral composite with loose mES and tlE requirements (III.l and III.2), and has a purity greater than 0.1. The BSemiExcl skim consists of events passing the BGFMultiHadron tagbit and containing one or more such candidates, where skim refers to a subset of a data or MC sample that pass a given set of tag bits, and a tag bit is a binary value associated with an event that indicates whether the event passes desired particle composition and event shape criteria. BGFMultiHadron is a tag bit requiring NCT > 2 and R2 < 0.98, where NCT is the number of ChargedTracks in the event and R2 is the ratio of the second to zeroth Fox-Wolfram moments. Fox-Wolfram moments are defined as HI = L IPil~pjl Il(coseij ), where Evis is the total visible energy inE.i,j V2S the event, eij is the opening angle between hadrons i and j, and PI are Legendre polynomials. For two-jet events, common for cc and uds events, R2 peaks near R2 = 1.0, while events with particles more evenly distributed in the detector, typical of EOEo events, peak closer to zero. 38 The best B O for an event is defined as the tag B O candidate in the event with the highest integrated purity (and D..E closest to 0 if there is a tie for highest integrated purity). For events with multiple tag BOcandidates, the best B Ois used as the tag BO. Plots of mES, D..E, and integrated purity for background MC are shown in Figure 3.1, Figure 3.2, and Figure 3.3. Data are blinded in the region mES > 5.26 GeV, Eneu < 0.6 GeV where Eneu is the total energy in the CMS of neutral candidates not associated with tag side particles or the radiated photon of B O----+ invisible + f. Data in the blinded region, after the signal selection cuts are applied, is hidden to avoid any possibility of bias by the experimenter towards a particular final result, until the signal side cuts and systematic errors on background events are finalized. MC is not blinded, so this only affects plots and tables that include data. The mES sideband (5.22 < mES < 5.25 GeV, 0 < Eneu < 0.6 GeV) is a sample of incorrectly reconstructed tag BOs that can be used to compare combinatoric events in data and MC without unblinding the data. Yield The yield is defined as the number of correctly reconstructed Semi-Exclusive B O mesons in data after the hadronic tag B O selection described above, and is determined from mES in data and MC. The yield is calculated for use in the final branching fraction calculations. The combinatoric background shapes are obtained from ee, B+B- , uds, and combinatoric BOlJo MC. The peaking component of BOlJo MC is 39 removed from the BOlJo MC sample to get the combinatoric BOlJo sample using the cut eP * > 0.4 or Nt~Yf > 0, where eP * is the angle between the reconstructed BO momentum vector and the momentum vector of the BO generated for the MC event, and N;ifi is the number of tracks used in reconstructing the tag BO that aren't associated with the corresponding BO generated for the MC event (Figure 3.4). They are used as a straightforward method to determine whether the tag BO was properly reconstructed from one of the two BOs generated in the MC. The combinatoric MC samples are luminosity scaled and added together. The combined sample is then scaled to data in the region 5.22 GeV < mES < 5.26 GeV, with data a factor of 1.08564±0.00058 greater than combinatoric Me. The yield of true Semi Exclusive BO mesons is taken as the difference of the number of events in data and in combinatoric MC in the range 5.27 GeV < mES < 5.29 GeV. The yield is (500.8 ± 2.0) x 103 events (Figure 3.5). The process is repeated, fitting combinatoric MC to the full luminosity scaled background MC to obtain the correctly reconstructed BO mesons after tagging in the MC, giving a MC yield of (546.6 ± 1.5) x 103 (Figure 3.6). The ratio of the yield to the MC yield is CMC = 0.9163 ± 0.004439 which is used as a correction to peaking background MC for the cut optimization. 40 1.4 1.6 68 1.20.80.60.40.2o I Generic BOO I thetaphist x103 Entlie8 1.5S437'8lHfl1 ~OOO "M 0.•4,~ D.S5:z:l " Und....lltl. , VI "".~ ~:~iOOO 1"1"0". t.5~~7 C "!:!li000 - ~ c ~1000 - LU 3000 - 2000 - 1000 - 0 I-- I Generic BO track difference I trkdiffhist x103 Enlrle8 t.554318&f07 '1000 ..." 0.7102,~ """loooe- Underllo. , O.... tfIow 8.8498005 '" Intagn' 1.468&t07JlOOOF- C "[g000f-- - ~i OOO - - > "!;oOO- - 4000- - 3000- - 2000- I - 1000 0.5 1.5 2 2.5 3 3.5 4 # tracks Figure 3.4. gP* and Nt~lf for generic BOlJo events. 41 I DATA Yield I x106 til ffi 0.25 > LU 0.15 0.05 g.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.3 ffiES(GeV) Figure 3.5. mES plot for data (points) and combinatoric j\!IC simulation. 42 I Me Yield I x10· -al 0.4 ro (J (J)~0.35 T"" 0.15 0.1 0.05 g.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 Figure 3.6. mES plot for MC (points) anel combinatoric MC simulation. 43 Table 3.5. Signal Event Tag Efficiency Corrections raw B Uj3u events tags e ciency (%) generic BUBu 6.997 x 10l:l (1.840 ± 0.001) x lOb 0.1315 ± 0.0001 B D----+ invisible MC (5.828 ± 0.002) x 106 (10.30 ± 0.10) x 103 0.1767 ± 0.0017 B D----+ invisible + '"Y MC (5.828 ± 0.002) x 106 (10.45 ± 0.10) x 103 0.1793 ± 0.0018 B U ----+ invisible Correction: CB[L,vv = 1.344 ± 0.013 B U----+ invisible + '"Y Correction: CB[L,vv,,/ = 1.363 ± 0.014 Signal Yield Correction The efficiency to tag signal events differs from the efficiency to tag generic B DJ3D events. To correct for this in the branching fraction calculations, the ratios of the tag efficiency in signal MC and in generic B DJ3D MC are calculated, for both B D-----+ invisible and B D-----+ invisible + '"Y, and use them as a correction factor when calculating the final branching ratio (Table 3.5). The yields include mES > 5.27, eP * < 0040 GeV, diffN trk = 0, and IllE < 0.041 cuts. Signal Cuts Signal Side Definition and Preselection The signal side of an event is defined to be all ChargedTracks and CalorNeutral objects not used to reconstruct the tag B D, where ChargedTracks and CalorNeutral are the loosest collection of reconstructed charged particles and of reconstructed clusters in the EMC not associated with a charged track respectively. Two preselection cuts are applied: NCTL < 3 and Eneu < 1.5 GeV. The value Eneu is the total energy contained in electromagnetic calorimeter clusters on the signal side not associated 44 with a charged track not including the highest energy cluster for E°-----+ invisible + i. The value NaTL is the number of GoodTracksLoose, charged tracks on the signal side of the event originating from near the interaction point, 1.5 cm in x-y and 10 cm in z, with at least 12 hits in the drift chamber. For EO -----+ invisible+i, the cut Ehi > 1.0 GeV is applied, where Ehi is the CMS energy of the highest energy CalorNeutral cluster on the signal side of the event. Signal Box The signal box is defined as the region mES > 5.27 GeV and Eneu < 0.6 GeV. Most of the signal MC events lie in this region, as the lack of signal side particles suppresses combinatoric EO tags, causing signal EO tags to peak strongly in mES, and the lack of signal side particles leaves little extra energy in the EMC, causing signal events to peak at small Eneu . The variable Eneu will also be used as a signal side cut variable, allowing for tighter requirements for Eneu . The Eneu sideband is defined as the region mES > 5.27 GeV and Eneu > 0.6 GeV, and the double sideband as 5.22 < mES < 5.26 GeV and Eneu > 0.6 GeV. These sidebands, along with the mES sideband, do not have significant signal even if B(EO -----+ invisible) is measurably large, and so can be used to test the ability of background MC to model backgrounds in data. The Eneu sideband is rich in peaking events, and being sparse in signal can be used to compare peaking events in MC to data without unblinding the analysis. The double sideband is used to study combinatoric backgrounds for events with large Eneu to better understand the combinatoric backgrounds in the Eneu sideband. 