A SEARCH FOR EMERGING JETS IN THE DIJET INVARIANT MASS
SPECTRUM USING 139 FB−1 OF PROTON-PROTON COLLISION DATA AT
A CENTER-OF-MASS ENERGY OF 13 TEV WITH THE ATLAS DETECTOR
by
AARON KILGALLON
A DISSERTATION
Presented to the Department of Physics
and the Division of Graduate Studies of the University of Oregon
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
September 2022
DISSERTATION APPROVAL PAGE
Student: AARON KILGALLON
Title: A Search for Emerging Jets in the Dijet Invariant Mass Spectrum Using 139
fb−1 of Proton-Proton Collision Data at a Center-of-Mass Energy of 13 TeV With
the ATLAS 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
David Strom Advisor
Davison Soper Core Member
Michael Kellman Institutional Representative
and
Krista Chronister Vice Provost for Graduate Studies
Original approval signatures are on file with the University of Oregon Division of
Graduate Studies.
Degree awarded September 2022
ii
© 2022 AARON KILGALLON
This work is licensed under a Creative Commons
Attribution-NonCommercial-NoDerivs (United States) License.
iii
DISSERTATION ABSTRACT
AARON KILGALLON
Doctor of Philosophy
Department of Physics
September 2022
Title: A Search for Emerging Jets in the Dijet Invariant Mass Spectrum Using 139
fb−1 of Proton-Proton Collision Data at a Center-of-Mass Energy of 13 TeV With
the ATLAS Detector
A search for emerging jets in the dijet topology is presented here using
√
139 fb−1 of s = 13 TeV Run 2 ATLAS proton-proton collision data. Emerging
jets constitute a class of dark jet models that have long-lived hadronization
components, resulting in unique signatures within particle detectors. These jet
signatures are the result of phenomenological considerations of self-interacting
dark matter. These models provide an explanation for the baryon-antibaryon
asymmetry as well as a well-motivated dark matter candidate particle, which make
them particularly compelling. Due to the unusual nature of these jets containing
high displaced track and displaced vertex multiplicities that vary significantly on
the dark sector parameters, machine learning techniques such as unsupervised
classification are ideal in the search for these types of models. A Classification
Without Labels method known as the CWoLa method was used to extract limits
iv
on heavy Beyond the Standard Model vector boson Z’ particles that produce pairs
of emerging jets in the large-R dijet topology. Limits were set on the cross-sections
of these signatures and exclude Z’ particles decaying to emerging jets from 10 fb to
2 fb between masses of 1.3 TeV and 4.0 TeV. Production of Z’ particles with masses
up to 3.1 TeV and a fixed 20 GeV width were excluded for dark sector couplings
down to 0.015. Future considerations for emerging jets analyses are shown in the
context of dedicated emerging jets triggers that were designed for use at ATLAS in
Run 3.
This dissertation contains previously published and unpublished material and
is not an official ATLAS result.
v
TABLE OF CONTENTS
Chapter Page
I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Analysis Motivation . . . . . . . . . . . . . . . . . . . . . . . . . 1
II. THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. The Dark Matter Problem and Opportunities for Discovery . . . 5
2.2. Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3. QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4. Hidden Valley Models . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5. Parton Distribution Functions . . . . . . . . . . . . . . . . . . . 20
2.6. Vector Boson Interactions . . . . . . . . . . . . . . . . . . . . . . 21
III. DETECTOR AND ACCELERATOR . . . . . . . . . . . . . . . . . . . 27
3.1. Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2. Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3. Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4. Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . 42
3.5. Hadronic Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6. Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . 45
vi
Chapter Page
3.7. Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.8. Data Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.9. Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.10. Jet Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.11. Dijets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
IV. ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1. Dijet Bump Hunt Searches . . . . . . . . . . . . . . . . . . . . . 67
4.2. Data-Driven Background Estimate . . . . . . . . . . . . . . . . . 67
4.3. CWoLa Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4. Monte Carlo Events . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.5. Data Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.6. Bump Hunt Analyses . . . . . . . . . . . . . . . . . . . . . . . . 90
4.7. Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.8. CWoLa Method Validation . . . . . . . . . . . . . . . . . . . . . 99
4.9. Signal Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.10. Signal Search Phase . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.11. Validation Region Studies . . . . . . . . . . . . . . . . . . . . . . 118
4.12. Limit-Setting Phase . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.13. Systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.14. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
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Chapter Page
V. FUTURE STUDIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.1. Run 3 Emerging Jets Triggers . . . . . . . . . . . . . . . . . . . . 137
VI. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
APPENDIX: APPENDIX1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
A.1. Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
A.2. Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
REFERENCES CITED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
viii
LIST OF FIGURES
Figure Page
1.1. A schematic of pair production of jets from a pair of dark quarks that
emerge within a detector [1]. . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1. The Standard Model [2] of particle physics, showing all fundamental
particles in the model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2. Graphical representation of the interface between the dark sector and
the SM [1]. The dark energy scale ΛD is roughly at the same energy
scale as that of QCD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3. Feynman diagram of Z’ production from a down/anti-down quark pair
interaction. The dark quarks (Qd) will hadronize in the dark sector and
emerge in a detector due to their small coupling to the Standard
Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4. A graphical representation of how color confinement produces jets [3] in
the non-perturbative regime of the Lund string model. A back-to-back
pair of colored quarks separate in the center-of-mass frame and radiates
gluons and pairs of quarks / anti-quarks - this process continues until
around the energy scale of QCD. The attractive forces between the pair
narrow the color flux into a tube and the stored energy increases
linearly with the separation. At energies above the QCD energy scale,
this tube splits into sets of hadrons that continue their own
hadronization process until the average energy is below the energy scale
of QCD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1. The CERN accelerator complex, showing the four main experiments on
the ring, the linear accelerators and booster rings, and various smaller
experiment [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2. The ATLAS Detector layout showing the detector’s critical
subdetectors and magnet systems. Human figures are shown on the left
to demonstrate the scale of the detector. . . . . . . . . . . . . . . . . . . 32
3.3. The ATLAS Coordinate systems. . . . . . . . . . . . . . . . . . . . . . . 32
3.4. Average ATLAS µ profiles during data-taking years in Run 2 [5]. . . . . 36
ix
Figure Page
3.5. The ATLAS Inner Detector showing the various tracking layers and
technologies used for charged particle identification [6]. . . . . . . . . . . 37
3.6. The track reconstruction geometry at ATLAS. Relative to a defined
vertex, geometric descriptions of the closest approach and the
kinematics are reduced to 6 variables [7] . . . . . . . . . . . . . . . . . . 38
3.7. Electromagnetic interaction lengths as a function of η for the
electromagnetic calorimeter system [6]. . . . . . . . . . . . . . . . . . . . 44
3.8. Hadronic interaction lengths as a function of η for the hadronic
calorimeter system [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.9. A flowchart representing the data flow of events through the
data-acquisition system at the ATLAS detector. [8] . . . . . . . . . . . . 48
3.10. Trigger efficiency curves showing the effect of trimming on the large-R
trigger turn on points. The effect of standard pileup subtraction
methods is shown for reference [9]. . . . . . . . . . . . . . . . . . . . . . 52
3.11. A demonstration of the Anti-Kt algorithm for a simulated event that
shows the typical clustering of energy deposits for R=1.0 jets [10]. . . . . 54
3.12. A demonstration of the pileup correction as applied to reconstructed
jets matched to truth jets with pT = 25 GeV [11] as a function of (a)
NPV and (b) 〈µ〉. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.13. In-situ methods such as γ+jet measurements are used to validate the
previous calibration steps [12]. The JES response is shown to be
calibrated within 2%, and the JMS response is consistent within error
bounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.14. Calculated JER for R = 1.0 jets after application of the JES and JMS
calibrations [12]. An analytic fit to the MC JER√was used in the
systematic evaluation for this analysis - f(p ) = a2/p2 + b2T T /p
2
T + c
with a=5.018×10−4, b=1.092, and c=-2.090×10−2. . . . . . . . . . . . . 64
3.15. A high-mass dijet data event with mjj = 3.91 TeV illustrating a
back-to-back jet pair originating from a single vertex with 5
reconstructed pileup vertices. [13] . . . . . . . . . . . . . . . . . . . . . . 65
4.1. A visual demonstration of the SWiFt fitting mechanism for a given
window width [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
x
Figure Page
4.2. Visual demonstration of the CWoLa method combined with a SWiFt
fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3. A Feynman diagram of the Z boson + photon process used to
determine the associated track d0 distributions from QCD ISR jets. . . . 74
4.4. The d0 resolution function from Z boson recoil jet studies and its
analytical functional fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5. Z’ samples with mass 1500 GeV and data leading jet PTF distributions
for a variety of lifetimes and dark models. The data are scaled by an
appropriate factor to fit the plotting scale. . . . . . . . . . . . . . . . . . 77
4.6. QCD y∗ distributions for a given interacting parton at an energy scale
s. Forward scattering cross-sections tend to dominate in QCD due to
its t-channel predominance. . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.7. Invariant mass distributions for R=0.4 jets (top) and R=1.0 jets
(bottom) for a variety of 600 GeV Z’ samples and low-pT simulated
QCD background (labeled as JZ2). Significant model and lifetime
dependence is seen; this illustrates that at high dark meson lifetimes,
the signal follows the background distribution due to the missing
energy in the events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.8. A 1500 GeV Z’, cτ = 1 mm, Model A event showing the leading central
jet in the event and tracks with pT greater than 2 GeV, showing the
lack of reconstructed tracks associated to the leading jet in the
event. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.9. A 1500 GeV Z’, cτ = 5 mm lifetime, Model B event. Top left -
beampipe-transverse view of the event with pT> 50 GeV (R = 1.0) jets
and pT> 2 GeV tracks. Top right - same as the left plot but showing
all tracks associated to the PV. Bottom row, oblique projections
showing calorimeter energy deposits, jets, and all the tracks in the
event. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.10. A 1500 GeV Z’, cτ = 10 mm, Model B event with pT > 50 GeV
(R = 1.0) jets. Right and bottom plots - oblique and beamline
transverse plots with pT > 2 GeV tracks associated to the PV. . . . . . 84
4.11. Offline pT trigger efficiency plot for HLT j460 a10 lcw subjes L1J100
triggered events relative to HLT j390 a10t lcw jes L1J100 events for
2018 Period K data. Events are fully efficient down to the mjj =
1300 GeV cut with the conservative assumption of the mjj turn on
xi
Figure Page
point equaling 2× the pT turn on point. This trigger is the highest
pT threshold trigger for the unprescaled primary triggers, so the mjj
efficiency point here is applicable to the other primary triggers in the
dataset selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.12. Leading offline jet mass trigger efficiency plot for
HLT j460 a10t lcw jes L1J100 triggered event relative to
HLT j260 L1J75 events for 2018 Period K data. Triggered events are
shown here to be fully efficient down to the 35 GeV offline mass cut. . . 88
4.13. A visualization of the network architecture used for this analysis. Note
that the dropout layer is not shown. . . . . . . . . . . . . . . . . . . . . 94
4.14. Sideband 8’s (upper row) and 14’s (lower row) evolution of the AUC
(left) and loss function (right) over the training epochs. A small
amount overfitting is demonstrated by these networks, however
generalized hyperparameters that prevented overfitting for every bin
were difficult to find. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.15. Effects from varying the signal region width used in training. The
injected signal was a 2000 GeV Z’ with cτ=1 mm and Model A. The
signal peak at around bin 15 is enhanced the most by the 1 bin signal
region. The spuriously-selected events in the high mass bins away from
the peak are likely selected due to the autoencoder effect of this
method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.16. Invariant mass distributions of the signal samples sorted into 5 different
lifetime sets. Models A-E are shown at each defined lifetime. The
overall number of signal events are defined by the signal cross section
which is a function of the Z’ quark coupling gq, which is set to 0.001 for
these signal samples. The data are scaled to fit the plot’s scale. . . . . . 102
4.17. Leading jet mass distributions for 5 different signal lifetimes. Models
A-E are shown at each defined lifetime for production during Run 2.
The data distributions are scaled to show on the same plot. . . . . . . . 103
4.18. Leading PTF distributions for 6 different signal lifetimes. Models A-E
are shown at each defined lifetime, and the data are scaled to fit the
plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.19. Signal injections (2000 GeV Z’, cτ = 1 mm, Model A) done at 2000x and
20000x strength relative to the cross-sections defined from gd = 0.001.
The BumpHunter p-values for these injections were 0.77 and 0.0 for
these spectra after application of the 10% NN score cut. . . . . . . . . . 108
xii
Figure Page
4.20. Signal injections (2000 GeV Z’, cτ = 1 mm, Model A) done at 10x and
100x strength relative to the cross-sections defined from gd = 0.001 after
application of the 1% NN score cut. . . . . . . . . . . . . . . . . . . . . 108
4.21. Selection efficiencies as a function of leading and subleading jet mass
and leading jet promptTrackFrac distributions for data and an injected
1500 GeV Z’ signal. The trained neural networks tended to learn
information about high jet mass events and preferred to use these mass
variables as a discriminant. . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.22. Selected signal events and Gaussian fits from a 2000 GeV Z’ injected
with signal strength 50 after application of a 10% NN score cut. . . . . . 110
4.23. Signal injections (1500 GeV Z’, Model A) done at 50x (2σ fluctuations
in peak bin), 100x, and 200x strength relative to the cross-sections
defined from gd = 0.001. The top and bottom plots correspond to
cτ=1 mm and cτ=2 mm samples respectively. . . . . . . . . . . . . . . . 111
4.24. NN Signal efficiencies and Signal Significances for 1% NN score cut
criteria on (1500 GeV Z’, Model A, cτ = 2 mm). Large enhancements in
the signal sensitivity are seen relative to the 10% NN score cuts. . . . . . 111
4.25. Signal injections (1500 GeV Z’, Model B) done at 50x (2σ fluctuations
in peak bin), 100x, and 200x strength relative to the cross sections
defined from gd = 0.001. The top and bottom plots correspond to
cτ = 1 mm and cτ = 2 mm samples respectively. . . . . . . . . . . . . . . 112
4.26. NN Signal efficiencies and Signal Significances for 1% NN score cut
criteria on (1500 GeV Z’, Model B, cτ = 2 mm). Large enhancements in
the signal sensitivity are seen relative to the 10% NN score cuts. . . . . . 112
4.27. Signal injections (1500 GeV Z’, Model C) done at 50x (2σ fluctuations
in peak bin), 100x, and 200x strength relative to the cross sections
defined from gd = 0.001. The top and bottom plots correspond to
cτ = 1 mm and cτ = 2 mm samples respectively. . . . . . . . . . . . . . . 113
4.28. NN Signal efficiencies and Signal Significances for 1% NN score cut
criteria on (1500 GeV Z’, Model C, cτ = 2 mm). Large enhancements in
the signal sensitivity are seen relative to the 10% NN score cuts. . . . . . 113
4.29. Signal injections (1500 GeV Z’, Model D) done at 50x (corresponding
to 2σ fluctuations in peak bin), 100x, and 200x strength relative to the
cross sections defined from gd = 0.001. The top and bottom plots
correspond to cτ = 1 mm and cτ = 2 mm samples respectively. . . . . . . 114
xiii
Figure Page
4.30. NN Signal efficiencies and Signal Significances for 1% NN score cut
criteria on (1500 GeV Z’, Model D, cτ = 2 mm). Large enhancements in
the signal sensitivity are seen relative to the 10% NN score cuts. . . . . . 114
4.31. Signal injections (1500 GeV Z’, Model E) done at 50x (2σ fluctuations
in peak bin), 100x, and 200x strength relative to the cross sections
defined by gd = 0.001. The top and bottom plots correspond to
cτ = 1 mm and cτ = 2 mm samples respectively. . . . . . . . . . . . . . . 115
4.32. NN Signal efficiencies and Signal Significances for 1% NN score cut
criteria on (1500 GeV Z’, Model E, cτ = 2 mm). Large enhancements in
the signal sensitivity are seen relative to the 10% NN score cuts. . . . . . 115
4.33. Global signal selection efficiencies for 3000 GeV (cτ = 1 mm) samples by
NNs in overall spectrum as a function of injected signal strength
(efficiencies after 10% NN score quantile cut.) The overall signal
efficiency is not necessarily the target metric of interest in bump hunt
searches, but do indicate the general trend of the NN performance. . . . 116
4.34. Global signal selection efficiencies after a 1% NN score quantile cut for
1500 GeV (cτ = 1 mm) samples by NNs in overall spectra as a function
of injected signal strength. . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.35. BumpHunter outputs from application to the 10% NN score cut
Validation region spectrum. The upper plot indicates the formed
spectrum and the maximal BumpHunter bump region, its tomography
plot is shown on the bottom right, and the distribution of the
BumpHunter test statistic is shown on the bottom right. Bumphunter
evaluates the p-value for a range of intervals across the spectrum and
uses the range with the minimal p-value as the maximum discovery
region; these intervals are shown in the tomography plot. . . . . . . . . . 120
4.36. BumpHunter outputs from application to the 1% NN score cut
Validation region spectrum. The upper plot indicates the formed
spectrum and the maximal BumpHunter bump region, its tomography
plot is shown on the bottom left, and the distribution of the
BumpHunter test statistic is shown on the bottom right. . . . . . . . . . 121
4.37. Signal efficiencies from application of the derivation-level cuts, the
analysis cuts, and the NN selection for different lifetime samples. The
envelope of the five model variations defines the error bands of the
total efficiency and is an approximation of the hadronization
systematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
xiv
Figure Page
4.38. Signal efficiencies from application of the derivation-level cuts, the
analysis cuts, and the NN selection for Model A - E samples. The
envelope of the five model variations defines the error bands of the
total efficiency. This can also be interpreted as an approximation of the
effects of lifetime and width variance of the models on the limits,
although this is beyond the scope of the analysis presented here. . . . . . 126
4.39. The three parameter analytical function fit to the spectrum after the
10% NN score cut. The BumpHunter p-value score for this spectrum
was 0.90 for the nominal background, but the final value after inclusion
of the fit systematics was 0.917 ± 0.009. The BumpHunter tomography
plot is shown in the bottom plot, indicating the local p-value intervals
in the algorithm. The bump of maximum local significance was
between 1998 GeV and 2251 GeV with local significance 2.37932. The
global fit parameters were [7.84855×10−11, -21.1505, -12.4406] with the
SWiFt fit χ2/ndf = 0.711501. . . . . . . . . . . . . . . . . . . . . . . . . 130
4.40. The three parameter analytical function fit to the spectrum after the
1% NN score cut. The BumpHunter p-value score for the nominal
spectrum was 0.918, and after inclusion of systematics, the evaluated
p-value was 0.887 ± 0.01. The BumpHunter tomography plot is shown
in the bottom plot, indicating the local p-value intervals in the
algorithm. The bump of maximum local significance was between
1451 GeV and 1573 GeV with local significance 1.41454. The global fit
parameters were [4.3384×10−21, -51.8578, -21.5426] with the SWiFt fit
χ2/ndf=0.483154. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.41. (left) Gaussian BAT limits on Z’ production from the 10% NN score
cut spectrum. (right) Fiducial cross-section limit estimates after signal
efficiency corrections. 1 and 2 sigma bands on the expected limits are
shown. The black line indicates the fiducial cross-section for Z’
production with a gq coupling of 0.015. . . . . . . . . . . . . . . . . . . . 134
4.42. (left) Gaussian BAT limits on Z’ production from the 1% NN score cut
spectrum. (right) Fiducial cross-section limit estimates after signal
efficiency corrections. 1 and 2 sigma bands on the expected limits are
shown. The black line indicates the fiducial cross-section for Z’
production with a gq coupling of 0.015. . . . . . . . . . . . . . . . . . . . 135
5.1. Emerging jet trigger signal efficiencies with and without jet preselection
applied for a j175 seeded trigger with a 225 GeV preselection.
Efficiencies are computed for baseline low-mass Z’ models and one
xv
Figure Page
baseline H→ss sample (the decay of a 600 GeV BSM Higgs into two
150 GeV scalars with a cτ = 3.3 m.). . . . . . . . . . . . . . . . . . . . . 139
5.2. Trigger efficiency plots for the 200 GeV seeded emerging jets trigger
chain determined via the trigger simulated in BSM Higgs to LLP scalar
(1 TeV → 475 GeV) signal events. These indicate that the trigger will
be fully efficient in pT at approximately 250 GeV, as compared to over
500 GeV for a standard unprescaled large-R jet trigger. The trigger
curve is scaled to the fraction that pass the PTF cut to allow a plateau
at 1.0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.3. Invariant mass distributions and invariant mass resolution for 600 GeV
Z’ samples with lifetimes 1 mm (top) and 10 mm (bottom). The PFlow
algorithm has a definite lifetime dependence that affects the number of
reconstructed tracks associated to the jet, making the non-prompt jet
appear like a photon to the algorithm at sufficient lifetimes. . . . . . . . 141
A.1. Various jet and jet-track selections on R-Hadron samples with 0.1 ns
(left) and 10 ns (right) lifetimes. The timing selection refers to a
selection on the offline jet timing, the d0 selection refers to a selection
with a cut on the highest d0 track associated to the jet, and the inverse
pT cut is the PTF algorithm applied with varying cofactors in front of
the resolution function. . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
xvi
LIST OF TABLES
Table Page
2.1. The dark models (A - E) considered by this analysis. . . . . . . . . . . . 20
2.2. The dark sector particles considered in these simplified dark shower
models. Similarly to their analogous particles in the visible sector, dark
gluson gv, Z’ bosons, dark quarks Qd, and the dark rho particles decay
almost immediately after production. . . . . . . . . . . . . . . . . . . . . 25
2.3. The estimated cross sections from Pythia for each generated signal
mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.1. The lowest pT unprescaled primary large-R jet triggers operating
during Run 2 data-taking periods. . . . . . . . . . . . . . . . . . . . . . 86
4.2. Search and Validation region cuts applied to the data. The Validation
region cuts are identical unless specified otherwise. . . . . . . . . . . . . 89
4.3. Global signal selection efficiencies for a range of signal injection
strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.4. Unfiltered signal widths from Gaussian fits to cτ = 1 mm samples.
Models B and E have mass hierarchies closest to QCD and therefore
generally have smaller widths. . . . . . . . . . . . . . . . . . . . . . . . . 109
4.5. Signal widths from Gaussian fits to cτ = 1 mm samples after application
of the trained NNs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.1. HLT-level cuts applied for each emerging jet trigger topology. . . . . . . 137
A.1. Signal efficiencies for 1.5 TeV samples. . . . . . . . . . . . . . . . . . . . 154
A.2. Signal efficiencies for 2 TeV samples. . . . . . . . . . . . . . . . . . . . . 155
A.3. Signal efficiencies for 3 TeV samples. . . . . . . . . . . . . . . . . . . . . 156
A.4. Signal efficiencies for 4 TeV samples. . . . . . . . . . . . . . . . . . . . . 157
xvii
CHAPTER I
INTRODUCTION
1.1. Analysis Motivation
Despite the successes of the Standard Model (SM) [15] of particle physics in
providing an excellent model and explanation for interactions of visible matter
over a large energy scale, a number of unknowns in physics prompt the need
for a more comprehensive model of the natural world. However, the nature and
phenomenology of dark matter, the baryon / anti-baryon asymmetry seen in the
Universe, and recent tensions in Standard Model measurements [16, 17] point to
a large scope of unexplored particles that have yet to be directly measured. A
number of searches are ongoing with the ATLAS experiment at the Large Hadron
Collider (LHC) for these undiscovered particles; the theoretical phenomenology
of their interactions range from Super-Symmetric models to those of exotic dark
sectors that have couplings to SM particles.
Indirect evidence for dark matter makes searches for dark matter particles
promising avenues of discovery for new physics, and a direct particle discovery
would provide a massive boost in understanding of the likely interconnected
problems currently observed in the Universe at a wide variety of energy scales.
The dark matter hypothesis is a potential resolution for a generic set of energy
density over-measurements in the Universe that we currently have no confirmed
explanation for. Dark matter composes more than 80% of the matter density
and more than 20% of the total observed energy density observed in the Universe
[18]. It has no observed coupling with the photon and so it cannot be observed
1
directly in astronomical observations, but it does interact gravitationally and so
its existence can be inferred from large-scale observations of galaxies and galaxy
structures.
Dark matter has been traditionally considered in the context of Weakly
Interacting Massive Particles (WIMPs) that are a relic from the Big Bang era
[19], and while WIMP models are well-considered in the context of large-scale
galactic structure, observations at smaller galaxy-sized scales tend to point towards
models of self-interacting dark matter. The self-interacting aspect of these models
is due to the wide mass hierarchy and gauge structure of the proposed dark
sector where dark particles have strong couplings to each other, as compared
to the isolated and inert particles seen in other WIMP-like models. The set of
dark models that encompass these types of self-interacting dark sectors can also
naturally incorporate an explanation for the baryon / anti-baryon asymmetry in
the Universe when a portal from the dark sector to the visible matter sector is
considered and when the energy scale of dark matter is similar to that of visible
matter.
These two general ideas synergize into a unique topology of events that could
be observed in proton-proton collisions at the LHC. Known as “emerging jets,”
this topology involves the creation of either a pair of bifundamental scalars from
gluon fusion that decay into 4 fundamental particles that shower to form both
dark and visible jets, or the production of a vector boson Z’ that decays to pairs
of dark quarks that hadronize within the dark sector to form pairs of dark jets.
The small sector-to-sector coupling between the dark and visible sectors can cause
dark jets to eventually manifest as visible jets, and the small coupling to the SM,
in tandem with the similar energy scale between the two sectors, can make dark
2
mesons long-lived on a wide range of lifetime scales [20]. Therefore, as the progress
of the dark shower continues from the production point, this small coupling from
the GeV (giga electronvolts) to TeV (tera electronvolts) mass hierarchy in the
dark sector creates a cascade of emerging energy from the dark particle decays,
producing a set of secondary vertices and displaced tracks. This is known as
an emerging jet, and its unexplored dijet topology will be investigated in this
analysis. Figure 1.1 is a diagram showing pairs of emerging jets in the tracking
and calorimeter regions of a particle detector.
FIGURE 1.1. A schematic of pair production of jets from a pair of dark quarks
that emerge within a detector [1].
The theory of these dark decays is well-motivated in the context of the many
large-scale issues associated with dark matter. If the similarity between the energy
density of dark matter and visible matter is not a coincidence, then the baryon
/ anti-baryon asymmetry that’s seen in both the visible and dark sectors could
3
be due to the same fundamental asymmetry if there is a portal between these
sectors. This requires the dark energy scale to be on the order of the visible sector
(1 GeV - 10 GeV) if the number of dark and SM baryons produced during the Big
Bang are the same. The TeV scale of the fundamental fields in the dark sector, in
combination with this dark sector energy scale and the small SM coupling, ensures
that dark mesons in the theory have long lifetimes. The emergent SM particles
from decays of these dark meson are therefore produced at macroscopic (> 1 mm)
distances from their production point [1].
Dark jet topologies have been explored in the general dark jet searches that
have been ongoing at the LHC [21, 22], however, the unique topology produced by
the long lifetimes of the dark mesons provides an interesting search case. Rather
than relying on model-motivated jet substructure cuts or other specific event
attributes, a combination of an invariant mass dijet search with a model-agnostic
unsupervised machine learning technique allows a much more involved search for
these dark jets with emerging qualities, with less model dependence and enhanced
signal sensitivity. This thesis presents a first look at emerging jet signatures in the
dijet topology as observed by the ATLAS detector at the LHC using 139 fb−1 of
Run 2 data.
4
CHAPTER II
THEORY
2.1. The Dark Matter Problem and Opportunities for Discovery
There is overwhelming evidence for the existence of an abundance of
gravitationally-interacting unseen matter in the Universe. Evidence ranging
from rotation curves of galaxies, lensing effects, and the well-fitting nature of
inflationary models containing dark matter all strongly point to an overabundance
of matter that is not directly observable astronomically. The overall structure and
effects of dark matter can be indirectly observed, but a specific particle detection
and measurement would provide the jumping-off point to understanding the realm
of dark particles that are currently unexplored. There is potential for these effects
to be due to some other models such as modified gravity [23], however the focus on
this analysis is the search for detector-observable models.
Models that explain dark matter vary significantly in their phenomenology
and origin of the measured energy densities of visible and invisible matter in the
Universe. Standard cosmological models assume the existence of dark matter
as Cold Dark Matter (CDM) with some now-frozen relic density that is residual
from earlier phases of the universe. These CDM models generally contain Weakly-
Interacting Massive Particles (WIMPs); they are stable due to properties of their
respective theories and match the frozen relic abundance.
The CDM assumption generally fits well within the standard cosmological
model called ΛCDM [24], however, recent phenomenological studies indicate that
dark matter might [25] have a self-interacting component. The overall density of
5
galaxy clusters and large-scale structure appear to be consistent with the ΛCDM
model. N-body simulations of galaxy clustering [25] show good agreement between
large-scale clusters simulated with CDM dark matter candidates and dark matter
candidates that have a self-interacting component. However, discrepancies are
noted between these classes of models in the central halo (envelope) densities of
matter in galaxies, dwarf spheroid densities, and smaller-scale core substructure in
galaxies.
Known as the core-cusp problem [26], simulations of galaxy structure
formation indicate disparate core and halo densities from what is observed in
a large range of dark parameter space. N-body simulations show a relatively
over-dense core with rapidly dropping densities in the halo, however, observed
low-mass galaxy rotational curves tend to be consistent with flat dark matter
density profiles. In simulations incorporating dark matter with a self-interacting
cross-section, this discrepancy can be resolved by this theory in the range up to a
cross-section (interaction probability) per mass ratio of σ/m < 1 cm2/g. This is
comparable to the baryonic interaction cross-section - for protons interacting at
10 GeV, the proton-proton cross section is σ/m ≈ 0.023 cm2/g.
Additionally, the smaller-scale structures of galaxy clusters are significantly
different from the structures seen in simulations. The observed density of dwarf
galaxies and similar smaller-scale structures are several orders of magnitude
smaller than those predicted by CDM models [27]. This seems to occur in a
range of different star-forming regions, indicating that internal pressures such
as outgassing from star-forming regions may not provide a good explanation for
the structure-smearing effect seen in observations. In simulation with dark self-
interactions in the range of σ/m ≈ 0.1 cm2/g, both these smaller-scale structures
6
and the core density profiles appear to agree with observational constraints. In
order for kinetic energy from the core star-forming region to be flatly distributed,
the average interaction rate Γ(r) ≈ ρ(r) · (σ/m) vrms(r) must not exceed the age of
the structure, and so the center-of-mass velocity of the collisions is accounted for in
these cross-section per mass ratio estimates.
The number of baryons and anti-baryons produced during the Big Bang
are expected to be equal due to symmetries of Standard Model interactions.
However, the existence of the universe as we know it implies that some unknown
mechanism produced a slight asymmetry in the annihilation of early baryon/anti-
baryon pairs, leaving the visible matter as we see it now. No complete known
dark-baryon / dark-anti-baryon annihilation is seen due to the actual existence
of dark matter, so if equal dark baryon / dark-anti-baryon amounts were produced
during the Big Bang, an additional dark asymmetry must exist. If the unknown
asymmetry that produced the matter / anti-matter misbalance can be attributed
to some physics involving a self-interacting dark sector, then an interaction at
the same energy scale in the dark sector can explain the dark-matter asymmetry
due to the bifundamental interactions in the portal between the sectors. To be
consistent with the N-body simulated small-scale structure, the cross-section per
mass ratios must satisfy σ/m ≈ 0.1 cm2/g. However, the dark baryon cross-
section must be estimated from recent limits from direct detection experiments,
and the mass depends on the dark sector model of choice. With the estimate that
the upper limit of the dark matter cross-section is on the order of 1 b (1 barn =
1×10−34 cm2) [28] and if the dark sector baryon energy scale is similar to that of
QCD (O(5 GeV)), then σ/m = 0.112 cm2/g.
7
A recent set of phenomenology papers [1, 20] explore the unique model and
phenomenology of self-interacting dark matter in the context of a hidden valley
of dark particles. The gauge structure and properties of the confined dark sector
were presented by the authors, and the phenomenology of the 4-jet and 2-jet final
states were investigated for the LHC experiments. The gauge bosons associated
with this hidden valley would be produced in proton-proton collisions due to this
portal from the dark sector to the SM, and detection of these expected bosons at
the mass scale of hundreds of GeV to several TeV is possible by reconstructing
their resulting byproducts that are called “emerging jets.”
2.2. Standard Model
The Standard Model is a remarkably accurate Quantum Field Theory that
describes the nature and interactions of all known fundamental particles in the
Universe up to the TeV energy scale. Built on generations of successive sets
of experimental data and theoretical investigations, it has proven itself in its
naturalness and predictive ability over orders of magnitudes in energy scales and
cross-sections. With the sequence of particle discoveries made over the last 50
years and new theories to describe their interactions, it is a combined effort of
many physicists to build this remarkable theory. It is a union of the ElectroWeak
theory of Glashow, Weinberg, and Salam [29, 30] with the theory of the strong
interaction [31]. The ElectroWeak aspect of this theory merges the interactions
of photons and electrons in Quantum Electrodynamics (QED) with the dynamics
of the Weak force. The incorporation of Quantum Chromodynamics within this
theoretical framework brought the strong force and its color dynamics in to
explain the structure and interactions of baryons such as the proton. The Higgs
8
mechanism and subsequent prediction and discovery of the Higgs boson gave the
framework an explanation for the mass of the elementary particles. Finally, the ad-
hoc incorporation of neutrino masses gave an explanation to flavor-mixing in the
neutrino sector, and many further years of work have been spent constraining the
various parameters of the SM couplings.
The forces in the Universe are mediated by Gauge bosons (photons, Z and
W bosons, and gluons). The couplings of Gauge bosons define the type and
strength of the forces that they correspond to, which are the electromagnetic,
weak, and strong forces, however, the gravitational force is not incorporated into
the SM. Matter seen in everyday life, such as protons and electrons, primarily
interact via electroweak interactions. Nuclear forces are mediated by the weak and
strong nuclear forces, and large-scale structure of the Universe is dictated by the
gravitational force. The discrepancies from the Standard Model are seen at large
scale variations such as Universe-ranging energy inconsistencies in matter densities
and subatomic scale anomalies in measured flavor interactions. The wide range of
these discrepancies point to not just a misunderstanding of one aspect or sector
of interactions, but to a fundamentally-needed reshaping of our understanding of
particle physics.
The elementary particles in the standard model are the 12 primary fermions
(spin 1/2 particles), the 5 gauge bosons (spin 1 particles), and the scalar Higgs
boson (a spin 0 scalar). The 6 fermions that are associated with the electroweak
interaction are the electron, muon, tau, electron-neutrino, muon-neutrino, and
tau-neutrino, and the 6 fermions associated with the strong force are the up,
down, charm, strange, bottom, and top quarks. Each of these has their own
corresponding anti-particle that carries the opposite quantum numbers. The
9
electroweak interactions are mediated by the photon, the Z boson, and the W+/−
bosons, and a hypothetical graviton boson might mediate the gravitational force.
The discovery of the Higgs boson in 2012 effectively completed the theory, as
the Higgs mechanism provides an elegant explanation for how elementary particles
attain mass [32, 33]. The Higgs boson provides the mechanism that gives particles
their mass via interaction with the Higgs field; this is a symmetry violation called
the Higgs mechanism. A considerable validation of the model was made by the
discovery of the Higgs boson by the ATLAS and CMS collaborations at the LHC,
with validation of the predicted interactions of this boson within the Standard
Model and a measured mass of 125 GeV [34, 35].
The strong force is, appropriately, the strongest of the forces. At a distance
scale of the radius of the proton, ≈ 1 × 10−15 m, it has a strength of αs ≈ 1. The
weak nuclear force mediates nuclear decay and fusion and has a greatly reduced
strength, with an effective strength of ≈ 1 × 10−6 and an effective range of ≈ 1 ×
10−17 m. The electromagnetic force is mediated by the photon, with a strength of
αEM ≈ 1/137.
With the exception of gravity, these fields were combined into a gauge-
invariant quantum field theory that has been consistently verified across a large
set of energy scales and interaction channels. The gauge invariance manifests the
set of gauge bosons that mediate the four “distinct” forces (the Electromagnetic,
Weak, Strong, and Gravitational forces) in the Universe, and the renormalizable
quality of the Standard Model ensure that perturbative calculations can be done to
accurately predict the probabilities of these mediated interactions.
The gauge structure of the Standard Model is
10
GSM = SU(3)× SU(2)× U(1), (2.1)
where SU(3) dictates the gauge structure of QCD, which is described by the set of
interactions of 3 colors mediated by 8 gluons. SU(2)× U(1) is the combined gauge
field theory describing the electroweak interactions that is spontaneously broken
by the Higgs mechanism. At a high enough energy scale, QED and the Weak
interactions combine under this structure. U(1) describes the Electromagnetic
force mediated by a single spin-1 boson with U(1) invariance, the photon.
FIGURE 2.1. The Standard Model [2] of particle physics, showing all fundamental
particles in the model.
Particles in this Quantum Field Theory are described as fluctuations in
fields, and scalars are represented as fundamental fields with the spin-0 property.
Fermions are represented by spin 1/2 fields, usually denoted by χ (x), and vector
bosons are spin-1 fields denoted as Aµ (x).
11
Nature requires certain symmetries to produce gauge bosons in gauge theory.
A local invariance of the Lagrangian density (L) of the theory inherently produces
gauge fields that manifest with a certain set of interactions. These interactions are
restricted by certain conditions such as whether they carry the charge relevant for
each interaction, and relevant conservation laws must also be followed.
The Weak force involves interactions of particles containing two types of
quantum numbers, weak isospin (T) and weak hypercharge (YW ). Fermions in
the SM have either right or left-handed chirality, which indicates whether their
spins align or anti-align with the vector of their momentum. T = 0 for right-handed
particles and T = 1/2 for left-handed particles.
The relationship between EM charge, Weak hypercharge, and weak isospin
is Q = T3 + YW/2, with T3 the third component of weak isospin. Neither the Z
nor the W bosons carry Weak hypercharge, but as the W boson carries EM charge,
any interaction involving the W boson must inherently change T3, indicating a
change of flavor. As the Z boson doesn’t carry EM charge or T3, a much wider set
of interactions is possible for the Z boson, for example the allowed couplings to
particle/anti-particle pairs of the same flavor.
2.3. QCD
The SU(3) component of the Standard Model is formed by the set of
interactions that mediate the strong force via color charges. Three colors are
specified, known as red, blue, and green, and the color charge is carried by gauge
bosons called gluons. Due to a property called color confinement [36], no free
particles can contain a net color charge, so stable hadrons must contain no net
color. Baryons are an overall zero-color state with three quarks and any number
12
of quark-antiquark pairs and of gluons. Gluons are the massless, neutral, and
bicolored carriers of this color; they carry one unit of color charge and one unit
of anti-color charge.
The representation of the gauge group can be reduced to a set of basis
vectors (generators) that do not commute due to the non-Abelian nature of the
group. The eight generators of the group correspond to the eight gluons seen in
nature, and the generators can be expressed mathematically as the Gell-Mann
matrices [31], Ta =
1λa, a = 1, ..., 8.2
The QCD Lagrangian therefore contains the set of couplings between fields of
color-interacting particles, the 6 fermions (anti-fermions) from the 3 generations of
quarks, and the gluon interactions. As the gluons carry color charge themselves,
they have their own gluon coupling, and so the radiative processes of a gluon
splitting can be difficult to compute in a showering process, especially in the non-
perturbative regime.
The QCD Lagrangian can be written as
6
1 ∑
L a a,µν µQCD = − G
4 µν
G + ψ̄q (iγ Dµ −mq)ψq, (2.2)
q=1
with Dµ = ∂µ + ig
λaGas µ the covariant derivative containing the fermion and gauge2
field interactions, and Gaµν = ∂ G
a − ∂ Gaµ ν ν µ − g f b cs abcGµGν with fabc the commutators
of the Gell-Mann matrices ifabc Tc = [Ta, Tb]. This contains up to quartic terms of
the gluon self-interacting, which is responsible for the color confinement properties
consistently observed in a variety of hadronic experiments.
13
2.4. Hidden Valley Models
As motivated in Section 1.1, a natural extension to the SM gauge group
involving a copy of QCD constrained in its own dark sector can provide an
explanation for dark matter. This extension that is specified with a set number
of dark flavors Nd adds to the set of gauge fields:
GSM × SU (Nd) . (2.3)
This extension is confined in the same manner as QCD, and the lightest baryon,
the dark matter candidate, is stable due to conservation of a quantum number
called “dark baryon number.” The mesons do not carry this quantum number and
are therefore allowed to decay within the available phase space.
Naturalness arguments point to the number of dark colors (Nd) being
consistent between the SM and any hidden sector that has QCD couplings;
therefore we consider models with Nd = 3 [1]. The connection of this dark sector
to the visible sector is formed by interactions of two bosons, the complex scalar Xd
and the vector boson Zµd (referred to as a Z’ from here on). These bifundamental
particles carry both QCD colors and dark colors, thereby acting as a portal
between the two sectors. The number of dark flavors ndf is set to seven to be
consistent with arguments made by Schwaller et. el. - the number of dark flavors
can be different from that of QCD, but must lie in the range 2≤ndf < 4 ·Nd. This
requirement is set to ensure that the sector behaved similarly as QCD; at above
this 4 · Nd threshold, the behavior of the dark sector is no longer asymptotically
free.
14
FIGURE 2.2. Graphical representation of the interface between the dark sector
and the SM [1]. The dark energy scale ΛD is roughly at the same energy scale as
that of QCD.
The phenomenology of the analysis is concerned with only the hadronic
production and dijet decays of the Z’. The Z’ is assumed to be leptophobic (not
coupling to either SM leptons or dark leptons) as flavor violations would otherwise
by seen in the Standard Model measurements, so only the hadronic couplings to
the SM and the dark sector are considered. The most simple extension to the
Standard Model Lagrangian (LSM) involving just dark quark (Qd) and Z’ hadronic
interactions can therefore be written as [1, 37],
L ⊃LSM
1
+ Q̄ µνd (D −mi d )Qd (− Gi i 4 d Gµν,d1 ′ )
+ M2Z µ
′ ′
Z + Z µµ gq q̄γµq + gdQ̄γµQ .2
The dark quarks are Dirac fermions and interact with the dark mediators with
strength gd, and the bifundamental Z’ boson also has a small coupling to the
SM with strength gq. G
µν
d are the dark gluon field tensors, and the couplings of
15
the dark fermions to the dark gauge fields are contained within their respective
covariant derivatives. The set of terms in this Lagrangian define the field density
of kinetic energy, the mass energy from self-interactions, gauge-field coupling, and
cross interactions between the various fields in the theory. The vector boson Z’
is assumed to couple vectorially to SM and dark quarks with coupling strengths
gq and gd respectively; it is this coupling to the SM that leads to the visible final
state of the hadronization byproducts.
Similarly to the QCD sector, the dark quarks can form quasi-stable dark
mesons. In the simple dark sector structure considered for this analysis, only
dark pions, dark quarks, and dark rhos were allowed to be formed in addition
to the dark gluons. The Hidden Valley implementation in Pythia contains a set
of partner particles to the SM quarks. These particles, named Ud, Dd, Cd, Sd,
Bd, and Td, are implemented in the sector as generically-name Fd particles and
are charged under both the SM and dark colors. These decay to both sectors to
a fermion f via Fd → f qd, with the qd a heavy Hidden Valley particle in the
fundamental representation of dark color [38]. Additional quantum numbers such
as charge and SM color are carried by the SM fermion. An additional production
mechanism for qd particles is found from the interaction Z
′ → qd qd, which is
the channel considered in this analysis and is specified directly in the Pythia
configuration. The production of qd particles is possible through gluon-gluon fusion
via pairs of Fd particles, but this analysis is unlikely to be particularly sensitive to
this signal due to its topology.
The authors of the Hidden Valley module assert that the coupling strength
in the dark sector is relatively arbitrary [38]. Practically, it is difficult to separate
effects from the mass hierarchy from effects related to the dark sector coupling αd
16
and to its running. While the running of the coupling as a function of the energy
scale was not implemented in the Hidden Valley initially due to this argument, it
was later added to the sector in the Pythia 8.240 release. In the implementation,
dark pseudoscalar mesons πd,0, π
±
d are produced and dark vector bosons ρd,0, ρ
±
d
also couple during the hadronization. The dark scalar mesons have higher mass
than the pions and are therefore ignored within the hadronization due to their
subdominant production [39]. The emission of a dark gluon from a dark quark
qd → qd gd is allowed, in addition to the coupling gd → gd gd, which are necessary
for the dark jet production.
The dark pion and dark rho couplings were set manually in the production.
The neutral dark pion was allowed to decay to pairs of down quarks with 100%
branching ratio, and the neutral dark rho was given a 99% coupling to dark
neutral pions. The remaining 1% was given to the coupling to a down quark pair
to emulate the emerging aspect of the decays. The charged analog particles were
given identical couplings but only to their charged dark sector analogs.
The hadronization continues in this Hidden Valley sector to first order until
the dark mesons emerge into the visible sector due to their small coupling to the
down quark. This can occur via a number of diagrams such as the Z ′ interaction
or via a Yukawa coupling with a dark scalar Xd, although only the Z’ interaction
is considered in this analysis. The same symmetry-breaking mechanism that
produces the SM baryon asymmetry is assumed to produce the DM asymmetry,
so similar mass scales O (1− 10 GeV) are assigned to the dark sector energy scale
in the model, which is how the dark pions are long-lived. The dark particles in the
model are assumed to be on the order of 5 GeV as the dark matter mass density is
known to be approximately 5× the visible matter density [18], so the mass of the
17
lightest baryons in the model must be on the order of 5× the mass of the proton
if the baryon and the dark baryon abundances are approximately equal. This, in
combination with the TeV scales for the dark mediators Xd and Zd constraining
their coupling to the SM, forces the dark mesons to have long lifetimes due to their
small couplings and limited phase space available for decays due to the similar
energy scales between the QCD and dark sectors. This creates the “emerging”
aspect of the resulting jet, where the dark mesons will decay with exponentially-
decreasing probability with the√mean decay distance d = γβcτ , where γ is the
standard Lorentz factor γ = 1/ 1− β2 and β is the particle velocity relative to
the speed of light β = v/c.