45 B°--+ invisible Cuts After the reconstruction of the tag BO the next step is to apply further cuts to reduce the number of expected background events in the Signal Box. Cuts are chosen which maximize the figure of merit FOM (see Equation IlIA) FOM = N Sig [24] 3/2 + y!NBkgrnd ' (IlIA) where NSig is the number of luminosity weighted events in B°--+ invisible MC using the scaling of peaking and combinatoric MC, and N Bkgrnd is the total number of events in the luminosity weighted high statistics sample. To increase background Monte Carlo statistics during cut optimization and to provide an independent sample for checking the robustness of the cuts during optimi- zation, I create a high statistics sample as follows. Samples of uds, ee, B+B- , and T+ T- events are taken from the mES sidebands of the respective generic MC samples, weighted by the ratio of the number of events in the signal region to the number of events in the mES sideband region, after precuts. For BOJ3o, a Crystal Ball plus Argus are fit to the BOJ3o generic MC sample after precuts. The Crystal Ball distribution is a piecewise defined function combining a Gaussian with a power law tail, and is given in Equation IlL5-Equation III. 7: exp(-(x - x)2/(20.2)) , for(x - x)/O" > -0; f(x; 0;, 0", n, x) = N . (IlL5) A· (B - (x - x)/O")-n, for(x - x)/O" ~ -0; (IlL6) B = n/lal - lal 46 (III. 7) where a determines at what point of the Gaussian the tail begins, (J is the width of the Gaussian, n determines the size of the tail, and x is the mean of the Gaussian [25]. The high statistics BOJjo sample consists of events from the mES sideband of the BOJjo generic sample weighted by the ratio of the area of the Argus in the signal region to the area in the sideband region to model the combinatoric component, plus all the events from the BOJjo Cocktail MC sample weighted by the ratio of the number of events in the BOJjo Cocktail sample to the area of the Crystal Ball to model the peaking component, after preselection. The BOJjo Cocktail sample appears to lack a significant combinatoric component to mESo A comparison of the high statistics sample with generic MC can be found in Appendix A. The figure of merit is chosen over the significance, NSi91VNSi9 + NBkgrnd, and N Sig 1 VN Bkgrnd because the former is dependent on the choice of the signal branching ratio, and the latter is not well behaved as N Bkgrnd goes to zero, which is possible if tight enough cuts are chosen. The 312 in the equation optimizes the cuts for a signal present at the 3(J level. This is chosen as a compromise between setting a good upper limit if no signal is found and maximizing the sensitivity of the search for B°---+ invisible. Variables used in the cut optimization are • NCT- the number of reconstructed charged tracks on the signal side of the event, 47 • NGTL- the number of good quality charged tracks originating from the IP on the signal side of the event, • Eneu- the total energy in the CMS frame of neutral clusters on the signal side of the event, not including the radiated photon from B°---+ invisible +" • Nrro- the number of reconstructed neutral pions in the signal side of the event, and • R2- the ratio of the second to zeroth Fox-Wolfram moments. Both NCT and NGTL are considered to allow for the possibility of accepting events with a track not originating at the IP, such as those produced by a tag side particle looping in the detector's magnetic field or with a sharp change in direction due to scattering, resulting in the particle registering as more than a single track, or tracks from beam backgrounds or cosmic rays. The POM is optimized for each variable, in order, holding cuts on the other variables fixed. This is iterated until no cuts are changed by an iteration of the optimization. The cuts that optimize the significance for BO---+ invisible in this manner are N GTL = 0, Eneu < 0.16 GeV, NCT = 0, R2 < 0.62, and Nrro < 2 (Figure 3.7- Figure 3.10). NGTL is not shown, as GoodTracksLoose is a subset of ChargedTracks, so after the NCT = 0 cut is applied, the remaining events do not have any signal side GoodTracksLoose. The following plots show signal MC, generic background MC, and the figure of merit for these cuts, after all the cuts for the other variables have been 48 applied. The optimization is done in Y1C, to keep the data blinded. The upper left plot shows signal :v1 C scaled to a, branching fraction of 1O-/!; the lower left plot shows background MC. The right plot shows the figure of merit, FO !l1, for events in the acceptance region for the va.riable vs. cut value on that variable. The efficiency of signal and number of backgronnd events is given in Table 3.7. C :J !;. 2 ai 4 > W c: :J !;. 2 c Ql > W OTT Iuds Dec DB'S- anO I " I I I " i eneu, GeV a) b) Figure 3.7. Eneu in a) B°---,; invisible and b) background 49 .", TI " 'T' 'TTT" , I It::I udsof'; Dec >= Ds+s -'i ~ lB-C'ff -- :.: - - ._- - - 1-' - - - - - I ~~ I 0.5 1.5 2 2.5 3 3.5 4 6 u Q) 2 ro o (j) 18 ~ ,... 16 c: ::J ES 14 (j) ffi 12 > W 10 c: ::JfS 10 (j) 'E Q) > W ~ rr-<-.-rTrrrr,,"TT""'" "1-.-r-r-rorrr-.-nrrT...--rrT"..,~ 14 ro o (j) ~ 12 ,... ISignal Me I II CT IICT a) b) Figure 3.8. NeT in a) BO~ invisible a.nd b) ba.ckground .", =rn-'fT' OTT J .uds ;-0 Dec DB+B DROJ'f - - f- - I- - - ~ - - ,I ,I .1 1 I 1 II 0 0.5 1 1.5 2.5 3 3.5 4 4.5 5 10 18 16 12 14 00 ..L' 0~..t-U..,LLl..L'::-':o'-'--'-"!"-'-'-,=,:!-'-LJ~'-'-'::-'::'-'-~J...J...LU_.L.L.I-L.:!5 linD u uQ) Q) ro ro 0 0(j) 12 (j) ~ ~ ,... ,... c: c: ::J 10 ::J ~ ~ (j) (j) 'E 'E Q) Q) > > w w a) b) Figure 3.9. N7r0 111 a) BO_> invisible and b) background 50 o I J I I I I I ! , I , , , I I J l I I U L! I 1 iliu.J-Lj LU o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 '0 'I,m- Ql iii 0 (/J ~ .... C 2.5 :J !E- (/J E Ql > W 1.5 200 100- I]Ignal Me I 400 300 '0 Ql iii 800 o (/J W a) b) Figure 3.10 . .R2 in a) n°-t invisible and b) background 51 B°-t invisible + /' Cuts For BO-t invisible + /' the energy of the highest energy photon Ehi is separated from the energy of the rest of the signal side neutral energy, Eneu . The cuts that optimize the figure of merit for B°-t invisible + /' are NGTL = 0, Eneu < 0.28 GeV, NCT = 0, R2 < 0.62, and N1r0 = O. Plots Figure 3.11-Figure 3.14 show the cut variables for events in the signal box passing all other cuts but the one being plotted for B°-t invisible + /'. Again, there is a NCT = a cut, eliminating events with NGTL > 0, so the NGTL plot is not shown. The upper left plot shows signal MC scaled to a branching fraction of 10-4 ; the lower left plot shows background MC. The right plot shows the figure of merit, FOM, for events in the acceptance region for the variable vs. cut value on that variable. The efficiency of signal events and number of background events is given in Table 3.9. 52 I-l..-.I--L- 1.2 1.40.8 Total Neutral EMC energy 0.60.40.2 I Backaround Me In :0- 2.2f-- I Dudsa> (;j gee() 2f--lJ) := 8+8' "\' ~ 1.af-- loonO c :l !E. 1.6 (J) C 1.4 a> > 12W 1 0.8 0.6 0.4 I I h-0.2 0 --1..-, ,°0,LL.L...>..,,0"=-.2-'-"O>-' 0.4 *-" ola' , , 1' , ',12 '--'-'-f.t Total Neutral EMC energy :0- a> (;j () lJ) "\' ~ C :l !E. 4- (J) C a> > W 3 b) Figure 3.11. En e'1/ in a) n°--'} invisible + "( ane! b) backgronncl U 1- "1' t, iii' i' I'" ii'" rr- 1 I - a> (;j () lJ) "\' - - .,- 0.8 C :l !E. (J) ~ 0.6 - > W 0.4- - 0.2- - I I I I I I 00 0.5 1.5 2 2.5 3 3.5 Energy of Most Energetic EMC Neutral Energy of Most Energetic EMC Neutral a) b) Figure 3.12. Energy of E,,; Hl a) n°--'} invisible + "( a.nd b) background 53 en C Q) >W 6 -E 1.5- Q) > W 0.5 •I-U-L W I l. ! , ! l. ! ! , I II ' ,j I ! JJ I ! I I J I L..LJ 2 3 4 5 6 7 8 10 # rrO oo!'-"""lII....~--~..._~-'-'-!~L'L' JL.l'~~J..J!'--'-'L'j~11~ I I I I ~ LJ J 1 10 # rrO a) b) Figure 3.13. Nrro lD a) B°---7 invisible + I and b) background 2.5 3.5 # ChargedTracks 1.50.5 .,." OTt 4- I I I I 1:1:1 uds Dec 5- ClB+B r=1 ROnD 3- - 5- - 2 ______.=_ ~ 5 - 1 , - - ._. .. d_l-.L-J I0 0.5 I :0- Q) iii 0 - (J) 3. 