Lower limits on the dark pion lifetime are set by experimental constraints;
QCD lifetimes from the decay of B-hadrons limit analysis sensitivity below several
hundred µm. Upper limits are set by Big-Bang Nucleosynthesis constraints, where
the lifetime of the produced dark particles must be less than approximately 1
second [1]. It is within the experimental bounds of this lifetime range that this
analysis aims to search within, with proper decay distances in the range 1 mm
< cτ < 100 mm.
The lifetimes of the dark pions can be computed analytically as [37],
( )2( )2( )( )4
1 2 GeV 100 MeV 2 GeV MZ′
cτ = 80 mm× × (2.4)
g2dg
2
q fπ mq mπ 1 TeVd d
where gd and gq are the couplings of the dark quarks and SM quarks to the Z’,
fπ is a constant that is assumed to be on the same scale as the dark energyd
scale, and mq, mπ , and MZ′ are the masses of the dark quark, dark pion, andd
Z’, respectively. For an αs coupling of 0.1, an energy scale of 10 GeV, a quark
18
mass of 5 MeV, dark quark mass of 10 GeV, and Z’ mass of 1 TeV, the cτ is
approximately 3.6 m. These macroscopic decay lengths are significantly dependent
on the couplings, the flavor of SM quark that the decay is associated with, and
the mass of the Z’. Rather than varying the couplings and flavors of interactions, a
highly simplified version of this model is considered where the dark pion lifetimes
and Z’ masses are set independently within an acceptable grid.
The dark baryon contribution to the jet is expected to be on the order
of 10% when 3 dark colors are incorporated into the dark model [1], which is
roughly the same fraction as that of QCD. These will escape the detector, but the
loss in energy is roughly on the same scale as the Jet Energy Resolution (JER).
This detector energy resolution will be discussed in further detail in Chapter
III. So while the lifetime of the dark mesons is small enough to allow the decay
byproducts to decay mostly within the detector volume, significant experimental
sensitivity due to missing energy (MET) is not lost at reasonable lifetimes.
The five dark sector models considered in this analysis span the space
of potential dark sector parameters that Schwaller, Stolarski, and Weiler [1]
considered. These benchmark models, called Models A - E (Table 2.1), and the
dark pion lifetimes were sampled 7 times over these dark sector models to produce
5× 7 = 35 total models for each Z’ truth mass. The dark sector meson mass
range is motivated by the reconstruction capabilities of the ATLAS detector.
However, the dark sector lifetimes are theory-motivated, and the Z’ mass range
is limited at the lower end (1.3 TeV) by data-acquisition threshold inefficiencies
in the detector and at the upper end (4 TeV) by the analysis method. The lower
end of the dark meson mass range (0.8 GeV) is motivated by the reconstruction
capabilities of the tracker to reconstruct decays of this sort as a clean secondary
19
vertex. This is a relic of the adaptation of the existing 4-jet emerging jet analysis
to this search, where greatly enhanced QCD background jet rejection is expected
from secondary vertex counting. This lower range may need to be reconsidered for
future analyses in the context of soft-bomb-like signatures, which are signatures
containing a large multiplicity of very soft and relatively isotropically-decaying
dark particles which do not produce a traditional jet signature after they decay
into low-pT SM particles. The upper end (40 GeV) represents a unique signature
that is the limit of the emerging jets phenomelogy; this signature has most of the
jet energy contained within a single dark meson. It is expected that an analysis
such as the ongoing displaced jets ATLAS analysis will cover this region of the
dark sector parameters with greater efficacy.
Model A Model B Model C Model D Model E
Λd 10 GeV 4 GeV 20 GeV 40 GeV 1.6 GeV
mρ 20 GeV 8 GeV 40 GeV 80 GeV 3.2 GeVd
mπ 5 GeV 2 GeV 10 GeV 20 GeV 0.8 GeVd
TABLE 2.1. The dark models (A - E) considered by this analysis.
2.5. Parton Distribution Functions
The proton is a conglomerate sea of particles that are contained by the
strong force. Three on-shell particles are considered the standard composition
of the proton: two up quarks (q = +2) and one down quark (q = -1). However,
3 3
more than half of the momentum of the proton is carried by various intermittent
particles that include transient quark pairs and gluons.
The primary channel of consideration for this analysis is a leading-order s-
channel interaction ff̄ → Z ′d → QQ̄ that forms from interactions of on- and
off-shell fermion pairs within the colliding protons. Therefore, the simulations
20
that produce the signal samples needed for this analysis incorporate these PDFs
into their simulations of the parton kinematics in the hard-scatter interaction.
The kinematics of the resultant Z’ are dependent on the carried parton momenta
and the recoil of the proton remnants, and the resulting probability of the given
hard-scatter (known as the matrix element) is calculated by a convolution of these
PDFs over the cross-section of the interaction. The probability of finding a parton
of a particular flavor i at an energy scale µ with a momentum fraction x of the
proton p is incorporated into the PDF, fi/p (x, µ
2).
2.6. Vector Boson Interactions
BSM vector bosons are generally produced close to their truth mass (on-
shell); the probability of this depends on the flavors and energy scales of the
production partons. With the assumption that the flavor conservation in the SM
extends to the dark sector, standard processes that would produce a Z’ involve
pairs of fermions within the protons, such as uū→ Z ′ or dd̄→ Z ′.
FIGURE 2.3. Feynman diagram of Z’ production from a down/anti-down quark
pair interaction. The dark quarks (Qd) will hadronize in the dark sector and
emerge in a detector due to their small coupling to the Standard Model.
21
The approximated Z’ width in these hidden valley interactions was computed
from perturbative calculations by Schwaller et. al. [37] and is
( ) Nng2′ dMZ′Γ Z → XX̄ ≈ , (2.5)
24π
for a vectorial coupling of a generic particle X. This assumes a minimal
contribution to the width from SM decays. With a Z’ mass of 1 TeV, an assumed
equality between the number of QCD and dark colors (N = 7), three flavors of
dark quarks (n = 3), and a branching ratio to each quark flavor of 1/7, this width
corresponds to approximately 10 GeV.
The model’s full SU(3) dark sector is simplified into a phenomenological
model that can reproduce a dark jet to first order. Z ′ bosons naturally have a
coupling to dark quarks and are assumed to have couplings to SM quarks. This
coupling is set to a very small number (0.001 in the nominal sample generation) -
it is this small coupling that allows the jet to emerge. The dark quarks hadronize
in the dark sector at a rate that is dependent on the αS coupling, which is also
dependent on the coupling that is set in the model.
Pythia is a well-known program in high-energy physics that is designed
to produce Monte-Carlo simulated Standard Model and signal events [40]. The
various Standard Model matrix elements can be computed by the program
to a set order, and signal matrix elements needed in the signal generation are
approximated by the computation of a set number of Feynman diagrams in
the interaction. The program simulates the incoming beam effects, the parton
kinematics via the PDFs, the hard scatter interaction via the Feynman diagrams
specified in the production, and the final-state hadronization. The beam and
parton simulation is a critical part of the program, and the matrix elements for
22
a simplified Hidden Valley of dark interactions can approximate dark or emerging
jet processes.
Hadronization in both the Standard Model and the dark sector is computed
first in the perturbative regime. However, the hadronization at energy scales
closer to the dark energy scale is estimated via the Lund string model [41, 42]
for dark scalars, dark vector bosons, dark mesons, and dark gluons. Dark baryon
production is not included in the model, although this is estimated to contribute
a maximum of 10% to the jet energy. The Lund string model is a description
of the hadronization process that’s consistent with lattice simulations and is
consistently used as an accurate model of jet formation. The color gauge fields
are constrained along tubes that propagate between pairs of colored particles. The
energy density of the tubes increase as the separation increases, and at some point
the stored energy is higher than the hadronization energy scale, and the string
splits. The further cascade of color-charged particles progresses until the energy
of the interactions is close to the energy scale of the group. The running of the
coupling approaches ≈ 1 at these low energies and the non-pertubative dynamics
continue until the final-state Hidden Valley bound states have completed their
hadronization. Eventually, these quasi-stable states decay to the Standard Model
and emerge within the detector.
23
FIGURE 2.4. A graphical representation of how color confinement produces jets
[3] in the non-perturbative regime of the Lund string model. A back-to-back pair
of colored quarks separate in the center-of-mass frame and radiates gluons and
pairs of quarks / anti-quarks - this process continues until around the energy scale
of QCD. The attractive forces between the pair narrow the color flux into a tube
and the stored energy increases linearly with the separation. At energies above
the QCD energy scale, this tube splits into sets of hadrons that continue their own
hadronization process until the average energy is below the energy scale of QCD.
The dynamics of these hidden valley sectors are incorporated in Pythia 8, but
a limited set of dark sector interactions are considered as a simplified model. A
dark quark Qd is given a simplified set of couplings to dark pions and dark rhos.
The dark pions are defined with the model’s cτ and are given a small coupling
to down quarks in the Standard Model. To allow the dark showers to progress
kinematically, the dark quarks are given a mass of 2× the dark pion mass. To be
consistent with the SM, the dark rhos have a mass of 4 × the dark pion mass. The
6 dark particles considered in this simplified model of dark showers are in Table
2.2.
The events were generated within this limited fragmentation model for the
grid of mass hierarchies and dark meson lifetimes. Variations on the dark sector
mass hierarchy are used as systematics on the signal MC, resulting in systematic
changes to the signal efficiencies, acceptances, and overall limits obtained.
24
Particle PDG Id Mass cτ
Z’ 4900023 1500-5000 GeV -
gv 4900021 0 -
Dark Quark (Qd) 4900101 2·md -
Dark Pion (πd) 4900111 md 1-100 mm
Dark Rho (ρd) 4900113 4·md -
Off-diagonal Dark Pion 4900211 md 1-100 mm
Off-diagonal Dark Rho 4900213 4·md -
TABLE 2.2. The dark sector particles considered in these simplified dark shower
models. Similarly to their analogous particles in the visible sector, dark gluson gv,
Z’ bosons, dark quarks Qd, and the dark rho particles decay almost immediately
after production.
The cross-section measurements for these signals are dependent on the Z ′
coupling [37] and are estimated by Pythia by convolving the cross sections with
the PDF distributions. The variation of these cross section measurements on the
dark sector model were within the statistical uncertainty of the Pythia output;
the hard-scatter cross section is expected to be independent of the hard sector
hadronization at leading order. The decay cross-section of the leptophobic Z’ then
becomes a convolution over the parton PDFs (fi(x1) and fi(x2)) and the available
phase-space for this decay [37],
( ) ∑ ∫ ∫ g2g2 ( )
→ ′ → d q x1x2sσ pp Z QdQ̄d = dx1fi (x1) dx2fi (x2)× .
72π (x 2 2 2 21x2s−MZ′) + Γ Mi=u,d Z′
(2.6)
The cross-sections from Pythia were extracted from the output event
generation using the A14 tune of the NNPDF23LO PDF set, and they are listed
at a fixed coupling of gd = 0.001 in Table 2.2.
25
MZ′ [GeV ] gq σ [fb]
1500 0.001 1.714× 100 ± 7.809× 10−3
2000 0.001 3.425× 10−1 ± 1.448× 10−3
3000 0.001 3.398× 10−2 ± 1.049× 10−4
4000 0.001 7.613× 10−3 ± 1.837× 10−5
5000 0.001 2.776× 10−3 ± 5.375× 10−6
TABLE 2.3. The estimated cross sections from Pythia for each generated signal
mass.
26
CHAPTER III
DETECTOR AND ACCELERATOR
The complexity in design and operation of the Large Hadron Collider (LHC)
cannot be understated. As the world’s most powerful accelerator, with four main
experiments and numerous smaller experiments in the complex, it requires the
effort of thousands of physicists and engineers to design and operate the machine
as well as to analyze the enormous amount of data that is collected.
3.1. Accelerator
The LHC is a 27 km circumference particle accelerator that spans part of the
French and Swiss border near Geneva. It is operated by CERN and is capable of
performing proton-proton and heavy ion collisions at a number of collision points
along the ring. The accelerator ring is located 100 meters underground to greatly
reduce the background from cosmic rays, as well as to eliminate radiation leakage
in populated areas. The accelerator collides its accelerants at four main points
located at four main experiments around the ring by focusing the two beams using
powerful superconducting quadrupole magnets.
The maximum center-of-mass (CoM) energy of the accelerator design is 14
TeV, and the accelerator has been approaching this design limit over the run years.
√ √
The CoM energies were s = 8 TeV during Run 1 (2010 - 2012), s = 13 TeV
√
during Run 2 (2015 - 2018), and anticipated to be s = 13.6 TeV during Run 3
(2022 onward to 2025). This corresponds to a velocity of 99.996% of the speed of
light for the colliding protons, increasing the sensitivity of the machine to high-
mass exotic particles, Higgs bosons, and rare SM processes.
27
To probe the high-energy regime of these potential exotic particles, as well
as to allow greater sensitivity to the recently discovered Higgs particle, protons
are a good candidate for the beam particles at the LHC. They are stable and
relatively massive, which greatly decreases the power drain of the accelerator due
to synchrotron radiation at these energy scales. The rate of synchrotron radiation
is proportional to 1/m4 for a given particle of mass m, reducing the energy costs
for the accelerator; however, this does increase the needed circumference of the
beam ring with the same magnet technology. Lepton beams require smaller
accelerator rings with less-powerful magnets, but lose substantially more energy
due to radiation. While hadron (protons, anti-protons, etc.) accelerators allow for
the probe of much higher energy scales than an electron accelerator, this comes
at the cost of very contaminated and complex energy deposits in the detector
due to elastic and inelastic pileup collisions. Pileup are the extra energy deposits
from additional uninteresting collisions at the interaction point as well as energy
deposits from beam effects. Each time a proton bunch crosses another bunch, any
number of pairs of protons can produce an inelastic scattering. The typical number
of proton pairs interacting per crossing at the LHC is between 15 and 60, as Figure
3.4 shows. This requires complex tagging algorithms to select objects associated to
the hard scatter in each event, and the energy calibrations of the detector need to
correct for these pileup energy deposits.
The proton beams are formed and clustered into bunches by the preliminary
accelerators in the complex. First, hydrogen atoms are ionized by being passed
through an electric field; this ionizes the atoms and allows the field to collect the
resultant ions. These protons are then accelerated to 50 MeV through a linear
series of magnets called LINAC2 [43]. The electromagnets in the series rapidly
28
oscillate their fields in a manner where the protons are attracted to the forward
direction and repulsed from the back of the magnetic series. The protons then
travel to the next magnet in the sequence where the same oscillation occurs,
producing an incremental acceleration with each magnetic cycle.
These accelerated protons are then fed into the Proton Synchrotron Booster
which gives a preliminary boost of the protons to a CoM energy of 1.4 GeV.
They are then fed into the Proton Synchroton (PS) and then the Super Proton
Synchrotron (SPS) rings. These accelerators are recycled from older programs
and used as injection rings for the main accelerator. The final CoM energy of the
√
protons before injection into the main ring is s = 540 GeV after an acceleration
to 25 GeV by the Proton Synchrotron.
The bunching of protons into clusters (bunches) is a critical aspect of the
accelerator design. The timing separation between sequential bunches was reduced
down to 25 nanoseconds (ns) in Run 2 from a spacing of 50 ns in Run 1. To
accomplish this, 72 sequential radio frequency cycles of the PS are driven from
the PS ring into the SPS ring by a kicker magnet system within a time of 200 ns.
The SPS then uses another kicker system with a timing of 800 ns to inject the
proton bunches into the main ring. The timing ratio of these injections mean that
72× 4 = 288 bunches are injected into the main ring, but the timing separation
requires each grouping of 72 bunches to be separated by 8 empty (200 ns /
25 ns) bunch spacings, and each group of 288 are separated by 32 empty bunch
spacings (800 ns / 25 ns). The 2800 maximum total bunches are filled out with the
exception of 100 empty bunches that are designed to synchronize with the abort
system in the event of a beam dump. This operational configuration was used until
29
mid 2017, after which the bunch configuration was simplified to a sequence of 32
bunches followed by 8 empty bunches [44].
The main accelerator ring is then used to accelerate the protons up to their
final CoM energy. The ring is composed of 1232 dipole magnets spaced around the
beamline. These provide the Lorentz force to keep the protons contained inside
the beampipe as well as the acceleration needed to bring the proton energies from
450 GeV up to 6.5 TeV. This smears the beams though, so quadrupole magnets
placed before the collision points focus the beams from a width of 0.2 mm down
to 16 nm. Due to the extremely high fields required, powerful superconducting
magnets are needed, and liquid Helium-4 is used to keep them at 2 K to utilize
their superconducting capabilities to produce a maximum field of 8.3 Tesla (T).
The beams intersect at four collision points along the circumference which
correspond to the locations of the four main experiments at the LHC, ATLAS [6],
CMS [45], ALICE [46], and LHCb [47]. The accelerator complex is shown in Fig.
3.1. ATLAS and CMS are general-purpose detectors, whereas LHCb focuses on
B-physics and ALICE focuses on heavy ion physics during the dedicated heavy-ion
data-taking periods of the LHC.
The field strength needed by the magnets is derived by first considering the
effects of the Lorentz force law on protons moving through the ring,
F~ = q~v ×B~ , (3.1)
with charge q, velocity vector ~v, and magnetic field B~ . When the velocity is
perpendicular to the field, this simplifies to
|p~| ≈ EbeamR = . (3.2)
qB qB
30
FIGURE 3.1. The CERN accelerator complex, showing the four main experiments
on the ring, the linear accelerators and booster rings, and various smaller
experiment [4].
For protons, this reduces to Ebeam[TeV] = 0.3 · B · R, when B in is units
of Tesla. For a 27 km circumference ring with radius 4.3 km at a CoM energy
of 14 TeV, this corresponds to a minimal field strength of 8.33 T needed for the
magnets.
3.2. Detector
ATLAS is a general-purpose particle detector designed for comprehensive
particle detection at near-total volume coverage. The symmetric and cylindrical
detector spans the 4π polar angle surrounding the transverse region from the
31
beamline, and pseudorapidity (η = − ln tan (θ/2)) coverage for the calorimeter
extends up to |η|= 5.0.
FIGURE 3.2. The ATLAS Detector layout showing the detector’s critical
subdetectors and magnet systems. Human figures are shown on the left to
demonstrate the scale of the detector.
Figure 3.3 illustrates the coordinate systems used at ATLAS, showing the
cartesian and cylindrical coordinates used in object geometric and kinematic
labeling.
FIGURE 3.3. The ATLAS Coordinate systems.
The kinematic coordinate system at ATLAS uses the variable rapidity (y)
32
( ( ))
· E + pz ≈ · θy = 2 ln 2 ln tan = η, (3.3)
E − pz 2
where y simplifies to η in the case of massless objects or when |p| >> m. η is
generally preferred to y as geometric measurements have better resolution than
kinematic measurements at ATLAS. In addition, differences in η are invariant to
boosts up or down the beampipe, so distance measures using this difference are
invariant across the detector for relatively massless objects. One such example is
the distance measure ∆R, which characterizes the 2D separation of two objects,
√
∆R = (∆η)2 + (∆φ)2, (3.4)
where for two objects with (η0, φ0) and (η1, φ1), ∆η = η0 − η1 and ∆φ = φ0 − φ1.
The major detector components consist of the Inner Detector (ID), the
Electromagnetic Calorimeter (ECAL), the Hadronic Calorimeter (HCAL), and
the Muon Spectrometer (MS), as well as the associated magnet systems for each.
An overview of the detector layout is shown in Figure 3.2; this image also shows
the impressive scale of the detector, which weighs over 7000 tons.
A range of pileup (exteranous proton-proton collisions in a typical bunch
crossing) conditions were present during the data-taking process in Run 2. At
maximum design luminosity, approximately 1000 charged particles are expected to
be produced within the tracking volume for each event, requiring a precise tracker
in a radiation-proof inner detector.
During a bunch crossing, the vast majority of protons in a bunch will not
interact with other protons in the opposing collision bunch. The beam focusing
defines the resolution of the beamspot in the transverse direction, and the
33
bunch crossing is spread over a defined range along the beamline (z) to allow for
discrimination between the primary collision in the event and the uninteresting
pileup vertices. This greatly increases the physics capabilities of the machine, as
soft inelastic interactions of the protons are not interesting relative to hard scatter
events that have the capability of producing rare Standard Model (SM) processes
and Beyond the Standard Model (BSM) signatures. The rate of these background
events in the bunch collisions, known as pileup, depend on the beam focusing and
the proton density in the bunch. After the initial injection of the 100+ billion
protons into the accelerator, the density of the bunch starts to decrease. Proton-
proton collisions reduce the number of protons available in subsequent crossings,
and protons are also knocked out by beam effects. This reduces the amount of
pileup in the events towards the end of a standard injection run, which presents
the opportunity for lower threshold triggers to run during this lower-luminosity
environment.
Cross-sections in most particle experiments are listed in unit of barns (1 b
= 1×10−28 m2) and overall integrated (time-summed) luminosity is listed in the
inverse units, so the product of the cross-section and luminosity gives a number of
expected events for that production channel over that given period of integrated
data-taking,
L 1b × σpp = 1→ Lb = . (3.5)
σpp
For N1 and N2 protons in each bunch of the bunch crossing, this instantaneous
luminosity becomes
34
L N1N2b = . (3.6)
σpp
The rate of pileup events affects the total luminosity captured by the
experiment. These N1 and N2 protons circulate around the ring many times
per second, so replacing this with an average approximation over the circulation
frequency f and average number of interactions per bunch crossing 〈µ〉 gives
L 〈µ〉fb = . (3.7)
σpp
For Nb bunches within the ring, the instantaneous luminosity becomes
L 〈µ〉fint = Nb . (3.8)
σpp
With a circular frequency of 11246 Hz, a peak µ of around 80 collisions per bunch
crossing, a proton-proton cross-section of 68 millibarns, and a 32 filled / 8 empty
bunch structure, the peak instantaneous luminosity becomes approximately Lint =
2 ×10−34 cm−2 s−1. The pileup profiles for the 4 data-taking years in Run 2 are
shown in Figure 3.4.
3.3. Inner Detector
The Inner Detector of ATLAS is composed of a series of tracking layers that
are designed to detect and compute the kinematics of charged particles coming
from the collision point. The silicon technologies in the ID utilize ionization energy
loss from the motion of charged particles through the material to measure their
curvature and interaction point (IP) position. The detector lies within an axial
magnetic field of strength 2 T produced by a thin superconducting solenoidal
35
FIGURE 3.4. Average ATLAS µ profiles during data-taking years in Run 2 [5].
magnet; this field produces the curvature of the charged particles’ tracks that is
needed for momenta measurements.
The layout of the ID is shown in Figure 3.5, which shows the Pixel, SCT,
and TRT subdetectors [6]. The ID is immersed inside an axial field produced by a
5.3 m long and 2.5 m diameter solenoidal magnet. The silicon layers in the ID span
a range of |η| < 2.5 and are arranged coincentrically in the barrel region (|η| < 1.7)
and in disks surrounding the beamline up to the maximum η acceptance (1.7 <
|η| < 2.5).
3.3.1. Track and Vertex Reconstruction
The curvature of a charged particle in a magnetic field is dependent on
the particle’s charge, mass, momentum, and the strength of the field. Charged
particles in an perpendicular field follow a helical path, with the orientation of the
path dependent on the charge of the particle.
36
FIGURE 3.5. The ATLAS Inner Detector showing the various tracking layers and
technologies used for charged particle identification [6].
Charged particle tracks are defined by 6 independent quantities that
represent the particles’ kinematics relative to either the relevant primary or
secondary vertex in the event, (q/p, θ, φ, d0, z0,m).
The trajectory of charged particles moving through the ID’s magnetic field
are curved by the Lorentz force law; the geometric location and curvature of
the measured hit positions within the ID are used to construct the origin and
kinematics of the charged particle producing this curved track. Analytic functional
forms are fit to the layer hits and used to measure the track parameters such as
the track’s η and φ, which is critical for the ∆R association of the track to its
corresponding jet.
The variable q/p is the ratio of the track’s charge to its momentum, both
of which are determined by the curvature of the track in the magnetic field. The
curvature direction defines the charge, and for a particle of given mass m, the
37
track has a defined curvature within the measured magnetic field. θ is the polar
angle of the track’s initial vector relative to the beamline, and φ is the azimuthal
angle of the track’s initial vector. d0 and z0 are positional variables indicating the
location of the track’s perigee relative to a given vertex. d0 is the signed quantity
indicating the shortest distance between the track and the vertex in the azimuthal
plane (x-y plane). Similarily, z0 is the signed quantity indicating the perigee in the
polar plane (r-z plane). A schematic of this coordinate system is shown in Figure
3.6.
FIGURE 3.6. The track reconstruction geometry at ATLAS. Relative to a defined
vertex, geometric descriptions of the closest approach and the kinematics are
reduced to 6 variables [7]
.
For every bunch crossing, 10 - 60 pairs of protons (on average) interact and
produce a set of charged and neutral particles that can be associated back to
their interaction points. The pointing of neutral particles such as photons is very
38
uncertain, so precise measurements of the tracks are relied on to locate the x, y,
and z locations of these IPs. The interaction of interest, the hard-scatter event,
is associated to a vertex by requiring at least two tracks with pT> 500 MeV that
originate from this vertex, and the vertex with the highest scalar sum of track
pT measurements associated to it is labeled the event’s Primary Vertex (PV).
∑
PV← max pT (p > 400 MeV) (3.9)track Ttrack
tracks
3.3.2. IBL
The Insertable B Layer (IBL) is the first set of tracking layer that charged
particles coming from the IP will interact with. This subdetector consists of a
series of silicon pixel sensors located 32.5 mm from the beamline. This layer was
added in 2016 and was designed to improve tracking sensitivity in the ID, allowing
for better primary and secondary vertexing resolution. The resolution of the pixels
in this layer is 50µm× 250µm, adding an additional 12 million readout channels
to the ID hardware.
A charged particle passing through a silicon pixel at a sufficient momentum
is likely to produce least one electron-hole pair within the material. An applied
voltage attracts the electrons towards electronics that register the electron
accumulation as an energy hit within that pixel. This amplified electron signal
that’s collected is used to define an ionization energy deposit if this energy
deposit is well-measured and sufficiently above noise fluctuations. The sensor
detects an ionization hit if the accumulated charge passes defined “time-over-
threshold” (TOT) thresholds that are calibrated to ensure consistent performance
39
of the pixels over the detector. The addition of this layer increases the d0 and z0
resolution of the ID by 40% [48].
3.3.3. Pixel Detector
The next three layers comprise the Pixel detector [49], which is a high-
resolution set of tracking layers. The coverage of the pixel detector spans up to
|η|= 2.5, and its coverage is composed of a central barrel (|η|< 1.7) and an endcap
region (1.7≤ |η|< 2.5. This subdetector is composed of a series of silicon pixels
of size 40µm× 500µm arranged in three layers. The first layer starts 50.5 mm
from the beamline and the last layer extends out to 122.5 mm. The high granular
resolution of the subdetector, especially in the φ coordinate, allows precision
measurements of the curvature of the tracks that produce sufficient numbers of
hits in the ID. The 92 million channels in the Pixel detector are fed to the readout
system that stores the hit information if the event passes a trigger.
The high 3D spatial resolution of these layers are utilized in b-tagging, where
it is necessary to have precision tracks that point to the secondary vertex created
by long-lived B-hadrons in a jet.
3.3.4. SCT
The Semiconductor Tracker (SCT) is subdetector containing the next series
of tracking layers [50]. The barrel region (|η|< 1.4) is composed of 4 layers of
silicon strips arranged orthogonally to each other. This gives resolution along the
two measured coordinates - along φ for each hit radius, and similarly for each z
position. The forward regions (1.4≤ |η|< 2.5) are covered by 9 disks with a similar
orthogonal orientation of the strips.
40
This subdetector has slightly worse spatial resolution than the preceding
layers due to the use of coarse strips instead of pixels, however, most tracks are
well separated at that distance from the IP. So the 200µm track resolution in this
subdetector is sufficient for proper track reconstruction and provides a similar
contribution to the track’s momentum resolution as the precision layers closer
to the IP. This subdetector adds an addition 6.3 million channels to the detector
hardware readout.
3.3.5. TRT
The Transition Radiation Tracker (TRT) is a series of straw tubes filled
with an argon and xenon gas mixture [51]. The 300,000 4 mm diameter tubes
fill a substantial volume of the inner detector. The tubes act as cathodes and a
wire running through the center of each tube acts as an anode, so the presence of
charged particles produced in that volume induces a voltage through the tube that
can be amplified and read out. Transition radiation is created by the boundaries
between the layers in the tube structure, as well as the transitions from the
gases inside and surrounding the tubes themselves. This radiation interacts with
electrons in the tube’s gas and accumulates them towards the readout electronics.
The induced voltage in the tube gives the geometric location of the hit in the
φ coordinate. They are arranged parallel to the beamline in the barrel region and
in rings surrounding the beamline in the forward regions, meaning that they only
provide r -φ geometric hit locations. However, charged particle reconstruction is
significantly enhanced by the addition of these high-radius hits, so the dramatically
worse spatial resolution in this region complements the momentum measurements
of the tracks, rather than relying on a costly set of silicon layers. The geometric
41
resolution is 130µm in this region, although the large number of high-radius
hits results in a roughly equal momentum resolution between the SCT and TRT
regions.
3.4. Electromagnetic Calorimeter
The ID is intended to measure charged particles’ properties while inducing a
minimal effect on the kinematics of the particle itself. However, the calorimeter’s
purpose is to induce interactions from incoming particles to measure their energy.
An electromagnetic or hadronic interaction with the incident particle will produce
additional byproducts; these daughter particles will continue to cascade through
the calorimeter layers. As each subsequent interaction produces additional
interactions at a lower energy scale, the cascade will eventually complete its
showering. The number of interaction lengths in the calorimeter is designed to
ensure that little-to-no energy is lost out of the calorimeter. At some high energies,
a sizable portion of the energy punches through all the detector layers, but this is
accounted for by the jet calibration sequence. Other missing energy in the event
is usually associated with low electromagnetic and hadronic cross-section SM
particles - in particular the high SM background by neutrinos that pass readily
through the detector.
The Liquid Argon Calorimeter (LAr) is the first detector in the calorimeter
system [52]. It is designed to induce showering processes for electromagetically-
interacting particles via Brehmsstrahlung with the highly dense liquid argon
contained within the detector. Layers of absorbing lead allow greater absorption
of the incoming energy by inducing more electromagnetic interactions, thereby
greatly reducing the volume of cryogenically cooled liquid argon needed. LAr
42
is stable and relatively radiation-proof, allowing the detector resolution to stay
constant over the lifetime of the detector.
LAr is composed of two half barrels, each with length 3.2 m, inner radius
2.8 m, and outer radius 4.0 m. It is designed with 3 main layers, with the highest
granularity in the first layer to allow photon identification. The granularity
decreases to the second layer and further on to the third layer. The final layer’s
purpose is to provide an energy measurement to correct for energy leakage due to
punch-through [11].
The LAr system resides in the region of |η|< 3.2 and is composed of a barrel
calorimeter with coverage up to |η|< 1.475 and two endcap wheels completing
the remaining coverage. The granularity of this detector is η dependent and is
the most granular in the first layers of the central region with cell dimensions
of 0.003× 0.1 in η - φ space. This granularity in the region of the ID allows for
precision electron energy measurements as the particle track can be reliably
extrapolated to the corresponding calorimeter cell hit. Less precision in the
showering shape is needed, so the granularity of the second and third layers are
0.025× 0.025 and 0.05× 0.025.
The energy resolution of calorimeter systems can be approximated by the
functional form
σE a b
= √ ⊕ ⊕ c. (3.10)
E E E
The variable a parameterizes the energy resolution component that is caused
by sampling errors. The b variable term parameterizes the resolution due to
electronic noise, and c is a constant term associated to the innate resolution of
the technology. In the case of the ATLAS LAr calorimeter, the noise contribution
43
is insignificant and the total resolution can be parameterized by Equation 3.11,
which is the design resolution of the detector [53]
σE √ 10%= ⊕ 0.7%. (3.11)
E E/GeV
FIGURE 3.7. Electromagnetic interaction lengths as a function of η for the
electromagnetic calorimeter system [6].
3.5. Hadronic Calorimeter
Interactions in the ECAL rely on Bremsstrahlung interactions with electron
clouds within the detector material, whereas measurements of interactions in the
HCAL rely on hadronic interactions with high-mass nuclei in the detector.
The HCAL sytem is composed of several sampling calorimeters with varying
resolution and detector technologies. The barrel region has the highest design
energy resolution and is composed of a scintillator tiles with steel absorbers in
the region |η|< 1.7. LAr calorimeters comprise the region 1.7< |η|< 3.2 and also
the forward regions 3.2< |η|< 4.9 near the beamline.
The HCAL barrel region has an inner radius of 2.28 m, an outer radius of
4.25 m, and is 5.8 m long. It is composed of three layers with interaction lengths λ0
of 1.5, 4.1 and 1.8. The material budget decreases slightly in the forward region,
44
where the three layers have λ0 values of 1.5, 2.5, and 3.3. The material budget for
each of these regions is shown in Figure 3.8.
The layering of these tiles is accordion-shaped to allow relatively seamless
transition between the modules and the central and forward regions. The central
region is composed of 64 modules that contain samplers with resolution ∆η ×
∆φ= 0.1× 0.1 for the first two layers and 0.2× 0.1 for the last layer [54].
The LAr technology is incorporated in the forward regions to allow for
radiation hardening against the significant amount of pileup seen in those regions.
FIGURE 3.8. Hadronic interaction lengths as a function of η for the hadronic
calorimeter system [6].
3.6. Muon Spectrometer
The MS is a tracking system that surrounds the calorimeter systems and is
designed to precisely measure muon charges and momenta. Muons pass through
the calorimeter systems with little energy loss due to the mass dependence of
Bremsstrahlung processes. Muons can produce tracks in the ID, but their heavy
mass induces very little curvature in the tracks, making the track pT resolution
45
worse in that region. The high radius of the tracking layers in the MS creates an
extension to the tracking system that is used for precision muon detection and
measurement.
The MS is formed of a series of layered tracking technologies. The tracking
measurements are done with high-precision tracking chambers that are composed
of monitored drift tubes (MDTs) and cathode strip chambers (CSCs), with the
triggering enabled by resistive plate chambers (RPCs) and thin gap chambers
(TGCs). These systems are immersed in a ≈ 2 T magnetic field that is provided
by barrel and end-cap air-core torroidal superconducting magnets.
3.7. Trigger System
With a bunch crossing rate of 40 MHz, approximately 1 billion proton-
proton collisions occur per second at peak luminosity. The full raw detector
information can be stored in 1.6 MB, so a disk-writing capability of 64 TB/s would
be required to store all the data taken at the detector. As this is not possible with
the currently available resources, a complex data acquisition system is needed to
reduce this to a manageable rate.
The ATLAS trigger system, shown in Figure 3.9, is a sequence of hardware
and software decisions used to record events usable for physics studies. The Level-
1 (L1) system is a hardware-level set of trigger decisions used to reduce the raw
trigger rate from 40 MHz to 100 kHz. These events are then sent to the High Level
Trigger (HLT) system, which further reduces the data to a manageable rate of
roughly 1 kHz. The trigger system is sensitive to a variety of objects at both L1
and HLT levels, such as muons, photons, and jets. The triggers can be prescaled,
46
meaning that a fraction of events are randomly discarded to reduce the output
rate, or they can be unprescaled.
At L1, events are characterized by processors searching for energy deposits
that are selected algorithmically for certain signatures. The L1Calo system
will reconstruct calorimeter energy deposits and tag them using simple jet
reconstruction algorithms. For example, a simple jet-finding algorithm is computed
on topoclusters by considering calorimeter energy deposits in square 0.4× 0.4
regions and summing them. Other systems, such as the photon trigger, look at
isolated energy deposits within a small number of topoclusters that deposit most
of their energy in the ECAL; these are indicative of a photon signature [55]. The
regions surrounding these L1 objects are lumped into Regions of Interest (RoIs)
and are passed to the next steps of the trigger system.
These hardware decisions and RoIs are passed to the Central Trigger
Processor (CTP). This processor collects decisions and ROIs from the preceding
systems and computes general event trigger decisions based on kinematics, trigger
object separation, and multiplicities of the various L1 objects fed to it. The
decisions incorporate the subdetector timing information to ensure that decisions
from the trigger system are consistent with the collision timing. These decisions
are made within 2.5µs and objects for events that pass a trigger in the menu have
their ROIs sent to the HLT system.
At the HLT trigger system, the ROIs are fed to a series of reconstruction
algorithms that reconstruct the physics objects for each event within 300 ms.
Software-level trigger decisions on these physics objects (referred to as “online”
trigger objects) are made based on an HLT trigger menu which is run on a CPU
farm with 40k cores. Approximately 1 kHz of the events passing these HLT
47
decisions are fed from the detector read-out system to permanent storage on disk.
Later reprocessing on these raw events converts them to calibrated and further
defined physics objects (referred to as “offline” reconstructed objects).
FIGURE 3.9. A flowchart representing the data flow of events through the data-
acquisition system at the ATLAS detector. [8]
3.8. Data Reconstruction
A variety of data streams exist at ATLAS with applications that range
from detector monitoring to the stream containing the critical physics data. The
“physics Main” stream is the general stream at ATLAS; this stream contains event
that are output from the Physics trigger menu that are suited for general physics
analysis. Other monitoring streams such as the monitoring stream outputs a small
fraction of events to enable monitoring of detector conditions and the software
48
reconstruction. The Enhanced Bias stream is used to determine the average pileup
and detector conditions by using minimally-biased triggers to select low-energy
events that characterize an average event in the detector.
The data in the physics Main stream are stored in RAW output format in
preparation for reconstruction. Events are reconstructed by being passing through
a series of algorithms sequenced by the ATLAS central software, Athena [56]. The
detector objects such as the ID hits and the calorimeter energy deposits are sorted
from the RAW file and the physics object reconstruction begins. For Run 2 data,
tracks are reconstructed algorithmically from ID hits, and tracks that have |d0|
values greater than 10 mm are discarded. However, in the special DAOD RPVLL
stream reconstruction applied to a filtered set of data for the 4-jet emerging jets
analysis in Run 2, this range is extended out to 300 mm. In Run 3, this restriction
will be lifted at both the trigger level and at the reconstruction level, so high d0
tracks and high-radius displaced vertices will be reconstructed and available for the
analysis. However, in the dataset available for this analysis, this information is not
available and unfortunately cannot be used as a background discriminant. The use
of this track reconstruction in the trigger will be discussed further in Chapter V.
3.9. Jets
Byproducts of standard hard-scattered quarks or gluons will undergo QCD
hadronization, and the stable resultant particles will interact with the detector,
unless they are particularly long-lived. Jets tend to consist of approximately
60% hadrons, with the majority of these being charged mesons such as pions
which interact with the ID and then shower in the calorimeter. A smaller fraction
(roughly 10%) are baryons such as protons and neutrons or mesons such as KS or
49
KL particles. Neutral pions will immediately decay into photons; in combination
with additional photons from Final State Radiation (FSR) during hadronization,
these constitute approximately 30% of the jet energy.
Energy deposits in the calorimeter can be clustered into jets with a variety of
algorithms that vary in their resolution, choice of physics objects in the clustering,
and clustering radius. The simplest jet algorithm will simply sum energy in a
square surrounding the jet seed. This algorithm is used at the hardware level in
the ATLAS trigger system; energy deposits in the calorimeter are formed into
topoclusters and the topoclusters surrounding a 0.4× 0.4 area from the jet seed
are summed to form the jet. A slightly more complex algorithm would sum the
energy in a cone of defined radius around the seed, however this increases the
computational difficulty.
The final jets reconstructed at the HLT and offline levels in ATLAS use
algorithms that are colinear and infrared (IR) safe. Due to the stochastic nature
of jet fragmentation, jets can vary wildly in their clustering properties. Splittings
of high-pT incident particles and emissions of soft gluons during the hadronization
can change the substructure, and colinear and IR safe algorithms are designed to
be insensitive to these random processes within jets [57].
Topocluster energy reconstruction starts from the definition of the seed
locations. Seeds are formed from cells that contain energy deposits that are greater
than 4σ from the noise baseline, where σ is the standard deviation of the expected
noise thresholds. Neighboring cells are then added to the topocluster sum if the
energy deposit within the cell exceeds 2σ, and the process continues until there are
no more cells within the topocluster region to add.
50
Calorimeter-only jets (EMTopo jets) use these topocluster energy deposits
as inputs to the clustering algorithm. However, the pT precision of the tracker
motivates the use of tracks as inputs to the jet reconstruction. Tracks extrapolated
to the topoclusters can provide a more accurate measurement of the contribution
of the particles’ momenta than the topocluster measurement. In the Particle-
Flow (PFlow) algorithm, tracks associated to topocluster energy deposits are
used within the clustering. If a track from the PV is associated to one or more
topoclusters and the momentum measurement of the topoclusters is sufficiently
close to the track’s pT, the associated topocluster(s) are removed and the track’s
kinematics is used in lieu of the topocluster(s). For emerging jet signals that are
of interest here, the multiplicity of displaced tracks in the signature discourage
the use of this algorithm, as a significant fraction of the energy in a signal jet will
not be associated to a well-measured track. However, due to resource limitation
in the TDAQ system, the Run 3 emerging jets trigger will be required to use
this algorithm at the trigger level. Appendix A.1 and Chapter V contain further
discussion of the trigger and the reconstruction’s effects on the signal.
The large-R jets used in this analysis utilize the anti-Kt algorithm [10], and
are reconstructed with a radius of 1.0 in η-φ space on the EM-scale topocluster
energies (EMTopo). To reduce pileup and hadronization dependence of jet energy,
Kt-reconstructed topoclusters that form each jet are discarded from the clustering
if they contain less than 5% of the jet’s total energy. These jets are referred to as
trimmed anti-Kt R=1.0 LC jets, and they are designed to be highly resilient to the
substantial pileup contributions that can be seen in large-R jets. The effects of this
trimming relative to the standard pileup subtraction method are shown in Figure
3.10.
51
FIGURE 3.10. Trigger efficiency curves showing the effect of trimming on the
large-R trigger turn on points. The effect of standard pileup subtraction methods
is shown for reference [9].
3.9.1. Anti-Kt Algorithm
The Anti-Kt algorithm belongs to a class of jet reconstruction algorithms
that include the Kt, Cambridge-Aachen, and Anti-Kt algorithms [10]. These
algorithms utilize a subjet weighting scheme to recluster subjets in a self-consistent
method. The variables considered within this algorithm are:
( ) 2
d = min k2p 2p
∆ij
ij ti , ktj for i 6= j (3.12)R2
di,i = k
2p
ti (3.13)
where ∆2 2ij = (yi − yj) + (φi − φ )
2
j is the rapidity-φ distance between a pair
of subjets and kti is the transverse momentum of the ith subjet. The variable p is
the exponent that defines the algorithm type: p= 1 for the Kt algorithm, p= 0 for
the Cambridge-Aachen algorithm, and p=−1 for the anti-Kt algorithm.
52
The algorithm first computes dij and dii for each pair of subjets and
finds the minimum over all the sets of dij and dii. If a minimum dij exists, the
corresponding ith and jth subjets are combined in energy and position and replace
the original pair of subjets and all the dii,ij variables are recomputed. If the
minimum is one of the dii, this subjet is considered a fully reconstructed jet and
is removed from the list of subjets.
The algorithm is designed to cluster the soft radiation around an energetic
energy deposit into a full jet. The highest kt subjets will cluster first and
incorporate the surrounding radiation into a roughly conical collection of energy.
This algorithm also handles situations with isolated splashes of energy in the
detector; isolated subjets with no other weighted kt within the jet radius will
be considered full jets. This is shown in Figure 3.11 where the highest pT subjet
generally resides in the center of the jet, with soft radiation within the jet radius
typically clustered close to the hardest subprocess. It handles overlaps in energy
deposits by associating overlap energy to the high-pT neighboring jet.
Standard jet algorithms that are IR safe are preferred, meaning that they are
invariant to any additional emission of radiation during the fragmentation process.
The hardest subprocess in the jet region will tend to form the seed of a jet, with
additional soft radiation in the jet radius tending to be clustered alongside the
hardest subprocesses. This makes the measured jet energy relatively invariant to
the hadronization process or model for the jet, as changes to coupling parameters
such as αs will generally change the contribution of soft radiation, which will be
absorbed by the Kt algorithms.
Typical QCD-originated jets can be readily clustered within R = 0.4 jets,
so this is the typical jet radius used at ATLAS at 13 TeV. However, many
53
FIGURE 3.11. A demonstration of the Anti-Kt algorithm for a simulated event
that shows the typical clustering of energy deposits for R=1.0 jets [10].
boosted topologies produce much larger jets and the typical jet radius for the
reconstruction of a top quark is R = 1.0. As Figure 4.7 shows, emerging jet
signatures can contain large amount of soft and wide radiation, making the R = 1.0
algorithm optimal for this analysis. The same jet radius was used by the original
ATLAS CWoLa analysis [58] that is a precursor to this analysis. That previous
search was searching for heavy boosted decays producing a pair of R = 1.0 jets;
further details on this will be discussed in Chapter IV.
Truth jets are reclustered from final-state truth particles, and represent a
collection of the final states of a hadronization process. Truth jets are used in the
context of the emerging jet signal generation, and are simply formed via anti-Kt
reclustering of the Pythia final-state particles, with the final-state label determined
by the particle’s stored barcode that is produced during the generation. Standard
truth jets are clustered with a radius of R = 0.4.