'f' ... <: ::l - ~ en C 2. Q) > - w - 1. - III:0- Q) iii o (J) 'f' ... <: ::l ~ en C Q) > w a) b) Figure 3.14. NCT in a) B°---" invisible + I and b) background 54 :0- Q) iii 900 o UJ Cf 800 ,.... c ::::s 700 fS I/) +"" 600 c -Q) - > W500 400- 300 200 100 a.) round Me On: uds Dec B+B- o ~l--(0i50--0._-, I/) 1: Q) > W "'JlJ0< i I ~ ~ Jo ' I L.l , .1 I I ...LLo 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 R2 R2 b) Figure 3.15. R2 111 a) BO-> invisible + I a.nd b) background 55 Efficiencies After optimization, the number of combinatoric background events for E°----. invisible is given in Table 3.6. The combinatoric events are scaled to data using the mES sideband. Table 3.7 gives the cumulative efficiency of signal to pass the EO----. invisible signal side cuts, with the tag EO selection and preselection included in the efficiencies. It also gives the number of peaking background and combinatoric background events, the total number of background events, and number of events in data for E°----. invisible. The peaking background in Table 3.7 is scaled to the peaking data in the Eneu sideband, where the peaking data in the Eneu sideband is calculated by scaling combinatoric background to data in the double sideband, and subtracting combinatoric background from data in the Eneu sideband using this scaling. Cocktail MC is used for the peaking events, to enhance statistics. The scaling factors and a comparison of generic MC versus cocktail MC can be found in Appendix B. E°----. invisible + r Efficiencies After optimization, the number of combinatoric background events for E°----. invisible is given in Table 3.8. The combinatoric events are scaled to data using the mES sideband. Table 3.9 gives the efficiency of signal to pass the E°----. invisible signal side cuts, with the tag EO selection and preselection included in the efficiencies. It also gives the number of peaking background and combinatoric background events, the total 56 number of background events, and number of events in data for B°-----+ invisible. The peaking background in Table 3.9 is scaled to the peaking data in the Eneu sideband, where the peaking data in the Eneu sideband is calculated by scaling combinatoric background to data in the double sideband, and subtracting combinatoric background from data in the Eneu sideband using this scaling. Cocktail MC is used for the peaking events, to enhance statistics. The scaling factors and a comparison of generic MC versus cocktail MC can be found in Appendix B. Table 3.6. BO -----+ invisible combinatoric background cutflow table. Combinatoric BOlJo events are those that have eP * > 0.4 or N;Yf =I- O. Combinatoric background is given as a number of events. Combinatoric is scaled to the mES sideband. Cut T+T Ud8 cc B+B Comb BUBu Comb tot. Signal Box 82±20. 439±24 441±18 179±8.9 515±17 1655±46 R2< 0.62 20.6±5.0 387.3±22.3 422±18 177.7±8.9 517±17 1525±42 N 7r0 < 2 15.3±4.3 312±20. 330.±15 122.0±7.1 399±14 1178±35 NCTL = 0 9.1±3.5 74±10. 84.2±8.5 14.4±2.5 47.2±5.1 229±18 NCT =0 7.7±3.5 17.5±5.3 32.4±5.7 5.3±1.7 15.9±3.1 79±11 E neu < 0.16 3.9±2.9 7.4±4.0 6.6±2.9 1.23±0.91 2.5±1.4 21.6±7.2 Table 3.7. B°-----+ invisible cutflow table. Peaking BOlJo events are those that have eP * < 0.4 and N;:f! = 0; combinatoric events do not. Signal is given as an efficiency for tagged events, background and data as a number of events. Combinatoric is scaled to the mES sideband, peaking to the Eneu sideband. Cut B U-----+ invisible Peaking BUBu Comb tot. Bkg tot Data efficiency (10-4 ) Signal Box 14.8±1.6 2011±80. 1655±46 3666±92 3633±60. R2< 0.62 13.2±1.5 1955±52 1525±42 3480±67 3393±58 N 7r0 < 2 12.9±1.5 1755±6 1178±35 2933±75 2803±53 NCTL = 0 12.7±1.5 127±25 229±18 356±31 376±19 NCT =0 1O.0±1.3 33±14 79±11 112±18 BLINDED E neu < 0.16 6.5±1.1 6.9±3.1 21.6±7.2 28.5±7.8 BLINDED 57 Table 3.8. B D---+ invisible + I combinatoric background cutflow table. Combinatoric BDHD events are those that have eP* > 0.4 or N~Yf i- O. Combinatoric is scaled to the mES sideband. Cut T+T 1f,ds cc B+B Comb BUBu Comb tot. Signal Box 176±14 1559±43 1573±33 591±16 1415±27 5314±79 R2 < 0.48 8.9±3.1 933±33 1132±27 542±15 1335±26 3951±62 Ehi > 1.0 O±O 98±11 83.9±7.4 34.2±3.6 73.5±5.9 290.±18 N7[o = 0 O±O 27.6±5.6 22.1±3.7 6.7±1.5 17.2±2.7 73.5±8.8 NCTL = 0 O±O 3.6±2.2 4.9±1.9 1.19±0.72 2.03±0.97 11.7±3.5 NCT =0 O±O 3.7±2.8 3.8±2.1 0.62±0.64 1.26±0.95 9.4±4.2 Eneu < 0.28 O±O 2.6±2.7 1.3±1.4 0.86±0.91 O±O 4.8±3.5 Table 3.9. B D---+ invisible + I cutflow table. Peaking BDHD events are those that have eP * < 0.4 and Nt~Yf = O. Signal is given as an efficiency for tagged events, background and data as a number of events. Combinatoric is scaled to the mES sideband, peaking to the Eneu sideband. Cut B U----+ invisible + I Peaking BUBu Comb tot. Bkg tot Data efficiency (10-4 ) Signal Box 14.99±0.16 4784±185 5314±79 10098±201 9975±100. R2 < 0.48 12.06±0.14 4257±165 3951±62 8208±176 8097±90. E hi > 1.0 8.77±0.12 295±27 290.±18 584±33 664±26 N7[o = 0 7.08±0.1l 129±31 73.5±8.8 203±32 177±13 N CTL = 0 6.96±0.1l 24.3±9.4 11.7±3.5 36±10. 29±5.4 NCT =0 5.561±0.098 20.5±8.5 9.4±4.2 29.9±9.5 BLINDED Eneu < 0.28 4.85±0.091 9.3±4.3 4.8±3.5 14.1±5.5 BLINDED 58 Systematic Errors Some of the systematic errors only apply to events that are peaking in mES, or to combinatoric events. Because of this, I calculate the systematic errors on N Bkgrnd in terms of number of events, using the numbers of background events predicted in Table 3.7 and Table 3.9. Tag B D Yield Systematics To check the dependence of the yield on the relative amounts of B DJ3D, ee, uds, and B+B- , the yield is recalculated with the relative amounts allowed to float when fitting the combinatoric Me to the data. This results with a fit yield of (505.9 ± 2.0) x 103 in data, 1.01% more than the tag yield, (500.8 ± 2.0) x 103 (Figure 3.16). To determine the dependence of the yield on the combinatoric B DJ3D shape, the eP* cut on B DJ3D is varied and the yield is recalculated. For a eP* of 0.35 GeV a low- eP* yield of (493.8 ± 2.0) x 103 is obtained in data, 1.4% smaller than the tag yield with eP * > O.lOGeV For a eP * of 0.45 GeV, a high-eP * yield of (507.1 ± 2.0) X 103 is obtained, 1.2% bigger than the tag yield. Letting Nt~Yf < 2, a loose-Nt~f! yield of (517.2 ± 2.0)x103 is obtained in data, 3.3% larger than the tag yield. Taking the largest discrepancy as a systematic error on peaking events, this gives a systematic error for signal efficiency of 3.3%. 59 I DATA Yield I x 106 I: ::Ja: 0.3 III -g0.25 > LIJ 0.15 0.1 0.05 Figure 3.16. Tag BO yield with combinatoric contributions floated. 60 A Yield C :::Ja: 0.3 -Ul -~ 0.25 > W 0.15 0.1~ _ 0.05 Figure 3.17. Ta.g nO yield with ee, 'U.ds, and T+T- sca.led to offpca.k data.. 61 Control Sample Systematics After finding the tag B O and applying a loose set of signal side cuts to generic MC in order to select events like the ones that would pass the final selection, the simulated B O decays used to produce the events were examined, for B O-----t invisible and B°-----t invisible + "I, and many of the events were found to contain neutrinos or K~ mesons. To check the ability of MC to model events with neutrinos and koons, I use low multiplicity e-, f-l-, and K~ control samples. The e- control sample is required to contain a single e±, the f-l- control sample a single f-l±, and the K~ control sample a single K~ reconstructed in the mode K~ -----t 7[+ 7[- plus a single charged pion. The signal side of each control sample is then redefined to be the tracks and neutral clusters that are not associated with the tag B O or with the particle or particles that identify the event as an e-, f-l-, or K~ control sample event. Eneu for the samples are shown in figures Figure 3.18, Figure 3.19, and Figure 3.20. Using the B O -----t invisible cuts, the number of events in the e- control sample is 70±8.4 in data and 61.8±6.3 in MC, for a ratio of 0.883±0.139. The number of events in the f-l- control sample is 62±7.9 in data and 65.1±6.8 in MC, for a ratio of 1.050±0.172. Combined, the two control samples give a MC/data ratio of 0.961 ± 0.163. The error of this ratio is taken as a systematic on the total number of background events, giving a total error of 16.3%, or 4.65 events in B°-----t invisible. As a check, the number of events in the K2 control sample is 56±7.48 in data and 45.5±7.01 in MC, for a ratio of 0.813±0.166. 