54
3.10. Jet Calibration
Jet calibration is an intricate process designed to shift the energy scale of the
jets in the data to be consistent with the overall energy scale of the MC and to
increase the pT resolution of the jets. The data and simulated events are known
to have quite differing responses in the detector, and so these energy scales must
be calibrated to be consistent, in addition to correcting energy measurements from
problematic regions of the detector. Jets are reconstructed with a baseline energy
scale that is defined algorithmically, potentially followed by trimming, and then
followed by a defined set of calibration steps.
The calibration steps depend on the jet algorithm and radius that are used
in the reconstruction. Energy resolution is a critical component of R = 0.4 jets, and
so effort is made to increase the energy resolution using pileup residual corrections
and sequential calibrations for high-pT jets. Mass resolution is a critical aspect of
large-R jets as large-R jets are typically used to reconstruct heavy objects such
as top quarks, W-bosons, and other boosted objects that have a crucial measured
mass component.
The first calibration step for R = 0.4 jets start at the electromagnetic scale,
so energy measurements in the topoclusters are made consistent with the energy
that would be seen in the ECAL. Jets are origin-corrected to have η values that
are consistent with the location of the PV in the event, instead of the online
definition - at the center of the detector. This improves the η resolution of the
calibrated jets as the momentum vector of the jet more closely aligns with truth
particles from the PV. A pileup correction is then applied to the jets that corrects
the jet’s response to the in- and out-of-time pileup environments from the various
data-taking conditions. The overall jet energy scale (JES) is then corrected to be
55
consistent with MC events to ensure that energy measurements are meaningful for
physics analysis. The higher-order response of the detector to jets with different
track multiplicity and substructures is then corrected in the Global Sequential
Calibration (GSC) step. Then, data-driven in-situ methods are applied to correct
the varying response as a function of pT and η, in addition to correcting effects
from troublesome regions in the detector.
In the case of the large-R jets utilized in this analysis, they are set to a
baseline energy scale at the hadronic energy scale using a local weighting scheme
called LCW [11]. The previously mentioned η correction is applied and is followed
by the JES calibration step. In a very similar vein to the JES calibration, the jet
masses are also corrected in the Jet Mass Scale (JMS) calibration step [59]. Insitu
methods utilizing the balance of a large-R jet to a well-measured set of small-R
jets, a well-measured photon, or a well-reconstructed Z→ µ+µ− decay correct the
JES and JMS of the barrel region. An η-intercalibration then corrects the forward
region JES and JMS relative to the barrel region.
3.10.1. Pileup Correction
Pileup contributes a relatively isotropic distribution of energy to the detector
on average. Therefore, to reduce the expected pileup count (µ) and event Number
of Primary Vertices (NPV) dependence of the subsequent calibration steps, an
average pileup correction is derived and applied to R = 0.4 jets. The first step is an
area-based correction that removes the median contribution of in and out-of-time
pileup contributions to the jet pT that distort the true jet energy.
pareaT = ρ× A (3.14)
56
The computation of the median ρ energy contribution must be sensitive
to low pT contributions from soft particles in the event. Therefore, the pileup
contribution is computed from R = 0.4 Kt reconstructed jets within the |η|< 2.5
domain. The Kt algorithm is more sensitive to soft radiation further from the jet
seed, and ρ is derived from the median energy deposit within these jet areas.
The area A is computed by ghost track association. Many ghost tracks with
infinitesimal pT are randomly added to the jet cone and are clustered along with
the topoclusters used in the clustering algorithm. The small pT values do not
affect the clustering or jet measurement itself, but the average fraction of clustered
ghosts over the total associated jet cone area becomes the jet area.
This area correction is only derived from jets within the central detector
and is insensitive to effects that are dependent on NPV. The contributions to
the jet energy from in and out-of-time pileup can be approximated by examining
differences between truth and reconstructed jet pT measurements as a function
of NPV and µ, thereby representing effects of both in and out-of-time pileup
contributions. The second step of the pileup correction corrects these contributions
using MC simulation of hard-scatter QCD events to estimate the jet exposure
to pileup. Truth and reconstructed jets are matched with a ∆R< 0.3 and the
reconstructed pT difference between the truth and reconstructed jets is measured
as a function of ηdet, the central detector η. The difference is histogrammed as a
function of µ and NPV and a functional form is fit to the difference, allowing for a
sequential removal of the pileup dependence.
The correction uses this measured functional form in the calculation across
both NPV and µ,
57
∂pT
α (ηdeta) = (ηdet) (3.15)
∂NPV
∂pT
β (ηdet) = (ηdet) (3.16)
∂µ
The total correction from this calibration step starts from the EM-scale
reconstructed jet, subtracts the average pileup contribution over the jet, then
applies the ρ correction in sequence.
presidualT = α× (NPV − 1) + β × µ. (3.17)
The corrected jet pT then becomes
pcorr = preco − parea − presidual = precoT T T T T − ρ× A− α× (NPV − 1)− β × µ. (3.18)
This calibration was performed on Run 2 ATLAS data and is shown in
Figure 3.12.
3.10.2. JES Correction
The stable components of MC truth jets have a well-defined response in
the simulated detector, and so the four-momenta of simulated reconstructed jets
can be corrected on average to match the true energy distributions seen in the
calorimeters. This relies on having a fairly accurate detector model to use in the
simulation, however mismodeling of the detector can be corrected for in the in-situ
methods described in the following sections.
58
FIGURE 3.12. A demonstration of the pileup correction as applied to
reconstructed jets matched to truth jets with pT = 25 GeV [11] as a function of
(a) NPV and (b) 〈µ〉.
Simulated reconstructed jets are matched and corrected to their
corresponding truth jets within a radius cut of ∆R < 0.3 (∆R < 0.6 for large-
R jets). Events are classified into various bins of Etruth and ηdet. The distributions
of Ereco/Etruth are formed for each bin; the means of Gaussian fits to the cores of
these distributions indicate the average energy scale to be corrected to. The actual
response of Ereco at each Etruth and ηdet bin is derived from a numerical matrix
inversion, and the overall correction factor is the inverse of this response and is
applied to each jet [11].
The η correction is an additional correction applied to the JES after the
energy correction. A similar approach is applied as in the energy correction.
Jets are placed into a series of Etruth and ηdet bins, and an average response is
determined from the ηdet/ηtruth distributions. This is a smaller-order correction
to the energy vector of the jets, but helps increase the jet energy and reconstructed
invariant mass resolution.
59
3.10.3. Jet Mass Scale Correction
The Jet Mass Scale (JMS) correction is a set of correction factors derived as
a function of η and the mass that is applied to the uncalibrated jet’s mass. They
are derived in an identical manner to the JES factors, only binned and applied
to the jet mass instead of the jet pT. MC samples are examined to determine the
ratio of the truth to the reconstructed jet mass, and the ratio becomes a response
factor that can be inverted to derive a calibration factor for the data. This method
is validated by examining the jet mass shape in tt (top/anti-top quark event) data.
The JMS mass resolution can be seen in Figure 3.13.
3.10.4. GSC Correction
The Global Sequential Calibration (GSC) corrects higher-order jet energy
from pT-dependent and parton-level effects [11]. Jets from different initiating
partons have varying responses in the detector. Jets originating from the
hadronization of a quark tend to have a lower multiplicity of tracks associated
to the jet, and these tracks tend to have higher pT distributions. Gluon initiated
jets tend to have a wider and softer set of energy deposits that do not penetrate as
far into the detector.
Since this series of sequential calibrations utilizes energy deposits in various
detector layers to account for the penetration depth of the energy deposits, it is
natural to consider the effect of high pT jets that have significant missing energy
in the context of this calibration step. High pT jets can stochastically have a
significant fraction of their true energy lost out of the detector due to punch-
through of the energy through all the calorimeter layers. This energy will be
60
visible as a set of energy deposits in the muon system geometrically close to the
energy deposits of these high pT jets.
Similarly to the previous procedure, a series of calibration curves that correct
the data to the MC energy scale were derived. These corrections are functions of
the energy fractions in the first layer of the HCAL, to account for higher pT effects
from, in particular, high pT quark-initiated jets. Variables such as the number of
jet-associated tracks and the number of topoclusters are also incorporated into
the correct to account for the quark/gluon jet differences. These derived response
curves sequentially account for detector response differences to these various
hadronization and punch-through effects.
3.10.5. In-Situ Corrections
The η-intercalibration is an in-situ calibration method that is applied to jets
after the GSC stage. This method is a data-driven method to perform a higher-
order correction to the JES to account for problematic regions of the detector and
to correct the overall scale differences between the forward and central regions.
Transition regions in the detector such as shifts between regions of different
granularities or detector technologies create both symmetric and asymmetric
response differences for jet measurements. The η dependence of these response
difference will not be captured by the JES correction step, and so this higher-order
correction is applied afterwards.
Well measured dijet events have a back-to-back pair of jets that have
minimal contributions from pileup jets or out-of-cone radiation from leading jets in
the event. To leading order in QCD, these events are expected to be pT balanced
at the truth level and also at the reconstruction level, if the events are well-
61
measured and calibrated properly. This is utilized in the intercalibration; a shift
in the average pT balance of these dijet events is attributed to detector-level
miscalibrations from previous calibration steps and is corrected for in probe bins
of η and pT. Events are selected from data and from MC QCD events that have
leading and subleading jets that are back-to-back in φ with a |∆φ| > 2.4 cut.
To reduce asymmetries in the dijet pair caused by third jets in the events, the
third jet is required to have no more than 40% of the average pT of the leading
and subleading jets. To reduce the effect of pileup contamination of the event-
level asymmetry, the Jet Vertex Tagger (JVT) is applied with a “Tight” threshold
to reject jets that are not from the PV in the event. This is a hybrid machine-
learning method that tags R = 0.4 jets as originating from the PV or from pileup
vertices using jet and jet-associated tracks, however, this is not derived for R = 1.0
jets. Events are then sorted into their respective calibration bins of pT and η with
event performance trigger selections which ensure that events are selected with at
least a 99%-efficient trigger.
The pT asymmetry within each of these bins is computed, where the
asymmetry of two jets is defined as
pT,0 − pT,1
A = . (3.19)
pT,avg
These distributions are computed for every pair of bins and reflect the asymmetry
shift for every probe bin relative to every other reference bin. Gaussian fits to the
core of these asymmetry distributions determine the mean of this asymmetry
shift for that particular set of bins, and well-fitting distributions are taken as
appropriate bins to use in the calibration. In the traditional “central” method,
events in the barrel (|η| ≤ 0.8) region are considered well measured due to the
62
flat response of the JES in this barrel region, and events in the forward (|η| ¿ 0.8)
barrel region are corrected relative to the central region. However, this method
is statistics-limited and a matrix method was developed midway through Run 2.
In this method, every probe bin is defined relative to every other reference bin
in the detector. An overall calibration loss function is defined via product of the
asymmetry matrix of the bins and parameterized response factors in a similar bin
matrix. The product of these matrices is minimized via matrix inversion and the
simultaneous set of response coefficient equations corresponding to the correction
factors for each bin are solved for.
The ratio of these response coefficients of the MC and the data then become
the calibration factors needed to push the data’s JES scale to that of the MC’s
for each bin. Spline fits are then applied to the calibration factors to smooth the
detector response and to allow interpolation for any jet pT and η.
An additional in-situ method using the event asymmetry of either a
Z+γ event or a Z→µµ event provides a higher-order correction to the eta-
intercalibration. Barrel-region photons are precisely calibrated, so the absolute
JES of the recoil jet can be determined, and an overall correction factor can be
derived. Similarly, a recoil jet off a dimuon pair can have its absolute energy scale
corrected for [60].
The combination of these calibration methods gives very precise Jet Energy
Resolution (JER) for jet measurements, in particular at low pT. For R = 0.4 jets,
the final jet energy resolution at 300 GeV is roughly 6% [61], and for R = 1.0 jets,
it is roughly 12% at 400 GeV [12]. Figure 3.13 shows precision of the JES and JMS
corrections for R = 1.0 jets
63
FIGURE 3.13. In-situ methods such as γ+jet measurements are used to validate
the previous calibration steps [12]. The JES response is shown to be calibrated
within 2%, and the JMS response is consistent within error bounds.
FIGURE 3.14. Calculated JER for R√= 1.0 jets after application of the JES andJMS calibrations [12]. An analytic fit to the MC JER was used in the systematic
evaluation for this analysis - f(pT) = a
2/p2 2T + b /pT + c
2 with a=5.018×10−4,
b=1.092, and c=-2.090×10−2.
3.11. Dijets
This analysis focuses on the dijet topology, where balanced pairs of jets are
expected to lie relatively back-to-back in the transverse plane. An example of one
such event is shown in Figure 3.15.
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FIGURE 3.15. A high-mass dijet data event with mjj = 3.91 TeV illustrating a
back-to-back jet pair originating from a single vertex with 5 reconstructed pileup
vertices. [13]
During trigger development, the resulting jets from simulated Hidden Valley
samples were examined for their ability to properly reconstruct Z’s that were
generated with mass 600 GeV. It was found that R = 0.4 jets that are standard
for properly reconstructing QCD jets are insufficient for containing most of the
energy of these dark jets, as Figure 4.7 shows. The total invariant mass loss away
from the truth Z’ mass was reduced from up to 40% with the R = 0.4 jets to 10%
with the R = 1.0 reconstruction. This motivated both the trigger strategy and the
analysis methodology to focus on pairs of large-R jet events.
The next chapter shows the analysis method wherein these physics objects
that were reconstructed from the detector are analyzed for the presence of signal.
A set of cuts and machine-learning taggers separate out the signal-like events and
the resulting invariant mass spectra are then analyzed statistically. The Search
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Phase and Limit-setting phases are detailed, indicating the level to which this
analysis can conclude on the presence of signal (Search Phase), and the cross-
section limits that can be placed on excluded signal (Limit-Setting Phase).
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CHAPTER IV
ANALYSIS
4.1. Dijet Bump Hunt Searches
Searches for exotic particles within the dijet and multijet spectra can be
hampered by the statistical dominance of QCD events, even after the application
of optimized cuts designed to reduce the background contamination and enhance
the signal sensitivity. However, the dominance of these background events can
be taken advantage of by providing a background-rich set of data for training
autoencoders or machine-learning classifiers, and these analyses can use aspects
of the background dominance to utilize data-driven background estimates that
rely on significant statistics in the data set. This analysis takes advantage of both
methods using a modified weak classification method - a modified Classification
Without Labels (CWoLa) method.
4.2. Data-Driven Background Estimate
Due to the predominance of these QCD events, the dijet invariant mass
spectrum fits well to a series of analytic functional forms. The smooth response
of QCD cross-sections with PDFs, with a relatively smooth jet calibration, can
make these spectra fit to a variety of power-law functions, and the global or local
applicability of these fit functions depends dramatically on the luminosity. The
relatively small width of any resonances compared to the overall acceptable fit
range of the spectrum means that these resonances will appear as a small bump in
the invariant mass (mjj) spectrum. The invariant mass in natural units is
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m2jj = (E
2
1 + E2) − |p~1 + p~2|2 , (4.1)
but in collider experiments is usually computed as
m2jj = 2 · p1 · p2 (1− cos θ), (4.2)
where θ is the angle between the momenta vectors. Depending on the analysis, the
masses of reconstructed objects can be small enough to be insignificant, in which
case the invariant mass becomes
m2jj = 2 · pT1 · pT2 (cosh(η1 − η2)− cos(φ1 − φ2)) . (4.3)
The analytic functions that are fit to invariant mass spectra have varied
in their functional form, number of fit parameters, and range of applicability to
increasing luminosities. Care needs to be taken that the choice of fit function
does not under- or over-fit the data, that the range of the fit does not obscure
any signal, or that the fit itself is not significantly affected by the presence of
detectable signal.
At small enough luminosities, these analytic functions typically fit globally
across the entire range of the spectrum. However, with an increase in statistics
in the spectrum, either by an increase in luminosity or a reduction in the lower
mjj limit of the data, these fit functions can fit within a narrower range of the
spectrum due to the decreased statistical uncertainty no longer masking higher-
order effects on the JES. The Sliding Window Fit (SWiFt) method was developed
to accommodate this.
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Most power-law functions that do not globally fit to the dijet spectra will
fit appropriately within some narrower range in mjj. So in the SWiFt method,
to derive a background estimate for each mjj bin, a chosen functional form is fit
to the bin of interest and the previous and subsequent N bins. N varies on the
choice of fit function and the statistics within the spectrum itself, but is generally
chosen to be as large as possible without under-fitting the data. An evaluation
of the χ2/ndf can indicate if either under or overfitting occurred in the fit. A
visualization of this is shown in Figure 4.1. At the lower end of the spectrum, the
background fit is more uncertain as it can only fit the upper N/2 bins from the
central bin. As the window slides down the center of the spectrum, the background
fits the previous and following N/2 bins. At the high edge of the spectrum, only
the previous N/2 bins can be fit.
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FIGURE 4.1. A visual demonstration of the SWiFt fitting mechanism for a given
window width [14].
4.3. CWoLa Method
The CWoLa method is a Weak Classification Machine Learning method
that is used to reject uninteresting events from the background-dominated mjj
spectrum and to enhance the signal contribution to the spectrum. The method
relies on classification theorems regarding optimal classifiers for mixed samples
[62]. Given two samples, both of which are dominated by background-type
events, in the presence of signal, one of the mixed samples might contain different
distributions in the feature space considered. Any classifier that learns the optimal
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classification of these mixed samples is the optimal classifier for distinguishing
individual signal events from background events [58].
Figure 4.2 demonstrates the classification procedure, where neural networks
are trained to classify events from the central signal bin (labeled as ‘1’ events)
from events in the sidebands (labeled as ‘0’ events). The same window width
is then evaluated for the next signal bin, thereby sliding the window down the
spectrum.
FIGURE 4.2. Visual demonstration of the CWoLa method combined with a
SWiFt fit.
The advantages of this are apparent as a specified signal model is not
required and generic signals with enhancement in physics-motivated feature space
can be searched for. The decision on the set of features to train the classifier
remains a choice that is motivated by the physics of interest. However, the
classifier will be naturally invariant to the signal model, making this method ideal
for discovery when there is a large parameter space to search.
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This method has been used previously at ATLAS in one preparatory analysis
[58], hereafter referred to as the “original CWoLa (ATLAS) analysis”. This
analysis searched for heavy pairs of large-R jets produced by a heavy resonance.
This analysis was intended to validate the use of unsupervised learning at ATLAS,
and so the input feature space that was used just contained the leading and
subleading jet masses. In practice, as long as the response of the networks across
the input feature space is relatively invariant across mjj, the feature set can be
expanded by the physics motivation of the analysis. This method could potentially
be extended as a deep learning problem, where the entire jet image (calorimeter
image) is processed with a Convolutional Neural Network and the associated tracks
are processed with Recurrent Neural Networks (RNNs). However, a more thorough
analysis method would be required to ensure this doesn’t induce bumps in the
spectra.
4.3.1. Feature Space
The authors of the original ATLAS CWoLa analysis [58] intended for
their analysis to be a proof-of-concept of the application of this method in dijet
searches, and so the only features trained on were the leading and subleading
jet masses in the event. This analysis searched for heavy LLP decays of the type
A → B + C with an agnostic approach to the coupling mechanics or byproducts,
with the exception of the assumption of central s-channel production of heavy
jets. However, the jet masses of emerging jet signals will have similar jet mass
spectra as in QCD as the initiator quarks have O(1 - 10 GeV) masses. In addition,
the overall jet mass spectrum is very model dependent due to the wide hierarchy of
particle masses in the dark sector decays, as shown in Section 4.9. So the feature
72
space was expanded by a number of variables that are motivated by the physics of
these events.
– The leading and subleading jet masses.
– The leading and subleading jet promptTrackFrac (defined in Equation 4.4).
– The number of jets in the event.
∣
– |y∗| = ∣y0− ∣y1 ∣ using the leading and subleading jets.
2
– |∆φ| = |φ0 − φ1| is the φ separation between the leading and subleading jets.
The macroscopic lifetimes of the dark pions in the dark showers produce
a set of displaced tracks with high |d0| values. These non-prompt tracks can be
associated to their resulting jet and used as a measure of the prompt and non-
prompt components of the jet. A new jet variable called promptTrackFrac (PTF)
is therefore introduced,
1 ∑ ( )
promptTrackFrac = pT |d0| < 2.5 σd (pT ) . (4.4)
p i 0,i iT jet
i∈tracks
Here, σd0 is the resolution of the track d0 measurement, and is very dependent
on the track properties. The 2.5 multiplicative factor was determined to be
the optimal factor via signal studies on R-Hadron LLP samples; more details
on this are in Appendix A.1. The track measurement error has a series of
complex dependencies that are interrelated with the ID efficiency, the track’s
pT and other kinematics, and the PV / beamspot uncertainty. However, a
generalized parameterization of this significance is applied in this analysis to be
consistent with the events that will be selected by the Run 3 emerging jets trigger.
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However, a more complex parameterization would include higher-order terms
in the power-law series used to parameterize σd0 , or an individualized track-by-
track computation would take the beamspot (and therefore the PV) geometric
uncertainties into account. This track-based uncertainty treatment is available
at the offline level in ATLAS, but to be consistent with the trigger selection, the
analytical fit is currently preferred.
The chosen functional form of σd0 was determined via a study of Z bosons
in “Enhanced Bias” data. Enhanced bias data is a separate data stream [8] in
ATLAS that is used to characterize standard bunch-crossings and pileup effects
within the detector, in addition to its used in the calibration of low-pT objects.
The stream uses a set of minimally-biased and highly-prescaled hit triggers to
select events just above the detection threshold of the detector. These so-called
“spacepoint” triggers search for a minimal energy-producing jet in the event or
a minimal threshold of energy that’s detected in the pixel system. This stream
is ideal for these sorts of performance studies requiring low-pT reconstructed Z
bosons with a standard pileup environment.
FIGURE 4.3. A Feynman diagram of the Z boson + photon process used to
determine the associated track d0 distributions from QCD ISR jets.
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To ensure minimal contamination from pileup tracks on the σd0
measurements, recoil jets off an s-channel produced Z boson (shown in Figure
4.3) were used to derive the d0 resolution. The selected events were required to
have two opposite-sign muons with |η|< 2.4 and 70<mjj < 110 GeV. A recoil jet
with |∆φ (Z, jet) |> 2.0 was required to have at least 50% of the Z boson’s pT.
Tracks were selected within a ∆R < 0.6 region from the jet and required to have
pT > 1 GeV and |PVz − z0| < 10 mm. The d0 distributions of these tracks were
binned in track pT in bins of width 0.5 GeV, and Gaussians were fit to the central
peaks of the d0 distributions to determine the width of the d0 distributions.
A power-law function was fit to the d0 resolution histogram for tracks
with 1.0 GeV≤ pT < 8 GeV, as shown in Figure 4.4, and defines the resolution
function used in the PTF variable’s definition. The functional fit was σd0 =
0.0436 / pT [GeV] + 0.0195, with the resolution function σd0 defined in mm.
FIGURE 4.4. The d0 resolution function from Z boson recoil jet studies and its
analytical functional fit.
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The PTF variable was originally designed for use as an LLP selector, so its
sensitivity was tested on R-Hadron samples with lifetimes 0.1 ns and 10 ns, and
the optimal multiplicative factor found was 2.5. PTF was later determined to
be an ideal variable of choice for separating emerging jets signals from the QCD
background. Figure 4.5 demonstrates PTF values for a variety of signal samples
shown relative to the background-dominated data. A clear separation exists
between these distributions, allowing both simple cut-based and machine learning
methods to enhance signal sensitivity in the analysis. Further information on the
derivation of this variable can be found in Appendix A.1.
For this analysis, the PTF definition was modified slightly from the original
studies. The ∆R association was changed to a radius of 1.0 to match the radius of
the large-R jets, and the track association z0 cut was changed to |PVz− z0| < 8 mm
to be consistent with the configuration used in the Run 3 emerging jets triggers.
These triggers and their configurations are elaborated on more in Chapter V.
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FIGURE 4.5. Z’ samples with mass 1500 GeV and data leading jet PTF
distributions for a variety of lifetimes and dark models. The data are scaled by
an appropriate factor to fit the plotting scale.
The event variable |y∗| is used in a variety of dijet analyses searching for
s-channel resonances. Most bump-hunt searches consider resonances such as
BSM Z’ particles with vector or scalar s-channel resonances over the t-channel
dominated QCD background. The |y∗| distribution peaks at high values for t-
channel QCD processes and at low values for s-channel processes. The authors
of the original ATALS CWoLa paper [58] estimated that the signal fraction of
most heavy resonances in the search region were enhanced by at least a factor of
5 by this cut. This is demonstrated in Figure 4.6, where the peak of each QCD
channel’s cross section for an incoming parton is at high |y∗| values.
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FIGURE 4.6. QCD y∗ distributions for a given interacting parton at an energy
scale s. Forward scattering cross-sections tend to dominate in QCD due to its t-
channel predominance.
The inclusion of |∆φ| as an input feature was intended to account for events
with hard radiation away from the leading or subleading jets. Effects from this
third-jet radiation are likely correlated with the number of jets, but will add
additional information into the NN that is correlated with how clustered jets are
along the back-to-back axis of the Z’ decay’s byproducts.
The number of jets in the event was used as a feature as it has been shown
to be a good discriminant in model-dependent machine-learning methods used
in the ongoing ATLAS 4-jet emerging jet analysis. QCD events tend to contain
smaller numbers of jets than dark jet events; at a pT scale of 100 - 200 GeV, the
small-R jet multiplicity is generally 4 or 5. Emerging jet models tend to have
a large tail in the number-of-jets distribution as the wide decays tend to have
substantial out-of-cone radiation. However, this effect is likely to be somewhat
diminished in this analysis as R = 1.0 jets are used instead of the standard R = 0.4
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jets. This is demonstrated in Figure 4.7 where most of the decay energy tends to
be captured by R = 1.0 jets and where R = 0.4 poorly reconstruct the Z’.
FIGURE 4.7. Invariant mass distributions for R=0.4 jets (top) and R=1.0
jets (bottom) for a variety of 600 GeV Z’ samples and low-pT simulated QCD
background (labeled as JZ2). Significant model and lifetime dependence is seen;
this illustrates that at high dark meson lifetimes, the signal follows the background
distribution due to the missing energy in the events.
Events passing the previously listed cuts were sorted into an mjj histogram
with binning that is consistent with the jet resolution. Then, events in each bin
and its sliding window were trained on to classify the events in the signal bin from
events in the sidebands using the input features. A cutoff threshold was defined
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by examining the neural network output scores for events in the sideband regions,
and the top 10% or 1% quantile becomes the threshold that was extrapolated to
the signal bin. The events with scores exceeding that threshold as evaluated by
the trained neural network on the test events in that signal bin were selected and
placed in a filtered histogram, and the BumpHunter algorithm was run on the
spectra after the background fits.
4.4. Monte Carlo Events
The analysis method employed in this analysis can determine limits on
generic signals, particularly Gaussian-shaped signals with a defined width and
strength. However, knowledge of how the emerging jet signatures appear within
the detector is critical for extracting the signal efficiency of these processes and
for extracting fiducial cross-section limits. To model the effects on these signals,
emerging jet Z’ events were simulated with Pythia 8.245 using the Hidden-Valley
module. The simplified model’s structure is specified in Chapter II, and the Pythia
configuration is shown in Appendix A. The PDF set used to simulate the nominal
samples used in this analysis was the NNPDF 2.3 LO set from the NNPDF
collaboration [63].
The subsequent decay of the Z’ into pairs of dark quarks is dependent on
the properties of the dark sector, where the coupling is set by the model and the
decay is further constrained by the kinematic phase space available to the dark
quark pair. The perturbative hadronization in the dark sector is performed by
Leading Order (LO) calculations in the Hidden Valley model of the cross-sections
and kinematics in the dark color sector. The small coupling to the Standard Model
down quark creates the long-lived nature of the dark pions and defines the Z’
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cross-sections. The lifetime specifies the emerging aspect of the dark jets such as
the displaced vertices and tracks that are produced after their hadronization has
completed.
The authors of the emerging jets phenomenology paper [37] calculated
approximations to the width of the Z’ decay - Γ(MZ′) ≈ MZ′/100. This
corresponds to a width of roughly 15 - 40 GeV in the mass range considered in this
analysis. The width was set to 20 GeV in the sample generation to be consistent
with these approximations. After simulation of the generated events was complete,
including the hadronization, events were filtered to those with two anti-Kt R = 0.4
truth jets in the central detector region with (|η|< 2.4) and pT > 125 GeV. As
detector simulation and reconstruction of events is resource-intensive, this filter
was set to remove events that are not likely to be reconstructed within the
detector or readily used in the analysis. The Pythia configuration and software
tags used in the Athena sample generation process are listed in Appendix A.1.
The response of the detector to the generated particles in these events was
simulated using GEANT4 [64]. This program uses the estimated detector model
to simulate the response of each region of the detector to the generated truth
particles produced by Pythia. An alternate and less resource-intensive program,
the ATLAS Fast (AF2) simulation program was found to be insufficient for the
modeling of the signal samples as it uses parameterized jet modeling and doesn’t
take the lifetime of BSM truth particles into account during the simulation.
The samples were then run through the standard ATLAS reconstruction
software, Athena [56]. Athena digitizes the simulated detector hits, overlays
simulated pileup onto the events with the data-appropriate pileup (µ)
distributions, and then outputs a software-readable file containing all the
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reconstructable objects from the detector, including large-R jets, tracks, tagged
electrons and photons, b-tagged jets, and muons. The overlaid pileup distributions
were generated using Pythia with the A3 tune of the NNPDF 2.3 LO PDF. These
samples were then reduced by the application of a derivation filter called EXOT3.
Derivation filters reduce the file size through a removal of unneeded objects,
apply the needed trigger decisions, and apply event-level vetoes. The cuts in the
EXOT3 derivation are pT > 120 GeV, m> 30 GeV applied at the trigger level to
the leading and subleading jets in the event, and application of all available single
and multi-jet unprescaled large-R triggers. Figures 4.8 - 4.10 are virtual displays of
some of these simulated and reconstructed signal events using visualization tools
incorporated within Athena.
FIGURE 4.8. A 1500 GeV Z’, cτ = 1 mm, Model A event showing the leading
central jet in the event and tracks with pT greater than 2 GeV, showing the lack of
reconstructed tracks associated to the leading jet in the event.
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FIGURE 4.9. A 1500 GeV Z’, cτ = 5 mm lifetime, Model B event. Top left -
beampipe-transverse view of the event with pT> 50 GeV (R = 1.0) jets and
pT> 2 GeV tracks. Top right - same as the left plot but showing all tracks
associated to the PV. Bottom row, oblique projections showing calorimeter energy
deposits, jets, and all the tracks in the event.
83
FIGURE 4.10. A 1500 GeV Z’, cτ = 10 mm, Model B event with pT > 50 GeV
(R = 1.0) jets. Right and bottom plots - oblique and beamline transverse plots
with pT > 2 GeV tracks associated to the PV.
4.5. Data Selection
Data were taken from Run 2 of the LHC as recorded in the “physics Main”
stream of ATLAS. Events were filtered to remove events that were not taken
during stable data-taking periods, such as those during unstable beam conditions
or during detector issues. The list of acceptable data-taking periods are listed in
Good Run Lists (GRLs), and the applied GRLs are shown in Appendix A.1.
These events lie in a range of data-taking conditions, such as during different
pileup conditions, trigger menu settings, and bunch-crossing configurations. Events
were selected that passed the lowest unprescaled single-jet hardware trigger,
known as L1 J100. The L1 trigger system performs square clustering on the
coarse topocluster calorimeter trigger-tower segments, and events not meeting the
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pT cutoff of 100 GeV (at the L1 energy scale) are discarded. These events represent
a large fraction of the total number of events triggered by ATLAS at L1.
Events were then filtered into the EXOT3 derivation format. The EXOT3
derivation is a filtered set of events and physics objects for specific analysis use,
particularly for high jet-mass events with decays to large-R jets. This derivation of
the data required “an OR combination of single large-R jet and HT triggers”, as
well as “at least two online jets with mass > 30 GeV and pT> 100 GeV, or two jets
with pT> 1 TeV.”
The leading jet masses for the MC are plotted in Figure 4.17. Data with
reconstructed large-R (R = 1.0) jets are known to be efficient above a jet mass cut
of 35 GeV due to the studies shown in Section 4.5.1. The jet mass distribution for
QCD jets is known to peak close to 0 GeV, so this cut reduces a large quantity of
background with little hit to signal efficiency.
The efficiencies of these signal samples after passing through the DAOD
step are listed in Appendix A. The table shows some reduction in signal selection
(30% - 60%), however these cuts are very efficient in removing background events;
the background-dominated data had a selection efficiency of 0.177% after these
analysis-level cuts. The fraction of events passing the sequential pT and η cuts, jet
mass cuts, |y∗| cut, and PTF cuts are 14.8%, 6.9%, 4.2%, and 0.177% respectively.
To ensure that the truth-level cuts in the generation were not significantly
affecting the efficiencies at the reconstruction level, the ntuple-level efficiencies
were determined for one signal sample (2000 GeV, cτ = 1 mm, Model A) without
the presence of any truth-level cuts. From the 1k events originally generated, 755
passed the analysis-level (DAOD+cleaning+event-level) cuts, and 738 passed the
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truth-level cuts for R = 1.0, while 694 passed based on cuts on the R = 0.4 truth
jets.
4.5.1. Trigger selection
The trigger menu changed significantly over the run-taking and varied over
the data-taking years to account for the expected pileup distributions in each
year. The primary triggers implemented for each year are listed in Table 4.1,
which represent the entirety of the unprescaled primary large-R dijet triggers that
collected data during this period of time. The backup triggers are not listed but
have insignificant luminosities and vary significantly on the pileup profile. Events
were filtered into the final selection using these triggers, and the efficiency point for
the highest-pT threshold trigger was used to derive a conservative measurement for
the mjj efficiency point for all the Run 2 data.
Year Lowest Unprescaled Online pT Offline mjj
Triggers Cut Cut
2015 HLT_j360_a10_lcw_sub_L1J100 360 GeV 1.3 TeV
2016 HLT_j420_a10_lcw_L1J100 420 GeV 1.3 TeV
2017 HLT_j460_a10_lcw_subjes_L1J100 460 GeV 1.3 TeV
HLT_j480_a10_lcw_subjes_L1J100 480 GeV 1.3 TeV
HLT_j460_a10t_lcw_jes_L1J100 460 GeV 1.3 TeV
HLT_j480_a10t_lcw_jes_L1J100 480 GeV 1.3 TeV
2018 HLT_j480_a10t_lcw_jes_L1J100 480 GeV 1.3 TeV
TABLE 4.1. The lowest pT unprescaled primary large-R jet triggers operating
during Run 2 data-taking periods.
Due to differences between reconstruction at the trigger level and offline
calibrated scale, the mass and pT cuts that are placed online are not fully efficient
offline at their specified online thresholds. Therefore, to apply an appropriate
set of cuts to ensure that the data is efficiently selected from the output stream,
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trigger efficiency plots were created. The efficiency of events selected by the probe
trigger relative to a lower-threshold reference trigger were plotted as a function
of the variable of interest, after appropriate cuts and calibration steps have been
applied.
Events are generally required to be at least 99% efficient in mjj in order
to appropriately apply a background fit, although this threshold is luminosity
dependent as higher luminosities increase the analysis’ sensitivity to these trigger
effects. Since the derivation specifies an online mass cut, the efficiency of the probe
triggers used through the data-taking years was plotted, and the mass cut was
chosen at the point where the trigger is 99% efficient.
An example of this method is shown in Figure 4.11 for the variable pT, from
which the mjj efficiency point is estimated. A conservative estimate is to assume
that the mjj turn on point is twice the pT turn on point, although in practice it
can be slightly lower than this. To ensure that the selected jet mass cut (35 GeV)
is trigger efficient, trigger efficiency plots were created as a function of the jet
mass. Events were required, at the offline level, to have jet cuts of pT > 500 GeV,
|η|< 2.0, and m> 35 GeV, in addition to the event-level cut |y∗|< 0.6.
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FIGURE 4.11. Offline pT trigger efficiency plot for HLT j460 a10 lcw subjes L1J100
triggered events relative to HLT j390 a10t lcw jes L1J100 events for 2018 Period
K data. Events are fully efficient down to the mjj = 1300 GeV cut with the
conservative assumption of the mjj turn on point equaling 2× the pT turn on
point. This trigger is the highest pT threshold trigger for the unprescaled primary
triggers, so the mjj efficiency point here is applicable to the other primary triggers
in the dataset selection.
FIGURE 4.12. Leading offline jet mass trigger efficiency plot for
HLT j460 a10t lcw jes L1J100 triggered event relative to HLT j260 L1J75 events
for 2018 Period K data. Triggered events are shown here to be fully efficient down
to the 35 GeV offline mass cut.
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Selection Search Region Cut Validation Region Cut
Trigger Unprescaled R = 1.0 Jet Triggers -
Offline Jet pT0 > 500 GeV -
Offline Jet pT1 > 200 GeV -
Online Jet pT0 , pT1 > 125 GeV -
Offline Jet |η0|, |η1| < 2.0 -
Offline m0, m1 > 35 GeV and < 300 GeV -
Online m0, m1 > 30 GeV -
|y ∗ | < 0.6 -
PTF0,PTF1 < 0.3 ≥ 0.3 and < 0.5
mjj > 1300 GeV -
TABLE 4.2. Search and Validation region cuts applied to the data. The Validation
region cuts are identical unless specified otherwise.
Due to trial-and-error experimentation during training, it was found that
the NNs tended to learn to prioritize information about the highest jet-mass
events, and were not necessarily selected due to their low PTF values. To reduce
the effect of these spuriously-selected high-mass events, a tighter set of PTF and
jet-mass cuts were applied; the jet masses were constrained to 35≤m< 300 GeV
and the PTF cuts were reduced to PTF< 0.3. This greatly improved the training
stability and signal selection of the networks, and the PTF cut greatly reduced
the overall training time due to the reduced number of events. This did come at
the expense of statistics available in the tail-end of the spectra, where the method
had issues extrapolating from the quantile NN score cuts in the sidebands to the
signal region. This pushed the upper mass bound of the limits down to 4088 GeV
and 3629 GeV for the spectra with the 10% and 1% neural network score cuts,
respectively.
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4.6. Bump Hunt Analyses
The general analysis procedure is: events matching the analysis cuts were
filtered into datasets to form the spectra and training sets after the calibration
sequence is applied. For each mjj bin, events in the neighboring 4 bins on each
side were used for the sideband training. The spectrum was filtered into separate
spectra for events that pass each quantile cut over the sliding windows. The
SWiFt method was then applied to the NN filtered mjj spectra for background
estimation using fits with a window width of 13 bins. The set of functions used
to fit to the spectrum are the three parameter dijet function and the UA1 fit
function, with the dijet function taking the form
( )
mjj 2
f x = √ = p0 xp1 (1− x)−p2−p3 ln(x)−p4 ln(x) . (4.5)
s
The three parameter function is Equation 4.5 with p3 = p4 = 0. In dijet (R = 0.4
jet) searches, the window width that is used for the fit is generally 11 - 25× the jet
mjj resolution, but it is adjusted to ensure that the function does not overfit or is
under-constrained given the degrees of freedom available to the fit. The binning
was chosen to be consistent with other dijet searches at ATLAS [14], where the
binning also matches the mjj resolution. The evolution of the binning starts at
around 30 GeV in width for the first bins at around 1 TeV and increases to over
100 GeV at the 5 TeV scale, and is listed in Appendix A.1. The UA1 function is
shown in Section 4.13 and was used as a fit systematic in the Search and Limit-
Setting procedures.
A resonance within the data will appear as a bump in the mjj spectrum
that must be evaluated in a statistical manner. The BumpHunter algorithm
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paper [65] elaborates on this algorithm that was developed to evaluate spectra
for localized resonances. A large number of pseudoexperiments are formed to
test the background hypothesis against the data. In each pseudoexperiment,
the background estimate is Poisson-fluctuated, the starting fit parameters are
varied, the fit function is varied, and a local test statistic is evaluated for each
possible signal interval along the spectrum. The interval widths are allowed to
vary from 2 to 5 maximum bins and define the range of potential bumps that
can be statistically evaluated by the algorithm. The local p-value is evaluated
in each interval by computing the Poisson probability of the data given that
pseudoexperiment’s fluctuated background estimate. A global test-statistic (t) is
then computed by taking the minimum of the local p-values: t=− log (pmin,intervals)
over all the evaluated intervals. The overall distribution of these test statistics
is formed and also evaluated on the data, and the fraction of pseudoexperiments
lying below the data’s global test-statistic value is the overall spectrum’s global
p-value.
The interpretation of the global p-value is that any similar cut-based method
used to rule out the null hypothesis would be incorrect at the p-value’s level. For
example, a p-value of 0.7 indicates that any attempt to refute the null hypothesis
with an alternate model, using the same test statistic, would be incorrect 70% of
the time. Therefore, the 0.01 cut that was placed on the p-value for the discovery
threshold in this analysis is a 99% indicator of the likelihood that an alternate
model (possibly a signal plus background model) exists that is more consistent
with the data.
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4.7. Neural Networks
In similar fashion to the behavior of neurons within biological systems,
artificial neural networks (NNs) are a series of layered and weighted nodal
decisions that are trained to match a desired output. While vastly less complex
than biological systems such as the brain, artificial neural networks are seeing
rapidly increasing use in many modern applications, and their complexity
and use are widely varying in application. They are used to solve a variety of
problems - common examples include reading handwritten digits and image
classification. Traditionally in particle physics, NNs are applied to separate events
by their background-like or signal-like qualities to provide a relatively accurate
classification. Other applications in particle physics include the use of Recurrent
Neural Networks (RNNs) to tag jets as b-quark initiated jets, the use of NNs in jet
calibration, and the use of NNs to classify complex event types that have difficult-
to-distinguish final-state topologies.
Preprocessed data are fed through the series of layers within a NN, with
normalization and weighting applied to the computed information that’s fed
forward to each layer. The final layer’s outputs are a set of numbers for each
output layer; these can give classification probabilities if the model act as a multi-
feature classifier. The action of this normalization, the individual and group
weighting of nodes in the layer, the learning algorithm, and the structure of the
network affects the overall accuracy and response of the network to its inputs. The
output of these neural networks in the case of a binary classification problem is
generally a set of numbers in the range from 0 to 1, with “1” indicating events
with the most signal-like qualities, and the network can then define a probability
of a particular output belonging to a particular class.
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The features that are fed into a NN are generally preprocessed in advance
for accuracy and numerical stability of the model. Normalization of the input
data features and expected outputs in the general range of [−1, 1] is preferred to
increase stability of the trained NN to both outlier events and overtraining. In
this analysis, event features were normalized by the subtraction and division of the
feature distributions’ approximate means. Further details on this normalization
are in Appendix A.1. This approximately centered the distributions at the central
values and normalized the features to their minima and maxima.
To allow for comparable results between this analysis and the original
CWoLa analysis [58], a similar NN structure was chosen, 7× 64× 32× 8× 2. The
input feature space was increased to 7 input variables from the 2 (jet masses) that
were previously used, but the same number and dimension of hidden layers was
chosen, with 64 nodes in the first hidden layer, 32 nodes in the second hidden
layer, and 8 nodes in the last hidden layer. A dropout layer between the first
and second hidden layers in the network was set with a dropout fraction of 10%.
If a network becomes too reliant on the information provided by a small subset
of nodes, it can learn a model that’s applicable only to the training data and
can be not transferable to the test or other similar data. This is referred to as
overtraining. By applying a dropout layer, a fraction of the nodes are dropped
randomly from the model during the training and the learned model is more
generalizable to additional data such as the validation data. A diagram of the
network is shown in Figure 4.13. The output has two classification nodes, and the
activation function is a softmax function to approximate the probability of each
output being from either output class. The softmax function is a generalization
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of the logistic function that allows the output values to represent approximated
normalized probabilities of each output class. Analytically, it can be expressed as,
∑K
s(z ) = ezi/ ezji (4.6)
j=1
for each nodal output zi.
FIGURE 4.13. A visualization of the network architecture used for this analysis.
Note that the dropout layer is not shown.
Networks were implemented in the Tensorflow framework [66] using the
Keras backend [67]. Optimizer parameters were chosen to be consistent with the
previous CWoLa analysis; the learning rate for the networks was 1 × 10−3 and the
networks were trained for a maximum of 1000 epochs on a GPU. To help prevent
overtraining, a scheduler reduced the learning rate by 0.25% for each epoch after
the first 100. 20% of the input events were randomly selected as the validation set,
and output plots of the AUC and the the validation loss were used to check for
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over- and under-training. The loss function defines the overall inaccuracy of the
network, and the learning algorithm attempts to minimize the overall loss function
on the training data. The weighted Binary Cross-Entropy loss function [68] was
used; it is a well-used loss function for binary classification problems. The analytic
form of this loss function (with no event or class weighting) is
∑N1
L( ~y ) = − yi · log (p(yi)) + (1− yi) · log (1− p(yi)) , (4.7)
N
i=1
with the true class label yi (for binary separation problems, this is 0 or 1) and
p(yi) is the evaluated probability of that label given the model, all for N evaluated
events. As the training problem is highly imbalanced, with up to a factor of
10× more sideband events than signal region events, class weighting was used to
prevent the trained models from getting stuck in a local minimum, such as the
situation where a false positive classification of all events as sideband events is the
most optimal model configuration. The class weighting applied to this loss function
effectively changes the representation of the number of events in each classification.
For example, the class weighting of the signal region events ws, with population Ns
is ∑
1 Ns
w = ∑ i wis , (4.8)
iwi(yi = 1) 2
for event i′s weight wi. With this weighting scheme, the value of the loss function
becomes meaningful; for a properly reweighted set of signal and sidebands with
identical distributions, if the relevant NN is unable to differentiate the mixed
samples, then the loss should approach ln (2) = 0.693.