62 Total Neutral EMC ener :c 22 Ql ili 20U III ~ 10 ~ ~ 16:;, a: ...... III -~Ql > W eneu,GeV a) Total Neutral EMC ener b) 1.1 1.2 1.3 1.4 1.5 eneu,GeV 8.6 0.7 0.8 0.9 5- I I I I I I Dec~UdS B+H 3- U TT f:::JBOSO 5- -Data 2- I - I- - 11- ~ ~, I I I .r II I 1.5 0.5 III -~Ql > W ~ -g 3. ili u III ~ ~ ~ :;, a: 2. ...... Figure 3.18. Enet, for the K2 sample In da.ta and rvIC for a)DO~ invisible anel b)BO~ invisible + 'I 63 a) 1.1 1.2 1.3 1.4 1.5 eneu,GeV 0.6 0.7 4 :c- IT] III 22m U en 20 U) 1:T I,.. BOSOc: 18 ::I -Data a: ....... 16 en -cIII > W otal Neutral EMC energ :c- I I III 6 m u en U) I 5,.. s:: ::I a: en 4 -CIII > W 3 eneu,GeV b) Figure 3.19. Enc1J for the It. Jl1 data and ]\lIe for 30)]]0 -7 invisible and b)B°-7 invisible + 'Y 64 I Total Neutral EMC energy :0- Q) iii u 1/1 ~ ... c: ::J !E- 1/1 - 15c: Q) >UJ eneu, GeV a) I Total Neutral EMC energy b) 1.1 1.2 1.3 1.4 1.5 eneu, GeV 8.6 0.7 0.8 0.9 5~ , I I I I I 'I Dec - .uds 10B+B' 31- OTT ID B'1f I- -Data 21-' I- .J 1 "" n (J IL 10.5 1.5 £l c: Q) >UJ c: ~ 2.5 Figure 3.20. E ne1/ for the e- in data and Me for a)BO~ invisible and b)BO~ invisible + "'( r 65 Using the B°---t invisible + "( cuts, the number of events with one e- is 11±3.3 in data and 8.0±4.8 in MC, for a ratio of 0.725±0.486. The number of events with one fl- is 8±2.83 in data and 16.0±6.72 in MC, for a ratio of 2.00±1.098. Combined, the two control samples give a MC/data ratio of 1.26 ± 0.521. The error is taken as a systematic on the number of background events, giving a systematic error of 52.1 %, or 7.34 events in BO ---t invisible + "(. As a check, the number of events in the K2 control sample is 7±2.65 in data and 10.4±5.87 in MC, for a ratio of 1.486±1.01. Combinatoric Scaling I apply a systematic error on the number of combinatoric events equal to half the combinatoric correction applied by scaling the combinatoric MC to data in the mES sideband. For B°---t invisible the correction is 1.74±0.38, for a systematic of 37% or 7.99 events. For B°---t invisible + "( the correction is 2.43, for a systematic of 72% or 3.40 events. 66 Table 3.10. B°-----'t invisible e- control cutflow table. Peaking BOBo events are those that have eP * < 0.4 and Nt~Yf = 0; combinatoric events do not. Signal is given as efficiency for tagged events, background and data as number of events. Combinatoric is scaled to the mES sideband, peaking to the Eneu sideband. Cut T+T uds cc B+B Comb BUBu Comb tot Signal Box 17.4±7.1 276±28 929±39 1071±35 2994±70. 5285±112 R2< 0.62 2.9±2.9 245±26 845±37 1074±36 2998±70. 5165±109 Nrro < 2 O±O 203±24 672±33 773±29 2426±61 4074±92 NGTL = 0 O±O 20.9±4.9 46.5±5.6 41.7±4.4 130.6±9.4 240.±16 NCT =0 O±O 1.2±1.2 6.7±2.1 9.8±2.2 39±5.5 56.7±7.5 Ene1i < 0.16 O±O 1.4±1.4 1.4±1.1 1.38±0.87 7.1±2.6 11.3±3.9 Cut Peaking BUBu Comb tot Bkg tot Data Signal Box 5286±123 5285±112 10571±166 15962±126 R2< 0.62 5220±122 5165±109 10385±163 15778±126 Nrro < 2 4546±106 4074±92 8620±140. 13279±115 NGTL = 0 677±40. 240.±16 917±43 81O±28 NCT =0 228±20. 56.7±7.5 285±22 258±16 Eneu < 0.16 50.5±5.0 11.3±3.9 61.8±6.3 70±8.4 67 Table 3.11. B°----" invisible /1- control cutflow table. Peaking BOlJo events are those that have eP* < 0.4 and Nt~Yf = 0; combinatoric events do not. Signal is given as efficiency for tagged events, background and data as number of events. Combinatoric is scaled to the mES sideband, peaking to the Enell sideband. Cut T+T uds cc B+B Comb BUBu Comb tot Signal Box 55±12 954±49 1437±46 1093±33 2922±62 6461±122 R2< 0.62 5.1±3.6 816±46 1364±45 1097±33 2945±63 6229±117 NJro < 2 2.5±2.5 692±42 1099±40. 789±27 2326±53 4910±99 NGTL = 0 1.0±1.0 51.0±7.4 82.9±7.4 50.0±4.6 142.8±9.3 328±19 NCT =0 O±O 8.5±3.1 15.3±3.~ 12.7±2.4 37.1±4.9 73.5±8.9 Eneu < 0.16 O±O 2.2±1.6 5.9±2.0 13.0±4.03.9±1.7 1.08±0.67 Cut Peaking BUBu Comb tot Bkg tot Data Signal Box 5364±135 6461±122 11825±182 17706±133 R2< 0.62 5293±133 6229±117 11522±177 17382±132 NJro < 2 4573±116 4910±99 9483±152 14560±121 N GTL = 0 677±41 328±19 1004±45 957±31 NCT = 0 213±21 73.5±8.9 286±23 268±16 E neu < 0.16 52.1±5.5 13.0±4.0 65.1±6.8 62±7.9 68 Table 3.12. B°-----+ invisible K,~ control cutfiow table. Peaking BOBo events are those that have eP * < 0.4 and N~~tt = 0; combinatoric events do not. Signal is given as efficiency for tagged events, background and data as number of events. Combinatoric is scaled to the mES sideband, peaking to the Eneu sideband. Cut T+T uds cc B+B Comb BOBu Comb tot Signal Box 7.5±4.3 3312±94 3708±75 1508±37 3859±66 12395±170 R2< 0.62 O±O 2974±88 3535±73 1501±37 3852±66 11860±164 NJro < 2 O±O 2400±78 2774±63 1053±30 2972±56 9198±138 NCTL = 0 O±O 303±18 379±16 129.4±7.0 412±15 1222±37 NCT =0 O±O 25.9±5.6 27.3±4.3 12.6±2.3 40.0±4.7 106±11 Eneu < 0.16 O±O 1.3±1.4 4.2±1.9 0.45±0.46 4.6±1.7 1O.5±3.4 Cut Peaking BOBo Comb tot Bkg tot Data Signal Box 5880±246 12395±170 18275±299 23358±153 R2< 0.62 5846±245 11860±164 17706±294 22804±151 NJro < 2 4740±250 9198±138 13938±286 18412±136 NCTL = 0 2097±116 1222±37 3319±122 3417±58 N CT =0 148±25 106±11 253±28 281±17 Eneu < 0.16 34.9±6.2 1O.5±3.4 45.5±7.1 56±7.5 69 Table 3.13. B O-----+ invisible + r e- control cutflow table. Peaking BOIJo events are those that have eP * < 0.4 and N:e = 0; combinatoric events do not. Signal is given as efficiency for tagged events, background and data as number of events. Combinatoric is scaled to the mES sideband, peaking to the Ene'll sideband. Cut T+T uds cc B+B Comb BOBo Comb tot Signal Box 42.4±8.7 760.±36 1906±42 1949±35 4506±58 9165±100. R2 < 0.48 O±O 440.±28 1378±39 1882±40. 4398±75 8098±126 Ehi > 1.0 O±O 106±16 144±14 99.8±9.3 231±16 580.±34 Nno = 0 O±O 41±11 45.2±8.4 19.4±4.3 60.4±8.7 166±20. NCTL = 0 O±O 6.6±3.2 6.1±2.4 1.75±0.94 4.0±1.6 18.4±5.4 NCT =0 O±O 1.3±1.4 2.1±1.6 0.45±0.48 0.46±0.49 4.3±2.6 Eneu < 0.28 O±O 1.8±2.0 0.9±1.0 0.59±0.67 O±O 3.3±2.7 Cut Peaking BUBo Comb tot Bkg tot Data Signal Box 10169±246 9165±100. 19334±266 25630±160. R2 < 0.48 9521±229 8098±126 17619±261 23817±154 Ehi > 1.0 408±32 580.±34 988±47 1266±36 Nno = 0 88±30. 166±20. 254±36 374±19 NCTL = 0 O±O 18.4±5.4 18.4±5.4 55±7.4 N CT =0 8.9±7.7 4.3±2.6 13.2±8.1 16±4.0 Ene'll. < 0.28 4.7±3.9 3.3±2.7 8.0±4.8 11±3.3 ------------,"--------- 70 Table 3.14. B D-----f invisible + 'Y /1- control cutfiow table. Peaking BDED events are those that have eF * < 0.4 and Nt~Yf = 0; combinatoric events do not. Signal is given as efficiency for tagged events, background and data as number of events. Combinatoric is scaled to the mES sideband, peaking to the Eneu sideband. Cut T+T uds cc B+B- Comb BUBu Comb tot Signal Box 68±1O. 1978±55 2939±51 1970±34 4447±57 11399±124 R2 < 0.48 O±O 1204±43 2160±43 1914±33 4374±56 9652±107 Ehi > 1.0 O±O 195±19 219±16 109.2±8.6 255±15 779±36 N 1r0 = 0 O±O 69±12 63.5±8.8 25.6±4.3 68.8±7.9 227±21 NGTL = 0 O±O 6.8±2.6 7.9±2.2 2.53±0.94 4.3±1.3 21.5±4.8 NCT =0 O±O 1.0±1.0 1.49±0.97 0.64±0.49 1.31±0.77 4.4±2.0 Eneu < 0.28 O±O 0.9±1.0 O±O 0.62±0.52 0.32±0.35 1.9±1.4 Cut Peaking BL'EU Comb tot Bkg tot Data Signal Box 10246±269 11399±124 21645±296 28516±169 R2 < 0.48 9763±250. 9652±107 19415±272 25910±161 Ehi > 1.0 549±33 779±36 1328±49 1545±39 N 1r0 = 0 154±34 227±21 381.±40. 434±21 N GTL = 0 35±17 21.5±4.8 57±17 47±6.9 NCT =0 22.±1O. 4.4±2.0 27±10. 11±3.3 E neu < 0.28 14.1±6.6 1.9±1.4 16.0±6.7 8±2.8 --------_._---- 71 Table 3.15. BO -----7 invisible + I K~ control cutfiow table. Peaking BOIJo events are those that have g?* < 0.4 and N:if! = 0; combinatoric events do not. Signal is given as efficiency for tagged events, background and data as number of events. Combinatoric is scaled to the 1nES sideband, peaking to the Enell, sideband. Cut T+T uds cc B+B Comb BUBu Comb tot Signal Box 7.7±3.9 5095±101 5514±79 1942±36 4757±61 17316±169 R2 < 0.48 O±O 3341±81 4188±68 1904±36 4683±61 14116±144 Ehi > 1.0 O±O 531±35 534±26 141±1O. 315±16 1519±54 Nwo = 0 O±O 131±18 146±14 31±4.8 74.7±8.0 383±29 NGTL = 0 O±O 21.7±4.7 21.1±3.5 4.7±1.2 12.2±2.2 59.8±7.8 NCT =0 O±O 1.8±1.3 3.2±1.5 1.20±0.67 0.92±0.58 7.2±2.6 E nell, < 0.28 O±O 2.4±1.9 2.5±1.5 1.19±0.83 0.41±0.44 6.5±3.3 Cut Peaking BUBu Comb tot Bkg tot Data Signal Box 8584±427 17316±169 25900±459 31340±177 R2 < 0.48 8263±407 14116±144 22379±432 27479±166 Ehi > 1.0 415±50. 