The AdaM (Adaptive Moment) optimizer [69] was used to minimize this
loss function due to its prevalent use in similar binary classification problems,
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including the original CWoLa analysis. This algorithm uses a momentum term
in the adaptation of the model parameters to help prevent the loss function from
getting stuck in a local minimum. The network parameters are adjusted for each
step of the algorithm proportionally to the first derivative of the loss function
and inversely proportional to the second derivative, and the momentum has been
shown to ensure quick and effective minimization of loss functions [70] across a
variety of machine learning applications. Additional AdaM optimizer settings that
are set are β1 = 0.8, β
−8
2 = 0.99, = 1 × 10 , and r= 0.0025, which correspond to
the exponential constant of the first and second moment calculations, a divisor for
numerical stability, and the learning rate decay constant, respectively. The batch
size was set to 1% of the total training events to be consistent with the original
analysis. In addition to the class weighting, individual sample weights were applied
to each event that were trained on. When signal events are injected into various
sidebands, they have a weight that depends on their estimated cross-section, the
number of events in the signal sample, and the overall strength of the injection -
this appropriately weights the events to their expected cross-sections. The event
weighting we for signal events is therefore
we = σfid · S / N, (4.9)
for N generated events with a fiducial cross section of σfid at a signal strength of S.
When the weighting of a particular event was well over unity, training instability
was found to be problematic, as highly weighted events in smaller training batches
have large effects on the computed loss function’s gradients. So, in the case that
a signal event’s weight was above 2, the weightings were replaced with 1’s and
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the signal events were over-sampled many times to match the expected signal
contribution for that particular weighting.
Outputs from the NN can have spurious values if the hyperparameters of the
network allow the node weightings to change dramatically, or when the inputs have
spurious values away from the normalized ranges from the training set. To reduce
sensitivity to this effect and ensure that information fed into the next layer is
appropriately normalized, each layer’s outputs can be passed through an activation
layer. Activation layers map output distributions to values generally between -1
and 1 by use of an analytical function. The choice of activation functions depends
on the use case of the NN; some examples are the tanh function, the sigmoid
function, and the rectified linear function.
The sigmoid function is the first layer’s activation function; this allows the
networks to be less sensitive to outlier features that might be overprominent in the
training after the width-normalized preprocessing. The suppression of the outliers
is due to the exponential powers in the sigmoid function. The three hidden layers
in the network have the leaky rectified linear (ReLU) function applied in sequence.
The use of these ReLU functions is a way to introduce non-linear effects into NNs
and their use is standard for many binary classification problems in the data
science field. ReLU is effectively a filter on information that suppresses negative
layer information at each layer in the network; this information leads to a zeroed
output and a negligible effect on the model’s training gradients. The discontinuity
and wider range of feature space that can be omitted from the NN’s learning
greatly improve the accuracy and resistance to overtraining, and introduces non-
linearities into the model [71]. The leaky ReLU function allows for negative layer
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information to still exert an influence on the NN’s training, albeit with a user-set
reduced scale (α = 0.3) for negative contributions. The function is defined as,
ReLUL(x) = {x for x >= 0; α · x for x < 0}. (4.10)
To account for situations where the network’s initialization state was a
local minimum that the solver could not adapt to, five independent networks
were trained for each signal bin. The samples were randomly shuffled before the
sample’s training and test set split. The network with the minimum loss function
was chosen as the network implemented within the analysis for each particular bin.
Since the highly-imbalanced nature of the datasets prevent the accuracy
metric from being particularly useful, the Area Under the Curve is considered. It
is the area under the true positive and true negative score ROC curve, and should
reach 1.0 for perfect classification. Some examples of the training loss and AUC
values from particular sidebands are shown in Figure 4.14.
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FIGURE 4.14. Sideband 8’s (upper row) and 14’s (lower row) evolution of
the AUC (left) and loss function (right) over the training epochs. A small
amount overfitting is demonstrated by these networks, however generalized
hyperparameters that prevented overfitting for every bin were difficult to find.
4.8. CWoLa Method Validation
The efficacy of the CWoLa method in selecting signals of interest was
determined via signal injection studies. The CWoLa method can act in two general
capacities for enhancing the signal sensitivity - as an autoencoder and as a mixed
classifier. Signal events are not guaranteed to be evaluated as “signal-like” by the
trained networks, however their NN scores are not necessarily consistent with
the “background-like” score distributions in each sideband. Therefore, the NNs
can act as autoencoders as the more variate signal scores are more likely to lie in
the upper 10% / 1% quantile of signal region scores. Of course, the signal events
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can be enhanced by the central intent of the CWoLa method - to enhance the
signal-like component of events in the signal regions as compared to events in
the sidebands. The performance of the CWoLa method as an autoencoder can be
tested by examining the signal efficiency of selection of injected signal for NNs that
were trained without the presence of injected signal. The CWoLa performance as
a signal classifier can be tested by examining the selection efficiency for NNs that
were trained with signal injected at a variety of cross-section strengths.
One unfortunate quirk of the CWoLa method is that if few signal events
appear in the signal region and if many appear in the sideband regions, the
network learns to anti-tag signal events. This results in an all-or-nothing type
enhancement of signal in this method; the signal sensitivity is sharply pointed
towards the peak of the signal distribution and tends to select fewer signal events
closer to the tails of the signal distributions. This greatly reduces the overall signal
width, which is shown in Table 4.5.
The original CWoLa analysis used a different bin configuration for the
construction of their signal regions and sidebands. Wide (1 - 2x signal width)
regions were selected for the signal region, which often corresponded to regions
of 5 - 10 bins. The same-sized neighboring regions were selected as the sidebands.
To determine the effects of the single-bin choice for the signal region in this
analysis, the signal region was varied by increasing numbers of bins in the plus
and minus directions. The signal efficiency for each signal region selection was
evaluated for an injected signal with the signal region width varying from 1 to 7
total bins. A dependency of the overall signal efficiency was found on the number
of bins, but this test case illustrates that the peak signal sensitivity is greatest
when 1 bin is selected as the signal region. This is likely due to the fact that this
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signal region definition contains the highest proportional fraction of signal, and
the classifiers learn to distinguish these mixed samples more readily. This effect is
illustrated in Figure 4.15.
FIGURE 4.15. Effects from varying the signal region width used in training. The
injected signal was a 2000 GeV Z’ with cτ=1 mm and Model A. The signal peak
at around bin 15 is enhanced the most by the 1 bin signal region. The spuriously-
selected events in the high mass bins away from the peak are likely selected due to
the autoencoder effect of this method.
4.9. Signal Evaluation
The 175 signal points that were generated for this analysis and in
preparation for future Run 3 analyses are composed of exotic Z’ particles produced
with masses 1500, 2000, 3000, 4000, and 5000 GeV. Models A - E were used in the
generation and the dark pion lifetimes were generated with cτ in the set of (1, 2, 5,
10, 25, 50, and 100 mm). These signal samples were reconstructed with an overlay
of simulated pileup samples pulled from a probability distribution that mimics the
pileup distributions for each of 2015+2016, 2017, and 2018 (referred to as mc16a,
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mc16d, and mc16e campaigns). The identical EXOT3 derivation filter was applied
to both these samples and to the data.
FIGURE 4.16. Invariant mass distributions of the signal samples sorted into 5
different lifetime sets. Models A-E are shown at each defined lifetime. The overall
number of signal events are defined by the signal cross section which is a function
of the Z’ quark coupling gq, which is set to 0.001 for these signal samples. The
data are scaled to fit the plot’s scale.
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FIGURE 4.17. Leading jet mass distributions for 5 different signal lifetimes.
Models A-E are shown at each defined lifetime for production during Run 2. The
data distributions are scaled to show on the same plot.
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FIGURE 4.18. Leading PTF distributions for 6 different signal lifetimes. Models
A-E are shown at each defined lifetime, and the data are scaled to fit the plot.
The training revealed that the neural networks tend to discriminate the
signal regions from the sidebands primarily from the jet mass information. The
signal efficiencies tended to peak at regions of high leading and subleading jet
mass, and the networks did not readily learn to use the PTF variable appropriately
with just the derivation and the analysis cuts, such as the |y∗| cut. The NN
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selection efficiencies also tended to peak in regions of high PTF, indicating that
spurious events with unusually high PTF values tended to bias the NN learning.
To reduce both of these effects, a PTF< 0.3 cut and the jet mass cuts were
placed on the leading and subleading jets in the events. The signal sample PTF
distributions tend to reach a maximum at 0.3, as shown in Figure 4.18. Therefore,
a tighter PTF cut was not applied in order to prevent dependence of the limits on
the sample lifetime, in addition to ensuring that there were reasonable statistics
available to fit the mjj spectra in the higher mass bins.
4.9.1. Signal Injection Studies
To test the learning capabilities of the trained networks, signal events were
injected into the data spectrum at varying strengths and the efficiencies of the
neural networks selections were evaluated. The overall cross-sections of the signal
spectra are quark-coupling dependent, but to avoid regenerating the signal samples
at each strength, the spectra were weighted by their respective strengths before
injection. The samples were generated at a quark coupling of 0.001, but events
were injected with strengths in the range (1x, 10x, 100x, 1000x). The efficiencies
listed in Table 4.3 reflect the signal efficiencies without factoring in the effects of
the derivation and analysis cut inefficiencies from the reconstruction and analysis.
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Inj. Mass Inj. cτ Inj. Model Strength Selection with 10% NN Cut
2000 GeV 1 mm A 0x 9.1 %
2000 GeV 1 mm A 20x 15.1 %
2000 GeV 1 mm A 200x 36.8 %
2000 GeV 1 mm A 2000x 42.1 %
2000 GeV 1 mm A 20000x 47.6 %
3000 GeV 10 mm B 0x 23.9 %
3000 GeV 10 mm B 20x 22.8 %
3000 GeV 10 mm B 200x 26.3 %
3000 GeV 10 mm B 2000x 37.1 %
3000 GeV 10 mm B 20000x 39.1 %
TABLE 4.3. Global signal selection efficiencies for a range of signal injection
strengths.
The 3 TeV signal samples starts at a selection efficiency of 23.9% when
no signal is injected, indicating that there is a correlation between the events
naturally in the data that are selected by the NNs and the injected signal. The
NNs’ predominance in selecting events with high jet masses is likely the cause of
this autoencoder-like effect. The 2 TeV signal starts at an approximately random
selection (10%) and increases to 47.6 % at the highest injected signal strength,
which is likely the fraction of the peak that is not rejected due to the anti-tagging
effect. If there is no enhancement in signal efficiency due to the response of the
√ √
NNs, the signal significance, S/ B, is expected to decrease by 10/ 10 = 3.2 if
signal is randomly selected. Therefore, at the point where a signal efficiency more
than 32% at a NN score of 10%, the baseline signal efficiency is improved relative
√
to a random selection. Similarly, at the NN cut of 1%, 100/ 100 = 10, indicating
that the signal significance is boosted once a signal efficiency of 10% is achieved.
The injections were performed on search spectrum data at varying strengths,
and the global signal selection efficiencies are listed in Figures 4.34 and 4.33.
The NN selection efficiencies and resulting signal sensitivities for 1500 GeV (cτ
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= 1 mm) injected samples for individual bins are shown in Figures 4.23 - 4.31.
They illustrate the significant model dependencies in the NN performances. The
anti-tagging quality of the CWoLa method is also demonstrated, where both the
significance and efficiencies of the NN selection are worse than random selection in
the tails far from the location of the signal peaks.
The background fits get skewed by the presence of localized signal above a
certain injection threshold, and the discovery potential is limited by the maximum
injected signal that can be statistically detected. This is demonstrated in Figures
4.19 and 4.20, although these plots illustrate injections done with approximately
29 fb−1 of data and a limited set of trigger decisions considered. The discovery
threshold lied between an injection strength of 2000x and 20000x at a 10% NN
score cut and between 10x and 100x at a 1% NN score cut.
In addition, the anti-tagging effect of these NNs resulted in an overall
reduction in the signal widths. This manifested in the analysis as a reduction in
the Gaussian widths for the determined limits. They resulted in a reduction of
the signal width from 12 - 18% to 5 - 10%, as can be seen in Tables 4.4 and 4.5 and
Figures 4.23 - 4.32. In these figures, the dashed lines indicate the “break-even”
point - the point where the signal sensitivity is enhanced relative to a random
selection.
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FIGURE 4.19. Signal injections (2000 GeV Z’, cτ = 1 mm, Model A) done at 2000x
and 20000x strength relative to the cross-sections defined from gd = 0.001. The
BumpHunter p-values for these injections were 0.77 and 0.0 for these spectra after
application of the 10% NN score cut.
FIGURE 4.20. Signal injections (2000 GeV Z’, cτ = 1 mm, Model A) done at
10x and 100x strength relative to the cross-sections defined from gd = 0.001 after
application of the 1% NN score cut.
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FIGURE 4.21. Selection efficiencies as a function of leading and subleading jet
mass and leading jet promptTrackFrac distributions for data and an injected
1500 GeV Z’ signal. The trained neural networks tended to learn information
about high jet mass events and preferred to use these mass variables as a
discriminant.
Z ′m Model Width Z
′
m Model Width
1500 A 18% 3000 A 13%
B 18% B 13%
C 18% C 13%
D 17% D 14%
E 15% E 12%
2000 A 19% 4000 A 11%
B 18% B 10%
C 18% C 11%
D 19% D 10%
E 13% E 10%
TABLE 4.4. Unfiltered signal widths from Gaussian fits to cτ = 1 mm samples.
Models B and E have mass hierarchies closest to QCD and therefore generally have
smaller widths.
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Z ′m Model Width Z
′
m Model Width
1500 A 5.6% 2000 A 6.9%
B 7.8% B 6.9%
C 5.6% C 7.8%
D n/a D 8.0%
E 7.0% E 5.6%
TABLE 4.5. Signal widths from Gaussian fits to cτ = 1 mm samples after
application of the trained NNs.
FIGURE 4.22. Selected signal events and Gaussian fits from a 2000 GeV Z’
injected with signal strength 50 after application of a 10% NN score cut.
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FIGURE 4.23. Signal injections (1500 GeV Z’, Model A) done at 50x (2σ
fluctuations in peak bin), 100x, and 200x strength relative to the cross-sections
defined from gd = 0.001. The top and bottom plots correspond to cτ=1 mm and
cτ=2 mm samples respectively.
FIGURE 4.24. NN Signal efficiencies and Signal Significances for 1% NN score cut
criteria on (1500 GeV Z’, Model A, cτ = 2 mm). Large enhancements in the signal
sensitivity are seen relative to the 10% NN score cuts.
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FIGURE 4.25. Signal injections (1500 GeV Z’, Model B) done at 50x (2σ
fluctuations in peak bin), 100x, and 200x strength relative to the cross sections
defined from gd = 0.001. The top and bottom plots correspond to cτ = 1 mm and
cτ = 2 mm samples respectively.
FIGURE 4.26. NN Signal efficiencies and Signal Significances for 1% NN score cut
criteria on (1500 GeV Z’, Model B, cτ = 2 mm). Large enhancements in the signal
sensitivity are seen relative to the 10% NN score cuts.
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FIGURE 4.27. Signal injections (1500 GeV Z’, Model C) done at 50x (2σ
fluctuations in peak bin), 100x, and 200x strength relative to the cross sections
defined from gd = 0.001. The top and bottom plots correspond to cτ = 1 mm and
cτ = 2 mm samples respectively.
FIGURE 4.28. NN Signal efficiencies and Signal Significances for 1% NN score cut
criteria on (1500 GeV Z’, Model C, cτ = 2 mm). Large enhancements in the signal
sensitivity are seen relative to the 10% NN score cuts.
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FIGURE 4.29. Signal injections (1500 GeV Z’, Model D) done at 50x
(corresponding to 2σ fluctuations in peak bin), 100x, and 200x strength relative
to the cross sections defined from gd = 0.001. The top and bottom plots correspond
to cτ = 1 mm and cτ = 2 mm samples respectively.
FIGURE 4.30. NN Signal efficiencies and Signal Significances for 1% NN score cut
criteria on (1500 GeV Z’, Model D, cτ = 2 mm). Large enhancements in the signal
sensitivity are seen relative to the 10% NN score cuts.
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FIGURE 4.31. Signal injections (1500 GeV Z’, Model E) done at 50x (2σ
fluctuations in peak bin), 100x, and 200x strength relative to the cross sections
defined by gd = 0.001. The top and bottom plots correspond to cτ = 1 mm and
cτ = 2 mm samples respectively.
FIGURE 4.32. NN Signal efficiencies and Signal Significances for 1% NN score cut
criteria on (1500 GeV Z’, Model E, cτ = 2 mm). Large enhancements in the signal
sensitivity are seen relative to the 10% NN score cuts.
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FIGURE 4.33. Global signal selection efficiencies for 3000 GeV (cτ = 1 mm)
samples by NNs in overall spectrum as a function of injected signal strength
(efficiencies after 10% NN score quantile cut.) The overall signal efficiency is not
necessarily the target metric of interest in bump hunt searches, but do indicate the
general trend of the NN performance.
FIGURE 4.34. Global signal selection efficiencies after a 1% NN score quantile
cut for 1500 GeV (cτ = 1 mm) samples by NNs in overall spectra as a function of
injected signal strength.
4.10. Signal Search Phase
The goal of the Search Phase of this analysis was to determine the
probability that the observed data was consistent with statistical fluctuations from
the smoothed background model. So given a smooth and analytic function that
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is fit to a given window, variations from the background estimate at the probe
(central) bin are expected to be due to statistical fluctuations from a Poissonian
distribution in the presence of no signal.
The BumpHunter program [65] is a toolkit designed to search for these
bumps in a given spectrum. The program handles two important aspects of a dijet
analysis that are difficult to account for, combined up or down fluctuations and the
“look elsewhere” effect. Poissonian fluctuations over the interpolated background
estimate are expected, however these fluctuations must be correlated under the
assumption of the presence of a signal, which will fluctuate the spectrum upwards
within the signal width. For example, six bin-sequential upward fluctuations in the
spectrum are far more signal-like than the same-sized fluctuations alternating in
sign. Therefore, any probability computation must use the sign of the fluctuation
as a measure of the signal-likeness. BumpHunter accounts for this by combining
bins within a combination width in sets of pseudoexperiments; this accounts for
correlations in these fluctuations.
In addition, in any statistical measure involving a large number of counting
experiments (i.e. a bump-hunt search with a large number of bins), a certain
fraction of the pseudoexperiments (bins) will fluctuate at a statistically significant
amount. For example, in a counting experiment where the threshold for discovery
is a 5% probable deviation from the background estimate, a discovery will be
made, on average, in 1 out of 20 bins. BumpHunter accounts for this “look
elsewhere” effect by performing an additional number of pseudoexperiments on
the spectrum itself. It estimates the fraction of times that a given statistical
fluctuation would produce a discovery at any other bin location in the spectrum
and utilizes this fraction in the p-value calculation. Pairs of bins are alternated for
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each psuedoexperiment; this accounts for situations where a random fluctuation
might align in one local region with other fluctuations and induce a bump.
BumpHunter computes probability values by looking at the set of
pseudoexperiments that are performed. Each bin is fluctuated by a Poisson
distribution relative to the background estimate and the test statistic is
computed. The p-value is the probability that, given the background estimate,
the BumpHunter test statistic will be greater than or equal to the test statistic
computed from the actual data. The statistical basis of this method is based on
a theorem that shows that the Type-I error (probability to wrongly reject the
null hypothesis / background estimate) is α if a well-defined test statistic has a
discovery threshold of α on its p-value [65]. In the case of this analysis, the p-value
criteria for discovery is set to 0.01 based on long-standing arguments from the
BumpHunter developers. The interpretation of this number is that an alternate
hypothesis other than the null hypothesis would have a 99% chance of fitting the
model better, and since signal plus background models are inclusive in that set of
hypothetical models, the presence of signal in the evaluated data can not be ruled
out by this criteria.
4.11. Validation Region Studies
To validate the methodology applied in the analysis, NNs were trained
and evaluated on a Validation region spectrum. Any “signal” discovery in this
Validation region would be attributable to an issue within the applicability or the
implementation of the CWoLa method within the analysis, or potentially due to
another issue such as spurious bumps induced by miscalibration. The signal-sparse
and background-enriched region that was selected for the Validation region was
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defined where both jets in the events satisfy 0.3 ≤ PTF0,1 < 0.5. An alternate
Validation region was tested that used an inversion of the |y∗| cut, |y∗| > 0.6,
however this region was severely affected by trigger inefficiencies up to 1550 GeV.
The selected Validation region contains events more kinematically similar to the
Search region events, with a selection that resulting in similar numbers of events to
the Search region, in order to validate this method for a similar luminosity.
Following the plan for the Search Phase in the Search region, a data set
was formed using the cuts specified in the Validation region column in Table 5.1.
Events were sorted into the same bins as the Search region, and NNs were trained
to separate the events from the signal bin from those in the sidebands. The Search
Phase was performed with BumpHunter searching for significant bumps in the
resulting spectra.
The results from BumpHunter indicate that the application of these NNs
does not seem to induce spurious bumps in the spectrum. The BumpHunter
p-values for the 10% and 1% spectra were 0.91 and 0.69 respectively, and the
results are shown in Figures 4.35 and 4.36. The conclusion drawn from these
Validation region studies is that detector-level issues or the CWoLa method did
not causing spurious bumps at the luminosities that were considered. In addition,
the methodology of extrapolating the NN score quantile from the sidebands to the
signal region does not seem to produce any spurious signal as long as sufficient
statistics are available for the training and evaluation. In the upper regions of
the spectra, the training statistics are O(100) applied to O(10) events in each
signal bin, forcing the potential upper mass limits of this analysis to below 4
TeV. Appropriate spectra fits could not be done above 4 TeV due to the statistical
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fluctuations caused by the statistics-poor extrapolation of the NN score quantiles
to the signal regions.
FIGURE 4.35. BumpHunter outputs from application to the 10% NN score cut
Validation region spectrum. The upper plot indicates the formed spectrum and
the maximal BumpHunter bump region, its tomography plot is shown on the
bottom right, and the distribution of the BumpHunter test statistic is shown
on the bottom right. Bumphunter evaluates the p-value for a range of intervals
across the spectrum and uses the range with the minimal p-value as the maximum
discovery region; these intervals are shown in the tomography plot.
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FIGURE 4.36. BumpHunter outputs from application to the 1% NN score cut
Validation region spectrum. The upper plot indicates the formed spectrum and the
maximal BumpHunter bump region, its tomography plot is shown on the bottom
left, and the distribution of the BumpHunter test statistic is shown on the bottom
right.
4.12. Limit-Setting Phase
Given the lack of indication of excesses or bumps in the spectrum, the limit-
setting phase follows. The general question asked in this phase is “Given that
no signal was observed, to what cross-sections can we place limits on the signal
model?” This is a complex procedure involving the many facets and variations
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possible in the analysis. For example, small changes in the JES can affect the
signal shapes observed, modifying the overall sensitivity to a bump of that sort,
and thereby affecting the final limits obtained.