1519±54 1934±74 2343±48 Nwo = 0 80.±62 383±29 463±69 631±25 N GTL = 0 36±28 59.8±7.8 96±29 119±11 NCT =0 7.6±9.2 7.2±2.6 14.7±9.6 15±3.9 Eneu < 0.28 4.0±4.8 6.5±3.3 1O.4±5.9 7±2.7 72 B°-----" invisible + i Photon Systematic The uncertainty due to the modeling of the high energy photon in B°-----" invisible+i events is 1.8%, determined by data/MC agreement in f1f1i control samples [26]. This is applied as a systematic error on B°-----" invisible + i signal efficiency. Signal Efficiency Systematic from Doubly Tagged Events To check the modelling of potential signal in data by signal MC, events with two independent hadronically tagged BOs are used, with the assumption that the tracks and neutrals remaining after tagging two independent BOs will correspond to the signal side of a singly tagged signal event. After all B°-----" invisible signal side cuts are applied to doubletag events, 48 ± 6.9 remain in data while 45.0 ± 3.7 remain in MC, for a ratio of 0.9365±0.156. This is an error of 15.6%, which is taken as a systematic error on the signal efficiencies. Total Systematic Error All the systematic errors are gathered together in Table 3.16, Table 3.17, and Table 3.18. The total systematic error on the number of background events is 8.57 events for B°-----" invisible and 8.09 events for B°-----" invisible+i. The error on the signal efficiency is 15.6% for B°-----" invisible and 15.% for B°-----" invisible + i. The systematic error on the tag BOyield is 3.4% for both B°-----" invisible and B°-----" invisible + i. 73 Table 3.16. Systematic errors on the background estimates, for E°-+ invisible and E°-+ invisible +,,/, in number of events. E U-+ invisible E U-+ invisible +"/ Combinatoric scaling 7.99 3.40 Control samples 3.11 7.34 Background tot. 8.57 8.09 Table 3.17. Systematic errors on signal efficiency, for EO -+ invisible and E°-+ invisible +,,/, in percent. E U-+ invisible E U-+ invisible + "/ Doubletags 15.6% 15.6% photon efficiency 0 1.8% Signal eff. tot. 15.6% 15.7% Table 3.18. Systematic errors on the tag EO yield, for EO -+ invisible and E°-+ invisible +,,/, in percent. EU-+ invisible EU-+ invisible + "/ EUEu combinatoric shape 3.3% 3.3% Yield method 1.0% 1.0% Yield tot. 3.4% 3.4% 74 CHAPTER IV CONCLUSIONS AND FURTHER RESEARCH Branching Fractions A branching fraction of a decay mode is the fraction of all decays of particles of the parent type that decay in the decay mode. The expected number of signal events in this experiment is the yield times the branching fraction of that signal mode, giving the number of correctly tagged events with the other neutral B meson decaying to the signal mode, times the efficiency of a signal event to pass the signal side cuts. As the total number of events that pass the signal cuts is the sum of the number of signal events and the number of background events, the branching fraction of B°-----+ vv( +"y) is given by: (IV.I) (IV.2) where N evt is the number of events seen in the signal box, NBkgrnd is the expected number of background events in the signal box, NYield is the number of tagged BOs, E:Big is the efficiency of signal tagged signal events to pass all cuts and fall in the signal box, and the sensitivity S is the constant of proportionality between the 75 branching fraction and the number of signal events, and therefore is a branching fraction independent measure of the ability of an analysis to detect a signal. From Table 3.5, the tagging efficiency for B°---" invisible is (0.1767 ± 0.0017)% and for B°---" invisible +, is (0.1793 ± 0.0018)%. Combined with the total efficiencies of (6.50±0.11) x 10-4 for B°---" invisible and (4.846±0.091) x 10-4 for B°---" invisible +" the signal efficiencies are ESig = 0.368 ± 0.007 ±0.057 for B°---" invisible and ESigGam = 0.270 ± 0.006 ± 0.042 for B°---" invisible +,. The yield is (500.8 ± 2.0 ± 17.0) x 103 , which is combined with the signal efficiency yield corrections CBo-"'vv = 1.344 ± 0.013 and CBo-"'vv, = 1.363 ± 0.014 to take into account the higher probability of B°---" invisible (+,) events to pass the tagging selection, and with the BO ---" invisible(+,) signal efficiencies to give sensitivities of S = 247.4 ± 39.9x 103 for BO ---" invisible and S = 184.5 ± 30.0x 103 for BO ---" invisible + ,. The predicted background is 28.5±7.8±9.2 in B°---" invisible and 14.1±5.5±8.1 in B°---" invisible +,. The number of events in data is 39±6.2 in B°---" invisible and 8±2.8 in B°---" invisible +,. This gives a branching fraction of B(Bo ---" invisible) = (4.2 ± 5.6) x 10-5 and B(B°---" invisible +,) = (-3.2 ± 5.4) x 10-5 . The upper limit of a decay at a given confidence for an experiment is the value that, if it were the true value of the branching fraction for the decay, would lead to a measured branching for the decay for repetitions of the experiment to be greater than the branching fraction actually measured at the experiment with a probability equal to the confidence. Therefore, the chance that an experiment would measure a branching 76 bestS mES vs. eneu bestS mES vs. eneu ~.4Dbackground Me 5lgllnl Me dala 0.8- 0.6 0.4 ~ Dbackground I.K; <:11.4 UJ In ro IL..l SI(;J'l w 15 "-"-,.,..".,,~-, ~.~ 1 • ...1. 5.28 5.3 :0 Q) ro IO- u W R2 5." 5.28 5.3 mES, GeV a) mES, GeV b) Figure 4.2. Data (points) and J\!1C simulatioll, after all cut.s. for a) 1I/.ES in n°-" invisible, b) mES in nO -" invisible + /. Background scaled t.o the mES and Ene" sidebands. fraction equal to that. measured in the real experiment if the true branching fract.ion of the decay was greater than the upper limit is less than one minus the confidence. To get. an npper limit on t.he branching fract.ions, t.he repetition of experiment.s for an assumed true branching fraction is simulated as follows [27]. A value for t.he 77 [ Total Neutral EMC energy J <: 12 ::J ~ W 15 20 eneu, GeV a) eneu, GeV b) Figure 4.3. Data (points) and MC simulation, after all cuts, for a) Enc1/. in nO~ invisible, b) E nell in EO~ invisible + f. Background scaled to the mES and Encll sideba.nds. branching ratio is guessed, and 100000 toy tvIC experiments are produced usmg t.he values for Nm.grnd and S given above, assuming the errors are Gaussian. Each MC trial is performed as follows. For a number of background events N Bkgrnd ± ERkllrnd, a sensitivity S ± ES, an upper limit guess N~~" and a number of da.ta events NeVI, a number of trial background events N~kq is sampled from a Gaussian of mean N IJkgrnd and width EHk:grnd' A trial sensitivity of S* is taken as S* = S x (1 + x), where :r: is sampled from a Gaussian of mean 0 and width ES/S. A mean number of events seen N;1JI is determined by N~v{ = N~~, x S* + N;kq' The trial number of events seen N~:Jt is sampled from a Poisson distribution of mean N~vt. This is repeated for 10000 MC trials, and the confidence that the upper limit is less than N~~, is taken as the fraction of MC trials with N~~Jt > N pvt ' This is repeated for different values of N~~, 78 until a confidence of 0.9 is obtained. Using this method, the upper limits given in Table 4.1 were obtained. Table 4.1. Upper limits for B°-----'? invisible(+/,) at the 90% confidence level. Upper limit Value N~~(Bu-----,? invisible) 11.7 x 10 -::), N~~(B°-----'? invisible + /,) 4.3 x 10-5 Conclusions This analysis measured branching fractions of B(B°-----'? invisible) = (4.2 ± 5.6) x 10-5 and B(B°-----'? invisible + /,) = (-3.2 ± 5.4) x 10-5 leading to upper limits B(B°-----'? invisible) < 11.9 x 10-5 and B(B°-----'? invisible+/,) < 4.3 x 10-5 at the 90% confidence level. The branching fractions do not indicate significant signals and therefore are consistent with the SM. The upper limit on B°-----'? invisible is still far above the 10-10 level needed to constrain the large extra dimension scenario. As shown in Figure 1.6, a limit on the branching fraction B(Bo -----'? X6V) constrains possible values of the X6 lifetime that result in the number of dimuon events seen at NuTeV. The upper limit of B(B°-----'? invisible) < 11.7 x 10-5 does not reach the 10-5 level needed to significantly restrict the neutralino lifetimes. In the previous search for B°-----'? invisible(+/,), an upper limit of B(B°-----'? invisible) = 22 X 10-5 and B(B°-----'? invisible+/,) = 4.7 x 10-5 were obtained [15]. It obtained these limits from a fitted signal of NSi9(B°-----,? invisible) = 17 ± 9 on top of a background of NBkgrnd(B°-----,? invisible) = 19~~0, and a fitted signal of NSi9(B°-----,? invisible + /,) = 79 -1.1~~:~ on top of a background of NBkgrnd(B°-----+ invisible +'Y) = 28~~. The analysis detailed in this dissertation obtains an upper limit on BO -----+ invisible almost a factor of two smaller than that obtained in the previous analysis. The upper limit on B°-----+ invisible + 'Y is a slight improvement over the previous analysis. Further Research An experiment in its planning stages that should be promising for an improved measurement of B°-----+ invisible(+'Y) is the SuperB experiment [28]. Its purpose would be to use precision measurements and rare decays of the BO meson to constrain new physics contributions, and in doing so help identify which theoretical models explain what new physics is found at the LHC and ILC. As with the BABAR and Belle experiments, SuperB would collide electrons and positrons with a center of mass energy at the Y(45) resonance, ECMS = 10.58 GeV. SuperB would have a design luminosity of £ = 70 X 1034 cm-2s-1 , leading to an integrated luminosity of 10 ab-1 /year. By its 3rd year of running, the SuperB would therefore collect a data sample of 30ab-1, approximately 60 times the data sample at BABAR. Assuming signal efficiencies and systematic errors equal to those in this analysis, a tag yield and predicted background 60 times larger than in this analysis, and a number of data events equal to the predicted background, upper limits of B(B°-----+ invisible) < 8.8 x 10-5 and B(B°-----+ invisible +'Y) < 5.2 x 10-5 could be obtained. The systematic errors are largely dependent on MC statistics, however. The SuperB should optimally 80 have generic MC simulation that is at least as large as the total dataset. At BABAR, the generic MC sample is 3 times larger than data, so MC at SuperB should have at least 20 times the statistics as BABAR. If the systematics were completely dominated by MC statistics, this would lead to the relative systematic error being improved by greater than a factor of 4. This is probably not obtainable, but assuming a relative systematic error half that used in this analysis, upper limits at the Super B factory of B(B°---7 invisible) < 2.4 X 10-5 and B(B°----'? invisible + 1') < 2.6 x 10-5 could be obtained. Also possible at SuperB would be the searches B~---7 invisible (+1'), by running at the Y(5s) resonance, which decays to B;fJ; with a branching fraction of 26%. B~---7 invisible+1' would have a SM branching ratio of order 10-8 and be sensitive to new physics [29]. 81 APPENDIX A CUT OPTIMIZATION B°---+ invisible Figure A.I-Figure A.5 show POM versus cut value for B°---+ invisible cuts for regular and high statistics samples. All cuts but the one on the variable plotted are applied, with the values of the other cuts chosen to maximize the POM for the high statistics sample. 82 ISignal MC I ~ .. ~ '9 " ISignal MC: · , 00 " "II GTl A2) • GTl i Background MCJ ~ ~ .. '9 .. 0 ~ "~~ " ., > w -;j 1 . 00 " D1) • GTl • GTl IFig_u!!! ,?f _rJI~r~ ] j sf" I'~u ,'0 '0 I; 4 ~ ·.>-.~u u- u: · , , j '"I J I, ,;.-j L~u jI I " .. " " . Of 001 I 1..5- '2 .. C1) Cut value C2) CUl value Figure A.I. NCTT, in A) 13°, D) background, and C) Nsig /(1.5+JNR/cgl'nd) for 1) regular and 2) high statistics samples 83 Si n 100 300 .. ~ MlO AI) eneu, GeV A2) [ Background MC I Bac_,,-g~Ufl • u: r .E • +- CUi value C2) 't J~'~.'7i'0.'<','U'-"'J-'7:.......~'....,......J-'c-'-'~*'" ........'-i! C1) ·.'c-'-'~""-J-'-!-'~---""~'-c!~~~~3 Cut value Figure A.6. Nc;'j'L in A) n°, 8) background, and C) NSi9/(1.5+)NBkgrnd) for 1) regular and 2) high statistics samples 89 FI ure of Merit '" L i .' , r-r'"T~,~'t r~ .~'fu. , :'L' -. .........1....'- o 0.2 0" ll.' OA , 1.2 1'* i i I'OJ io"-*~-l~~~...J Totol Neutral EP.1C energy ~J. CU 1.1 1.4 Total Neutral EMC energy E ~ 0.• B2) IFlgureof~ Total Neutral EMC energy Totol Neutral EMC energy AI) 131 ) Cl) Cut value C2) Cut value Figure A.7. Enel) in A) nO, B) ba.ckground, and C) NSig/(1.5+)NJJkgrnd) for 1) regular and 2) high statistics samples 90 ISignal M£] IS!gna~gl "!-'--'-,"",,,,~~""""I \L.L.Ut·..'·····rr-a--}+-~~. Energy of MOSI Energel/c EMC NeutralA2) ''''9 J -J 'I'I '''I'~ .. ' ~ : ~o.•:'5 ~ ~ t il I rl:u,~,,~"J, AI) Energy of MOSI Energellc EMC Neulral Background MC ,.........,.....,.rrr...-lDrr .uds co B'B' , Background MC B1) , Figure of Meili] 2.. :H Energy of Most Energellc EMC NeulrAlB2)~~'~"-FJEnergy of MOst Energetic EMC Neutral IFigure of Mei!!] ., C1) ••fo.o-'"*.....+-"""!'t--;-~~~~'"';,!t,,"'-'-'-.! Cut value C2) CUi value Figure A.8. Ehi in A) BO, B) background, and C) NSig/(1.5+jNBkqn,d) for 1) regular and 2) high statistics samples 91 ISignal MC ISignal Mf.1 I I" '1""1" 'I ~1-"",,,,,,,,,,,,,,,,!",",,,,nT'~II~ ~ ~ u II Ch,lfgedTracks 'Ii~~";"~{'-'-'--';';~~4't-"'+',4."",.s , ChargedTracks l Background MC I A2) , Figure 01 Merit -~..-iu 1__. it " l . I ''1 I l "" , '.5 , ChargedTracks r" o's II '! I ,.~ '! .1 o;,~~~~J II ChargedTracks FI ure of Merit AI) raac-'-kg-r-ou-n"""'d'"'M"'C" j • L. '9 '. Dl) .~ , .........."...,.,...,.~....,.....~~.,.....""'T'~.~..., :; (; ~u u: Cl) C2) CUl value Figure A.9. NeT in A) EO, B) nBkg, and C) NSig/(1.5+JNBI,grnd) for 1) regular and 2) high st.atistics samples 92 'l'll't"""""'r..-nt r~gnal Me IFI""I I" FI ure of ~erll :. Figure of Merit I j J j 1 , :10 11.,0 " • lids Uce B'B· Btl' P••k lU.I..I.""! '""t ,.,1",., """1 I t :I .. ~ , 1 • •00 B2) .:: 11:"1° 1I!IW!.....+-O-O+.i..I' ~ I.t ~.u.u;0 , ;,0 00 TIl) .os M' ". C2)Cl) liT" 'i::;':;;''~J::'~=~:;:;;::::;=~.~ Cut value l 'Us'o~~J......" "'-u...lf1~o~I'.lJ~'I~O.;.~f~O~.!-<"~''~'JL.."~, """" 'I ''J Jg"", ~ • UJSOO.- AI) IBackground MC -- ---OTT - ,~ u lids .. Dec eX , B'B Of§ I.' """-",,,,''----' ~I .• R2 j _' -l ........u,.!. '"I.",I""J 0.50 0' 01 I.' CHI I R2 R2 Cut value , Figure of ~eiliJ r.t' "., '/'<~:'=--l ~ I . u:: :u. ,~- f -J J 1 ;' ~r I > ~ OS~ I It ee L.e'I" I • I "I" I, ,e' ,I, "L,J o I' 0.2 03 0<11 0.6 0.' 0.7 0.' 0 .• I C2) 132) ] j R2 Cut volue 01 0,0 1 '~ I.' D,'01) 0.1 0.2 0 ~ 0 1.0 8.77 ± 0.12 O±O 109±11 93.3±7.1 38.0±3.7 Nrro = 0 7.08 ± 0.11 O±O 30.7±5.7 24.5±3.7 7.4±1.6 NGTL = 0 6.96 ± 0.11 O±O 3.2±1.8 4.4±1.5 1.06±0.61 NCT = 0 5.561 ± 0.098 O±O 2.1±1.5 2.2±1.1 0.35±0.35 Eneu < 0.3 4.846 ± 0.091 O±O 1.1±1.1 0.55±0.55 0.35±0.35 I Comb BDBD I Peaking BDBD I Comb tot I Bkg tot I Data I 1415±23 4004±47 5314±58 9318±75 9975±100. 1335±22 3556±45 3951±48 7507±65 8097±90. 81.7±5.4 259±12 322±14 581±19 664±26 19.1±2.6 77.3±6.3 81.7±7.4 159±9.7 177±13 1.80±0.80 8.8±2.1 10.4±2.6 19.2±3.3 29±5.4 0.72±0.51 1.22±0.88 5.4±2.0 6.6±2.1 BLINDED O±O 0.30±0.36 2.0±1.2 2.3±1.3 BLINDED 96 To remedy this, the combinatoric and peaking MC events are scaled using the mES and Eneu sidebands. To enhance the peaking MC statistics, the BOEo cocktail sample is used in place of generic peaking BOEo events. Table B.3 through Table B.14 show the yields and correction factors used in this scaling, and compare the peaking yields between cocktail and generic BOEo samples. For the Eneu sideband tables, Eneu low mES refers to the region 5.2 < mES < 5.26, .6 < Eneu < 1.5. The Eneu combinatoric correction is the ratio of MC to data in this region, and is used to scale the combinatoric background in the Eneu sideband. The peaking correction is obtained by dividing the cocktail MC yield in the Eneu sideband by the predicted peaking background, where predicted peaking background in the Eneu sideband is obtained by subtracting the scaled combinatoric background in the Eneu sideband from data. In the mES sideband tables, the combinatoric correction is the ratio of MC to data in the mES sideband. The total scaled MC in the signal box is the sum of the cocktail MC events in the signal box scaled by the peaking correction and the combinatoric events in the signal box scaled by the combinatoric correction. Table B.15 through Table B.20 give the number of events in the Eneu sideband and the signal box for generic and cocktail MC, as well as the ratio of signal box to Eneu sideband events for the two samples. The ratios are the same for the two samples, within statistics, and so, since the peaking MC in the Eneu sideband is used to scale the peaking MC in the signal box, the scaled peaking background using the 97 cocktail sample is in agreement with the scaled peaking background using peaking Me from the generic BOJjo sample. Table B.3. B°-----+ invisible Eneu sideband. Cut Data Eneu MC Eneu SB Comb. Cock MC Comb MC Data Peaking low mES low mES Carr. Eneu SB E neu SB Eneu SB Carr. SignalBox 25135±159 25450±125 0.99±0.01 6309±21 8530±71 13215±115 0.76±0.02 R2 < .62 24055±155 24400±122 0.99±0.01 6247±21 8080±69 12755±113 0.77±0.02 NJr0 < 2 8330±91 9004±76 0.93±0.01 2758±14 2978±43 4970±70 0.80±0.03 NCTL = 0 1643±41 1645±33 1.00±0.03 216.3±3.9 515±18 703±27 0.87±0.17 NeT =0 593±24 531±19 1.12±0.06 53.5±2.0 170±10 242±16 0.97±0.41 Eneu < .16 593±24 531±19 1.12±0.06 53.5±2.0 170±10 242±16 0.97±0.41 CD r::t:J Table BA. B°----t invisible mES sideband. Cut Data MC Comb. Cock MC Comb MC Scaled MC Data mES SB mES SB Correction SignalBox SignalBox SignalBox SignalBox SignalBox 4561±68 4246±53 1.07±0.02 2646±14 1547±31 3671±80 3633±60 R2 < .62 4124±64 3797±49 1.09±0.02 2573±14 1399±29 3492±76 3393±58 N 1r0 < 2 3255±57 3060±45 1.06±0.02 2194±13 1111±26 2944±82 2298±48 NCTL = 0 724±27 617±21 1.17±0.06 145.4±3.2 196±12 356±30 318±18 NeT =0 253±16 184±12 1.38±0.12 34.9±1.6 57.1±6.2 112±18 120±11 Eneu < .16 48.0±6.9 27.6±4.5 1.74±0.38 7.30±0.72 12.4±3.1 28.6±7.8 39.0±6.2 (,D (,D Table B.5. B°-----'7 invisible Eneu sideband e- control. Cut Data Eneu MC E neu SB Comb. Cock MC Comb MC Data Peaking low mES low mES Carr. Eneu SB E neu SB E neu SB Carr. SignalBox 24664±157 24580±108 1.00±0.01 6801±22 8812±63 17729±133 1.31±0.02 R2 < .62 24205±156 24170±106 1.00±0.01 6759±22 8645±62 17525±132 1.31±0.02 N1fo < 2 8163±90 8195±64 1.00±0.01 3330±15 3089±38 7459±86 1.32±0.03 NCTL = 0 1516±39 1539±28 0.99±0.03 488.2±5.9 518±16 1285±36 1.59±0.09 NeT =0 402±20 385±13 1.04±0.06 181.6±3.6 139.4±7.6 441±21 1.63±0.14 E neu < .16 402±20 385±13 1.04±0.06 181.6±3.6 139.4±7.6 441±21 1.63±0.14 f---' o o Table B.6. B°-+ invisible mES sideband e- control. Cut Data MC Comb. Cock MC Comb MC Scaled MC Data mES SB mES SB Correction SignalBox SignalBox SignalBox SignalBox SignalBox 11899±109 4561±46 2.61±0.04 4035±17 2025±30 10555±146 7324±86 R2 < .62 11594±108 4412±45 2.63±0.04 3985±17 1964±29 10389±143 7219±85 Nrro < 2 8905±94 3439±40 2.59±0.04 3470±16 1573±26 8639±145 5013±71 NCTL = 0 608±25 586±17 1.04±0.05 428.6±5.5 230±1O 919±42 658±26 NeT =0 159±13 143.0±7.9 1.11±0.11 140.1±3.2 51.1±4.5 285±21 209±14 Eneu < .16 25.0±5.0 19.1±3.0 1.31±0.33 31.0±1.5 8.6±2.0 61.7±6.2 69.0±8.3 f---' o f---' Table B.7. EO-----+ invisible Eneu sideband f-L - control. Cut Data Eneu MC Eneu SB Comb. Cock MC Comb MC Data Peaking low mES low mES Carr. Eneu SB Eneu SB Eneu SB Carr. SignalBox 32236±180 38220±143 0.84±0.01 7450±23 12830±82 19766±141 1.20±0.02 R2 < .62 31564±178 37430±141 0.84±0.01 7409±23 12470±80 19406±139 1.20±0.02 N7fo < 2 10923±105 13270±87 0.82±0.01 3567±16 4543±49 8019±90 1.20±0.03 NGTL = 0 1949±44 2429±37 0.80±0.02 551.4±6.3 840±21 1423±38 1.36±0.08 NeT =0 481±22 571±18 0.84±0.05 203.9±3.8 205±10 447±21 1.34±0.12 Eneu < .16 481±22 571±18 0.84±0.05 203.9±3.8 205±10 447±21 1.34±0.12 f---' o tv Table B.8. B°-t invisible mES sideband p,- control. Cut Data MC Comb. Cock MC Comb MC Scaled MC Data mES SB mES SB Correction SignalBox SignalBox SignalBox SignalBox SignalBox 16436±128 7269±63 2.26±0.03 4433±18 2859±38 11787±156 7935±89 R2 < .62 15867±126 6915±61 2.29±0.03 4374±18 2720±37 11490±153 7783±88 N7r0 < 2 12300±111 5455±54 2.25±0.03 3811±17 2182±33 9492±155 5463±74 NGTL = 0 847±29 930±23 0.91±0.04 497.4±6.0 360±14 1004±46 771±28 NeT =0 200±14 200±1O 1.00±0.09 157.7±3.4 73.5±5.9 285±22 229±15 Eneu < .16 29.0±5.4 28.5±3.8 1.02±0.23 38.6±1.7 12.8±2.6 64.8±6.6 62.0±7.9 f-" o w Table B.9. B°-----', invisible + "I Eneu sideband. Cut Data Eneu MC Eneu SB Comb. Cock MC Comb MC Data Peaking low mES low mES Carr. Eneu SB Eneu SB Eneu SB Carr. SignalBox 54350±233 56550±200 0.96±0.01 7822±24 17930±106 23329±153 0.78±0.03 R2 < .48 44930±212 46780±179 0.96±0.01 7438±23 14330±91 19553±140 0.78±0.02 E hi > 1.0 7452±86 8395±78 0.89±0.01 1098.0±8.9 2550±41 3104±56 0.77±0.07 N 1r0 = 0 382±20 456±19 0.84±0.05 61.0±2.1 130.1±9.3 182±13 1.20±0.28 NGTL = 0 90.0±9.5 105.0±9.0 0.86±0.12 8.16±0.76 27.1±4.2 46.0±6.8 2.79±1.05 NeT =0 33.0±5.7 42.3±5.7 0.78±0.17 2.08±0.39 11.5±2.6 27.0±5.2 8.69±3.28 Eneu < .28 33.0±5.7 42.3±5.7 0.78±0.17 2.08±0.39 11.5±2.6 27.0±5.2 8.69±3.28 f--' o ~ Table B.lO. B°-----'t invisible + I mES sideband. Cut Data MC Comb. Cock MC Comb MC Scaled MC Data mES SB mES SB Correction SignalBox SignalBox SignalBox SignalBox SignalBox 15150±123 15140±105 1.00±0.01 6133±21 5314±58 10098±183 9975±100 R2 < .48 11500±107 1151O±89 1.00±0.01 5458±20 3951±48 8196±153 8097±90 Ehi > 1.0 1059±33 1172±30 0.90±0.04 387.5±5.3 322±14 587±32 664±26 N 1r0 = 0 290±17 321±16 0.90±0.07 108.7±2.8 81.7±7.4 204±32 177±13 NCTL = 0 65.0±8.1 57.4±6.6 1.13±0.19 8.73±0.79 10.4±2.6 36±10 29.0±5.4 NeT =0 34.0±5.8 19.4±3.8 1.75±0.45 2.36±0.41 5.4±2.0 29.9±9.5 11.0±3.3 E neu < .28 18.0±4.2 7.4±2.2 2.43±0.92 1.07±0.28 2.0±1.2 14.1±5.5 8.0±2.8 f--' a CJl Table B.Il. B°---+ invisible + I Eneu sideband e- control. Cut Data Eneu MC Eneu SB Comb. Cock MC Comb MC Data Peaking low mES low mES Carr. Eneu SB Eneu SB Eneu SB Carr. SignalBox 38416±196 39290±155 0.98±0.01 6124±21 13040±80 20460±143 1.26±0.03 R2 < .48 34949±187 35660±146 0.98±0.01 5879±21 11690±74 18851±137 1.26±0.03 Ehi > 1.0 3284±57 3395±47 0.97±0.02 618.3±6.7 1126±25 1815±43 1.17±0.09 Nrro = 0 207±14 187±11 1.11±O.lO 46.9±1.8 62.3±6.1 110±10 0.88±0.30 NaTL = 0 47.0±6.9 41.1±5.2 1.14±0.22 8.73±0.79 16.7±3.1 19.0±4.4 -0.01±-0.77 NeT =0 10.0±3.2 10.2±2.4 0.98±0.38 3.58±0.51 5.9±2.0 11.0±3.3 1.45±1.26 Eneu < .28 1O.0±3.2 1O.2±2.4 0.98±0.38 3.58±0.51 5.6±2.0 11.0±3.3 1.53±1.25 f--' o O'l Table B.12. B°-----7 invisible + r mES sideband e- control. Cut Data MC Comb. Cod< MC Comb MC Scaloo MC Data mES SB mES SB Corroction Signa/Box Signa/Box Signa/Box Signa/Box Signa/Box 22595±150 14230±94 1.59±0.01 8135±24 5764±51 19394±274 16389±128 R2 <.48 19958±141 12450±87 1.60±0.02 7556±23 5061±47 17616±252 15163±123 Ehi > 1.0 1391±37 694±21 2.01±0.08 348.5±5.0 289±12 988±47 746±27 N 7r0 = 0 374±19 162±10 2.30±0.19 100.6±2.7 72.3±6.5 255±36 225±15 NGTL = 0 46.0±6.8 37.1±5.0 1.24±0.25 16.5±1.1 14.8±3.2 18±14 55.0±7.4 NeT = 0 12.0±3.5 9.5±2.7 1.27±0.51 6.08±0.66 3.4±1.5 13.2±8.2 16.0±4.0 Eneu < .28 8.0±2.8 4.8±2.0 1.67±0.90 3.08±0.47 2.0±1.2 8.0±4.8 11.0±3.3 ~ o --l Table B.13. B°-----+ invisible + I Eneu sideband f-L- control. Cut Data Eneu MC Eneu SB Comb. Cock MC Comb MC Data Peaking low mES low mES Carr. Eneu SB Eneu SB Eneu SB Carr. Signal Box 52705±230 65050±207 0.81±0.OO 7019±22 20750±108 24911±158 1.15±0.03 R2 <.48 46886±217 57570±192 0.81±0.OO 6754±22 17800±96 22413±150 1.17±0.03 E hi > 1.0 5110±71 6944±70 0.74±0.01 774.8±7.4 2130±36 2623±51 1.36±0.08 N 1r0 = 0 285±17 373±17 0.76±0.06 48.5±1.9 98.3±7.9 140±12 1.34±0.30 NCTL = 0 57.0±7.5 77.2±7.5 0.74±0.12 9.09±0.81 25.1±3.9 34.0±5.8 1.70±0.80 NeT = 0 18.0±4.2 27.9±4.5 0.64±0.18 3.44±0.50 6.8±1.9 14.0±3.7 2.80±1.27 Eneu < .28 18.0±4.2 27.9±4.5 0.64±0.18 3.44±0.50 6.8±1.9 14.0±3.7 2.80±1.27 f---' o en Table B.14. B°---+ invisible + I mES sideband j1,- control. Cut Data MC Comb. Cod< MC Comb MC Scale:! MC Data mES SB mES SB Corroction Signal Box Signal Box Signal Box Signal Box Signal Box 31163±177 23000±124 1.35±0.01 8910±25 8444±67 21722±289 17901±134 R2 <.48 26511±163 19310±112 1.37±0.01 8274±24 7045±59 19370±261 16226±127 E hi > 1.0 2227±47 1347±31 1.65±0.05 406.7±5.4 472±17 1334±50 850±29 N 7r0 = 0 607±25 333±15 1.82±0.11 114.2±2.9 124.8±8.8 380±41 238±15 NGTL = 0 59.0±7.7 73.3±7.3 0.80±0.13 20.7±1.2 26.8±4.2 57±17 47.0±6.9 NeT = 0 18.0±4.2 19.7±3.8 0.91±0.28 7.87±0.75 4.8±1.7 26±10 11.0±3.3 Eneu < .28 9.0±3.0 10.2±2.9 0.88±0.39 5.01±0.60 2.1±1.2 15.9±6.7 8.0±2.8 f-' o co Table B.15. B°-" invisible Peaking Ratio 110 Cut E ne1J SB SignalBox Ratio Eneu SB SigBox Cock Peaking Peaking Cock Cock Ratio SignalBox 4113±35 1671±23 0.41±0.0l 6309±21 2646±14 0.42±0.00 R2 < .62 4070±35 1630±22 0.40±0.01 6247±21 2573±14 0.41±0.00 N 1r 0 < 2 1894±24 140l±21 0.74±0.Ol 2758±14 2194±13 0.80±0.01 NCTL = 0 180.8±7.4 120.3±6.1 0.67±0.04 216.3±3.9 145.4±3.2 0.67±0.02 NCT =0 66.4±4.5 34.1±3.2 0.51±0.06 53.5±2.0 34.9±1.6 0.65±0.04 E ne1J < .16 66.4±4.5 7.6±1.5 0.11±0.02 53.5±2.0 7.30±0.72 0.14±0.0l Table B.16. B°-" invisible Peaking Ratio e- control Cut Ene1J SB SignalBox Ratio Eneu SB SigBox Cock Peaking Peaking Cock Cock Ratio SignalBox 7754±49 4549±37 0.59±0.01 6801±22 4035±17 0.59±0.OO R2 < .62 7722±48 4504±37 0.58±0.Ol 6759±22 3985±17 0.59±0.00 N 1r 0 < 2 3792±34 3895±34 1.03±0.01 3330±15 3470±16 1.04±0.01 NCTL = 0 594±13 503±12 0.85±0.03 488.2±5.9 428.6±5.5 0.88±0.O2 NCT =0 221.3±8.2 162.9±7.0 O.74±O.O4 181.6±3.6 140.1±3.2 O.77±0.02 Ene1J < .16 221.3±8.2 37.1±3.4 O.17±O.O2 181.6±3.6 31.0±1.5 O.17±0.01 Table B.17. B°-" invisible Peaking Ratio /-l- control Cut Eneu SB SignalBox Ratio Eneu SB SigBox Cock Peaking Peaking Cock Cock Ratio SignalBox 8425±51 5146±40 O.61±0.Ol 7450±23 4433±18 0.60±0.OO R2 < .62 8384±51 5100±39 0.61±O.Ol 7409±23 4374±18 O.59±O.OO N 1r 0 < 2 4008±35 4409±37 1.10±O.Ol 3567±16 3811±17 1.07±O.Ol NCTL = 0 645±14 597±13 0.93±0.03 551.4±6.3 497.4±6.0 O.90±O.Ol NCT =0 234.7±8.5 190.6±7.6 0.81±0.O4 203.9±3.8 157.7±3.4 0.77±0.O2 Ene1J < .16 234.7±8.5 45.7±3.7 0.19±0.O2 203.9±3.8 38.6±1.7 0.19±0.0l Table B.18. B°-----" invisible + I Peaking Ratio 111 Cut E nell SB SignalBox Ratio Eneu SB SigBox Cock Peaking Peaking Cock Cock Ratio SignalBox 5153±60 4004±47 0.78±0.01 7822±24 6133±21 0.78±0.00 R2 < .48 4914±59 3556±45 0.72±0.01 7438±23 5458±20 0.73±0.00 E hi > 1.0 790±23 259±12 0.33±0.02 1098.0±8.9 387.5±5.3 0.35±0.01 N1fo = 0 46.9±5.3 77.3±6.3 1.65±0.23 61.0±2.1 108.7±2.8 1.78±0.08 NCTL = 0 4.3±1.5 8.8±2.1 2.07±0.89 8.16±0.76 8.73±0.79 1.07±0.14 NCT = 0 0.91±0.88 1.22±0.88 1.33±1.61 2.08±0.39 2.36±0.41 1.14±0.29 E nell < .28 0.91±0.88 0.30±0.36 0.33±0.51 2.08±0.39 1.07±0.28 0.52±0.16 Table B.19. B°-----" invisible + I Peaking Ratio e- control Cut Enell SB SignalBox Ratio Eneu SB SigBox Cock Peaking Peaking Cock Cock Ratio SignalBox 6902±68 9251±70 1.34±0.02 6124±21 8135±24 1.33±0.01 R2 < .48 6699±67 8771±69 1.31±0.02 5879±21 7556±23 1.29±0.01 E hi > 1.0 685±20 400±15 0.58±0.03 618.3±6.7 348.5±5.0 0.56±0.01 N1fo = 0 48.7±5.3 114.5±7.6 2.35±0.30 46.9±1.8 100.6±2.7 2.15±0.1O NCTL = 0 8.8±2.5 19.2±3.1 2.17±0.70 8.73±0.79 16.5±1.1 1.89±0.21 N CT =0 3.7±1.5 5.2±1.5 1.42±0.71 3.58±0.51 6.08±0.66 1.70±0.30 Enell < .28 4.3±1.2 3.3±1.2 0.78±0.36 3.58±0.51 3.08±0.47 0.86±0.18 Table B.20. B°-----" invisible + I Peaking Ratio /1- control Cut Ene'll SB SignalBox Ratio Eneu SB SigBox Cock Peaking Peaking Cock Cock Ratio SignalBox 7944±74 10200±74 1.28±0.02 7019±22 8910±25 1.27±0.01 R2 < .48 7717±74 9660±73 1.25±0.02 6754±22 8274±24 1.23±0.01 Ehi > 1.0 921±24 468±16 0.51±0.02 774.8±7.4 406.7±5.4 0.52±0.01 N1fo = 0 57.2±5.7 136.7±8.5 2.39±0.28 48.5±1.9 114.2±2.9 2.36±0.11 NCTL = 0 10.7±2.8 23.1±3.4 2.17±0.66 9.09±0.81 20.7±1.2 2.28±0.24 NCT =0 3.7±1.6 7.6±1.9 2.08±1.04 3.44±0.50 7.87±0.75 2.29±0.40 Enell < .28 3.7±1.6 3.7±1.3 1.00±0.56 3.44±0.50 5.01±0.60 1.46±0.27 112 APPENDIX C PID LISTS Track Lists For the track list definitions the following variables are used: • PT- the transverse momentum of the track, • DOCAxy-the distance of closest approach of the track to the IP in the x-y plane, • DOCAz - the distance of closest approach of the track to the IP along the z-axis, • NDCH- the number of hits in the DCH associated with the track. The definitions for the track lists used in this analysis are: • ChargedTracks - candidates with non-zero charge, use a charged pion mass hypothesis • GoodTracksLoose - ChargedTracks with 0.1 < PT < 10 GeV, DOCAxy < 1.5cm, -10 < DOCAz < lOcm, and NDCH > 10 113 Neutrals Lists The following neutrals definitions use the following variables: E1ab- the energy of the cluster in the lab frame and £,-- the lateral moment of the cluster. The definitions for the neutral lists used in this analysis are: • CalorNeutral- Single unmatched EMC bumps • GoodPhotonLoose - Calor Neutral with E1ab > 0.30 GeV and £, < O. • GammaForPiO - GoodPhotonLoose with 0.030 < E1ab < 10.0 GeV PID Lists For the PID lists the following variables are used: • Ecand- the energy deposited by the candidate in the EMC, • dE/dx- the energy lost in the SVT and DCH, • Bc- the angle of the Cherenkov light cone in the DIRC, • N,- the number of photons in the DIRC, • N;xp- the expected number of photons in the DIRC, • E /p- the ratio of lab energy to momentum, 114 • N ery- the number of crystals with clusters associated with the track, • L y- the lateral moment in the EMC, • A42- the Zernike moment, • ~c/J- the separation between the track and the nearest unassociated bump, • NL - the number of IFR layers with hits associated with the track, • Ameas- the number of interaction lengths traversed by the track, • ~A- the difference between the expected (for muons) and measured number of interaction lengths traversed, • X}it- the chi squared per degree of freedom of a polynomial fit to the IFR hits, • X~at- the chi squared per degree of freedom of the track extrapolation to the hits in the IFR, • Te- the track continuity, • 1\1- the average multiplicity of hit strips per IFR layer, and • (JM- the error on M. The PID lists used in this analysis are: • K- - likelihood fit using de /dx, Be, N'Y' and N;xp 115 Composite Particles For the composite particle definitions the following variables are used: m- the invariant mass of the sum of the 4-momenta of the daughter particles, m poca- the invariant mass of the pion pair at their point of closest approach, E1ab- the energy of the composite particle in the lab frame, Lat is the photon lateral moment, mp with P as the parent is the theoretical mass of the parent particle, mx with X as the daughter particles is the invariant mass of the sum of the 4-vectors of the particles X, and Px is the momentum in the lab frame of the sum of the 4-vectors of the particles X. The composite particle definitions are given in Table C.1, with the theoretical particle masses in Table C.2 Table C.l. Reconstructed composite particles used in the SemiExcl skim. Parent Daughters Daughter requirements D H D U7r+ ImD*+ - mDO;r+ I < 2 MeV, PDQ < 2.5 GeV, PD*+ > 0.5 GeV D U K 7r+ ImDo - mK-;r+ I < 15 MeV K-7r+ 7r0 ImDo - mK-;r+;rO I < 25 MeV K-7r+ 7r+ 7r- !mDo - mK-;r+;r+;r-! < 15 MeV K°7r+ 7r- ImDo - mKg;r+;r-1 < 20 MeVs D+ K 7r+ 7r+ ImD+ - mK-;r+;r+ I < 20 MeV, 1.0 < PK-;r+;r+ < 2.5 GeV K-7r+ 7r+ 7r0 ImD+ - mK-;r+;r+;rO I < 30 MeV, 1.6 < PK-;r+;r+;rO < 2.5 GeV K°7r+ ImD+ - mKO;r+ I < 20 MeV, 1.0 < PKO;r+ < 2.5 GeVs s S K°7r+ 7r-7r+ ImD+ - mK8;r+;r-;r+ I < 30 MeV, 1.6 < PK8;r+;r-;r+ < 2.5 GeVs K 07r+ 7r0 ImD+ - mKg;r+;rO I < 30 MeV, 1.0 < PKg;r+;rO < 2.5 GeVs K U 7r+7r 0.47267 < m;r+;r- < 0.52267 GeV, 0.45 < m poca < 0.5s 7ru "f''f 0.115 < m"("( < 0.150 GeV, E"( > 0.3 GeV,L"( < 0.8 116 Table C.2. Masses of particles used in making the seed in the SemiExcl skim. mass value (MeV) m*u 2007D mO 1865D m+ 1869D 117 BIBLIOGRAPHY [1] R. Barate et al. (LEP Working Group for Higgs boson searches), Phys. Lett. B565, 61 (2003), hep-ex/0306033. [2] Phys. 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