The Bayesian Analysis Toolkit (BAT) is a high-energy physics framework
designed to evaluate model limits [72]. The BAT evaluates injected signals of
defined or approximated signal shapes and evaluates the maximum injection
strength before discovery is possible. The posterior distributions of the signal
cross-sections are estimated using a Monte-Carlo sampling method; this method
assesses the signal strength given an injection with plus and minus 1σ variations
from the systematics. The final limits obtained from the toolkit are uncorrected
cross section that do not incorporate model and analysis considerations such as the
signal branching ratio BR, total selection efficiency , and acceptance to produce
the fiducial cross-section σfid. The relationship between these variables is
σBAT = BR ·  · σfid. (4.11)
A determination of the final cross-section limits must therefore incorporate
the branching ratio and signal efficiency. For the assumption of a leptophobic
Z’ with decays purely to dark quark pairs, the Branching Ratio (BR) is 1.0. The
signal efficiency is more complicated, as a series of truth-level, derivation-level, and
analysis-level inefficiencies are aspects of this analysis that must be incorporated.
The truth-level inefficiencies arise from truth-level filters that are placed on
generated events to ensure that the produced events are likely to be resolved in
the detector. These truth-level cuts are listed in Section 4.4, but are not easily
reinterpretable by theorists, and so the final cross-sections can be more difficult to
interpret. So, a fiducial cross-section σfid was defined that incorporated the initial
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truth-level filters, and theorists can then define final-state efficiencies and fiducial
cross-sections to compare to these cross-section limits.
The injected signals were Gaussian signals that varied in their injected mass,
width, and amplitude. The largest number of injected events pulled from these
signal shapes becomes the observed limit for that particular signal. The systematic
parameters in the signal model, such as the JES and JER contributions, all
contribute to the posterior probability of each tested signal point. A Markov-
Chain Monte-Carlo (MCMC) algorithm [73] is used to define the central value
of the observed limit at each mass point, and the uncertainties on that observed
limit can be obtained by extraction of the CLs of each measured point. These
observed and expected limits, however, are not the fiducial cross-section limits.
The overall efficiencies of the signal selection and NN selection can be used to
correct for the analysis procedure to extract fiducial limits on the emerging jets
production process.
At the truth level, the fiducial cross-section is the product of the truth filter
efficiencies, the production cross-section, and the Branching Ratio (BR) to the
channel of interest.
σfid = truth · σprod · BR. (4.12)
At the analysis level, the BAT cross-section limits σBAT are a product of the
analysis efficiencies, the NN selection efficiencies, the derivation efficiencies, and
the fiducial cross-sections. ALso, the leptophobic assumption of the model ensures
that the BR can be set to 1.0 in the limit inference.
σBAT = analysis · NN · deriv · σfid. (4.13)
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So the measured limits can be corrected to match the fiducial production by the
correction,
σBAT
σfid = . (4.14)
deriv · analysis · NN
The BAT also produces expected limits that are used to give context to the
observed limits. The expected limits are calculated by Poisson fluctuating the
smooth background estimate in a number of pseudoexperiments. The ensemble
of the Poisson-fluctuated spectra that can be generated without triggering the p-
value discovery threshold becomes the expected limits, and 1σ and 2σ error bands
can be determined from this procedure. Plots of the various efficiencies used in this
analysis to convert the BAT limits to a fiducial cross-section are shown in Figures
4.37 - 4.38.
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FIGURE 4.37. Signal efficiencies from application of the derivation-level cuts, the
analysis cuts, and the NN selection for different lifetime samples. The envelope of
the five model variations defines the error bands of the total efficiency and is an
approximation of the hadronization systematic.
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FIGURE 4.38. Signal efficiencies from application of the derivation-level cuts, the
analysis cuts, and the NN selection for Model A - E samples. The envelope of the
five model variations defines the error bands of the total efficiency. This can also
be interpreted as an approximation of the effects of lifetime and width variance
of the models on the limits, although this is beyond the scope of the analysis
presented here.
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4.13. Systematics
A number of systematics in this analysis affect the overall resulting limits
and p-values. Uncertainties in measured quantities are affected by variances due
to statistical fluctuations, but other effects ranging from the calibration procedure
needed to reconstruct jets, the fitting procedure needed for a background estimate,
and the hadronization model used during the signal generation can have large
effects and must be accounted for in determining the final limits.
In any calibration procedure, uncertainties on the calibration method and the
applied cuts are varied in order to determine their systematic effects on the final
measurable quantities. There are a number JES systematics considered in analyses
that affect the invariant mass that is reconstructed from the jets in the event. The
standard JES variations for jet systematics in these analyses use variations of plus
and minus 1σ, and so the BAT toolkit will vary the JES as applied to the signal
shapes, shifting the spectra up and down from their nominal peak position [11]
by a percentage that’s defined by the JES uncertainty. For this analysis, the JES
uncertainty was conservatively set to 2%.
The overall calibration affects the pT resolution and the JES in a manner
that will shift and smear the Gaussian injected signals. Figure 3.14 shows the
uncertainty bands on the JER measurements, which hit a maximum of 2% close
to the low edge of the pT distribution. So convservatively, the JER systematic can
be approximated by a shift in the JER analytical function by 2%.
The fit type systematic approximates the variation in the background
estimate due to the choice of fit function. The standard procedure for dijet
searches is to use a different class of fit function as the systematic variation of
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the background estimate. To be consistent with previous dijet analyses, the UA1
function was chosen as the functional form for this alternate fit function.
( )
f(x) = p · x−p10 · ln (p2 / x) · ln p / x23 (4.15)
The fit error systematic defines the uncertainty on the background fit. If
a local fitter is used, marginally different background estimates can be formed
depending on the fitting algorithm and the starting point of the fit parameters.
The BAT accounts for this effect by performing fit pseudoexperiments to
determine the effect of varying starting parameters by the fitting algorithm on
the overall limits.
The luminosity uncertainty indicates the total uncertainty of the integrated
luminosity observed by the detector [74]. The luminosity calibration procedure
started with a baseline luminosity that was measured in low-luminosity detector
conditions using van der Meer scans [75]. These beam scans are intended to
measure the beam cross section and maximum visible luminosity using forward
detectors such as LUCID [76]. The overall uncertainty of the Run 2 luminosity
measurement is 1.7% after corrections to the baseline luminosity measurement are
made to account for pileup conditions.
The hadronization model affects the overall width of the Gaussian signal
shapes, as well as the signal strength. So the spread of observed limits for a variety
of signal widths becomes a measure of the hadronization uncertainty on the BAT
limits. The fiducial cross-sections are estimated by dividing by the analysis’ total
signal efficiency, and the envelope of the signal efficiencies approximates the effects
of the hadronization systematic on the final fiducial limits. Therefore, the final
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fiducial limits shown in Figures 4.41 - 4.42 have the hadronization systematic
incorporated into the bands of the plotted limits for each dark model.
4.14. Results
The Search Phase evaluated the spectrum to determine if there were any
statistically significant bumps using BumpHunter. The spectra were extracted
with the application of the NNs with 10% and 1% cuts on the NN scores, and
BumpHunter was applied to the resulting spectra with ranges 1300 < mjj <
4088 GeV for the 10% cut spectrum and 1300 < mjj < 3628 GeV for the 1%
cut spectrum. The limited range is due to the statistics available above each
corresponding cut after implementation of the NNs and analysis cuts, and the
spectra and BumpHunter statistical plots are available in Figures 4.39 and 4.40.
The standard evaluation for p-values that is used in ATLAS dijet searches
uses a threshold of 0.01 before evidence of a discovery can be determined. In the
event that a below-threshold p-value is found, a series of cross-checks of the data
reconstruction, calibration, and the fitting procedure would be done to check for
any source that can explain a spurious bump in the spectrum. In the event that
an experiment- or methodology-based explanation cannot be found for the excess
causing this p-value, this is considered evidence of an unexplained spurious signal
and more exhaustive checks would be required to understand why these simple
analytical functions cannot fit the spectra. However, the p-values of these fits were
0.90 and 0.92 indicating that there is good confidence in no observed excesses in
the spectra.
These computed p-values were obtained from a SWiFt-like fit to the data
with a window width of 13 bins with the 3-parameter fit function, with 10000
129
pseudoexperiments performed by BumpHunter. The fit systematic uncertainties
were evaluated with 1000 BumpHunter pseudoexperiments.
FIGURE 4.39. The three parameter analytical function fit to the spectrum after
the 10% NN score cut. The BumpHunter p-value score for this spectrum was
0.90 for the nominal background, but the final value after inclusion of the fit
systematics was 0.917 ± 0.009. The BumpHunter tomography plot is shown in
the bottom plot, indicating the local p-value intervals in the algorithm. The bump
of maximum local significance was between 1998 GeV and 2251 GeV with local
significance 2.37932. The global fit parameters were [7.84855×10−11, -21.1505, -
12.4406] with the SWiFt fit χ2/ndf = 0.711501.
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FIGURE 4.40. The three parameter analytical function fit to the spectrum
after the 1% NN score cut. The BumpHunter p-value score for the nominal
spectrum was 0.918, and after inclusion of systematics, the evaluated p-value
was 0.887 ± 0.01. The BumpHunter tomography plot is shown in the bottom plot,
indicating the local p-value intervals in the algorithm. The bump of maximum
local significance was between 1451 GeV and 1573 GeV with local significance
1.41454. The global fit parameters were [4.3384×10−21, -51.8578, -21.5426] with
the SWiFt fit χ2/ndf=0.483154.
The limits obtained from this analysis are presented for the spectrum with
a 10% NN score cut in Figure 4.41 and for the spectrum with a 1% NN score
cut in Figure 4.42. The observed limits and expected limits were scaled by the
signal efficiency to get the fiducial cross-sections as shown. The signal fiducial
131
cross-sections were excluded from approximately 20 fb at 1300 GeV down to 2 fb at
3000 GeV by the 10% NN score cut spectrum, and the signal fiducial cross-sections
were excluded from 10 fb at 1400 GeV down to 2 fb at 3000 GeV by the 1% NN
score cut spectrum.
This analysis was designed to provide model-independent limits on these
processes at a fixed width and at fixed lifetimes, to make it possible to evaluate
the limits for a variety of models. The black line on the fiducial cross-section
limit plots in Figures 4.41 and 4.42 indicate the Z’ production cross-sections as
a function of the truth Z’ mass with a gq coupling of 0.015. This indicates that
Z’ production with masses between 1.3 TeV and 3.1 TeV can be excluded for dark
sector couplings down to gq = 0.015. The dark sector coupling gd was set to 1 - gq
in this estimate to ensure that gd is greater than gq. The value does not have a
significant effect on the branching ratio or on the model curve shown in Figures
4.41 and 4.42 until the coupling to dark hadrons approaches that of the SM.
The Z’ width was set to the fixed 20 GeV width implemented within the nominal
Monte-Carlo production.
With the Z’ width set to 20 GeV, the dark quark couplings are 0.2, still at
least an order of magnitude above the SM coupling. This gives essentially the
same solid curve as in Figures 4.41 and 4.42. Reasonable lifetimes can be found
by allowing a wider width of the Z’ to allow dark sector couplings on the order of
gd = 1.0. In that case, for a 2 TeV Z’ with dark sector confinement scales at around
40 GeV, a strong coupling from the SM to the dark sector with strength O(10)
produces O(10 mm) lifetimes, within the detector acceptance region. Note that
if the Z’ is the only interaction contributing to the dark pion lifetime, then the
resulting lifetimes could be longer than 10 mm. This effect is fixed by the manual
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setting of the Z’ width to 20 GeV and the setting of the dark pion decay distance
to 1 mm.
The O(10 mm) lifetimes in some of the parameter space considered here
require an additional coupling of the dark sector to the standard model, for
example from a heavy scalar Xd particle which can induce dark pion decays via
a Yukawa coupling [1]. Also, in this work, the effects on the analysis presented
here of longer lived dark hadrons with cτ > 100 cm have not been studied. In this
case, detailed detector Monte-Carlo studies are needed for the range of possible
dark hadron lifetimes and are beyond the scope of this work. In cases where the
dark hadrons are so long-lived that they escape the detector, the ATLAS mono-jet
and mono-photon searches apply, but would become relevant for Z’ particles with
masses less than 2 TeV and SM couplings less than 0.25 [77].
O(1.0) couplings in both sectors at the 500 GeV mass scale readily produce
dark pion lifetimes at around O(10 mm), so the detailed Run 3 opportunities
shown in Chapter V present a good pathway to exploring a larger range of the
dark sector parameter space.
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FIGURE 4.41. (left) Gaussian BAT limits on Z’ production from the 10% NN score
cut spectrum. (right) Fiducial cross-section limit estimates after signal efficiency
corrections. 1 and 2 sigma bands on the expected limits are shown. The black line
indicates the fiducial cross-section for Z’ production with a gq coupling of 0.015.
134
FIGURE 4.42. (left) Gaussian BAT limits on Z’ production from the 1% NN score
cut spectrum. (right) Fiducial cross-section limit estimates after signal efficiency
corrections. 1 and 2 sigma bands on the expected limits are shown. The black line
indicates the fiducial cross-section for Z’ production with a gq coupling of 0.015.
135
The limits obtained by this analysis are very comparable to the limits
obtained by the previous ATLAS CWoLa analysis. Although a different signal
case was considered, similar data with similar cuts were evaluated, although the
original analysis was less inclined to provide additional variables in the models
such as the tracking variables used here. This analysis obtained very competitive
limits using both the 10% and the 1% NN score spectra; the 95% CL exclusion
limits obtained by the original analysis with a 10% cut were on the order of 1 - 20
fb, with significant dependence on the chosen models for the 3 TeV and 5 TeV
signals considered. The limits obtained here are all competitive at those mass
scales, where they range from 2 - 5 fb at 3 and 4 TeV.
Significant statistical effects were seen in the 1% spectrum by the original
CWoLa analysis, but competitive limits exist in the 1 - 5 fb range at 3 and 5 TeV.
This analysis achieved emerging jets cross section limits on the order of 2 - 3 fb at
that scale, which indicates the strength of this analysis method, especially applied
with track-based discriminating variables such as PTF.
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CHAPTER V
FUTURE STUDIES
5.1. Run 3 Emerging Jets Triggers
A specialized set of triggers were developed for the purpose of triggering on
emerging jets signatures during ATLAS Run 3 operations. These target the dijet
and dijet-plus-photon emerging jet signatures that are potentially detectable by
triggering on low-PTF events, allowing the potential mass and cross-section limits
to be enhanced in future analyses.
Type Dijet
Chain HLT j200 0eta180 emergingPTF0p08dR1p2 a10sd
cssk pf jes ftf preselj200 L1J100
|η| Range < 1.8
PTF Cut < 0.08
PFlow Threshold 200 GeV
EMTopo Threshold 200 GeV
L1 Seed L1J100
Rate 8.9 Hz
Type Dijet+photon
Chain HLT g45 tight icaloloose 2j55 0eta200 emergingPTF0p1dR0p4
pf ftf L1EM22VHI
η Range < 2.0
PTF Cut < 0.1
PFlow Threshold 2 × 55 GeV
EMTopo Threshold n/a
L1 Seed L1EM22VHI
Rate 11.4 Hz
TABLE 5.1. HLT-level cuts applied for each emerging jet trigger topology.
Substantial improvements to ATLAS computing has allowed tracking to be
run at the HLT level at much more competitive jet pT scales, allowing for greatly
137
enhanced trigger efficiencies for signatures that have a substantial track-based
component to their signatures [78]. For jet chains at ATLAS, tracking can only
be run on events that have a leading jet with pT greater than 200 GeV, which is is
due to the CPU resources available for the software trigger, at the time of writing.
This threshold is placed on the EMTopo jets (the standard jets used that utilize
ECAL-scaled energy deposits) before tracking is run. The online PTF variable
can therefore by computed on the jet Region of Interest after Fast Track Finding
(FTF) is run in the trigger, and an HLT-level selection on events with low PTF
values can be made at much lower mass scales than were ever possible. Due to
the greater precision of the Particle-Flow (PFlow) jet algorithm in reconstructing
jet energy, the PTF selection trigger algorithm will be applied to the PFlow jets
available above 200 GeV, once the fast tracking has been applied to the event. This
chain will be seeded on the unprescaled L1 J100 Level-1 jet trigger, which has an
L1 rate of 3.6 kHz at µ= 50.
The efficiencies of these chains with and without tracking resource
restrictions are shown in Figure 5.1. Above the 600 GeV mass point, this trigger
algorithm has relatively competitive signal efficiencies for several generated
emerging jet models and for a baseline BSM Higgs decay. The expected trigger
rate for this chain is 8.9 Hz at µ= 50 with a PTF< 0.08 cut.
The unfortunate situation where an EMTopo jet is a preselection before an
algorithm running on a PFlow jet will likely introduce some trigger inefficiencies
at the lower-mass region, pushing potential mass limits higher than desired. In
addition, these EMTopo and PFlow thresholds are close to the turn on of the L1
trigger system, which lies between 200 and 220 GeV, depending on the η selection.
138
For the dijet+γ signature, a trigger chain was developed that performs the
PTF calculation on the two leading jets in the event. In the event that the photon
passes the jet pT cut, the photon may be reconstructed as one of the leading or
subleading jets in the event. By applying the PTF algorithm to the two leading
objects in the event, this ensures that the trigger is not just selecting events with
a leading unconverted photon that mimics a non-prompt jet. The trigger is seeded
on the unprescaled EM22VHI L1 trigger that has an expected average L1 rate
of 2 kHz in Run 3 conditions. The HLT chain itself is expected to have a rate of
11.4 Hz.
FIGURE 5.1. Emerging jet trigger signal efficiencies with and without jet
preselection applied for a j175 seeded trigger with a 225 GeV preselection.
Efficiencies are computed for baseline low-mass Z’ models and one baseline H→ss
sample (the decay of a 600 GeV BSM Higgs into two 150 GeV scalars with a
cτ = 3.3 m.).
These triggers are intended to probe two general mass ranges. The single-
jet trigger was designed to target invariant mass ranges above 500 - 600 GeV, and
the dijet+photon trigger was designed to target mass ranges down to 200 - 250
139
GeV. The actual efficiency points will need to be determined after data-taking has
commenced, as sufficient luminosity will need to be taken by low-pT performance
triggers before these can be calculated.
FIGURE 5.2. Trigger efficiency plots for the 200 GeV seeded emerging jets trigger
chain determined via the trigger simulated in BSM Higgs to LLP scalar (1 TeV
→ 475 GeV) signal events. These indicate that the trigger will be fully efficient
in pT at approximately 250 GeV, as compared to over 500 GeV for a standard
unprescaled large-R jet trigger. The trigger curve is scaled to the fraction that
pass the PTF cut to allow a plateau at 1.0.
140
FIGURE 5.3. Invariant mass distributions and invariant mass resolution for
600 GeV Z’ samples with lifetimes 1 mm (top) and 10 mm (bottom). The
PFlow algorithm has a definite lifetime dependence that affects the number of
reconstructed tracks associated to the jet, making the non-prompt jet appear like a
photon to the algorithm at sufficient lifetimes.
An additional consideration for the single-jet trigger is from the
implementation of new Level-1 hardware trigger systems at ATLAS. The global
Feature EXtractor (gFEX) is a hardware trigger that is designed to provide
an event-wise large-R jet trigger system to the detector. Part of the Phase-I
hardware upgrade, It is composed of three FPGA systems that input coarse
0.2× 0.2 calorimeter regions and compute R = 1.0 Level-1 jets in each FPGA’s
corresponding detector region. The overall event is reconstructed from these
three regions in an additional FPGA and global event decisions are made at the
hardware level. Dark jet signatures such as emerging jets are expected to be
141
very efficiently selected at Level-1 due to this system, particularly due to the flat
pileup/noise energy subtraction applied in the reconstruction, which enhances
sensitivity to soft and wide energy deposits. The development and evaluation of
these emerging jet triggers with the use gFEX was not possible due to the lack of a
gFEX trigger simulation in Athena at the time of the development. However, this
system is likely a future promising candidate as a hardware seed for the developed
emerging jet triggers.
142
CHAPTER VI
CONCLUSION
This analysis placed competitive cross-section limits on emerging jets
production from exotic dark sector Z’s. These limits were evaluated down to 10 fb
at masses of 1300 GeV and to 2 fb at 3000 GeV. Production of Z’ particles with
masses up to 3.1 TeV were excluded for gq dark sector couplings down to 0.015.
A novel machine-learning technique using unsupervised learning was utilized to
enhance potential signal sensitivities by over 10× relative to cut-based analyses,
and this method is shown to be a powerful tool for the probe of these dark jet
signal types.
Despite the lack of discovery of emerging signals in the dijet topology at
invariant masses greater than 1.3 TeV, exciting physics opportunities for discovery
are available in much lower mass and cross-section regimes. The computing
and detector upgrades at ATLAS will open a realm of track-jet exotic particle
triggers for discovery. Dark jets, LLPs, and boosted soft exotic decays will all be
enhanced in discovery potential through the use of specialized jet-track triggers.
The discovery potential and limits of emerging jets, in particular, will be greatly
enhanced in Run 3 with the utilization of the specialized emerging jets triggers
in the dijet and dijet+photon channels. Mass sensitivity down to 550 GeV are
expected for the single-jet emerging jets trigger, and the dijet+photon triggered
data are expected to allow good sensitivity for Z’ bosons down to 250 GeV.
These new trigger chains have also been proven to be very efficient for the
selection of LLP signatures that include BSM Higgs decays to LLP heavy scalars
and long-lived R-Hadrons. A future analysis will require a dedicated analysis of
143
the scope of the data with respect to the correlated trigger inefficiencies due to
the overlap of the L1, EMTopo HLT jet, and PFlow HLT jet thresholds, but the
extremely competitive mass limits allow for a significant probe of a range of model
spaces.
144
APPENDIX
APPENDIX1
A.1. Appendix A
Scaling factors were applied to the data for NN training and evaluation.
These were applied to reweight the signal to the appropriate injection cross-
section, and they were also applied to weight events in the sidebands to be
identical to those in the signal region bins.
Before training, the m , m , PTF , PTF , ∆φ, y∗0 1 0 1 , and number-of-jets
distributions were scaled by the respective factors: 150 GeV, 150 GeV, 0.15, 0.15,
1.5, 0.3, 5. The corresponding event features were subtracted by these means and
divided by these means to make an approximate scaling between -1 and 1.
The chosen binning was based on resolution bins found by previous dijet
searches such as the high-mass dijet search and the ATLAS trigger-level analysis:
1049, 1093, 1139, 1186, 1235, 1286, 1339, 1394, 1451, 1511, 1573, 1637, 1704, 1773,
1845, 1920, 1998, 2079, 2163, 2251, 2342, 2437, 2536, 2639, 2746, 2857, 2973, 3094,
3220, 3351, 3487, 3629, 3776, 3929, 4088, 4254, 4427, 4607, 4794, 4989, 5191 GeV
A.1.1. Trigger Studies
To optimize the PTF definition, its selection on R-Hadron samples was
studied. R-Hadrons are the supersymmetric equivalent to glue-balls; they are
neutral balls of gluinos constrained by the model of choice. Two R-Hadron
samples were considered, one with lifetime 10 ns and one with 0.1 ns. These
R-Hadron samples were configured with a small mass difference between the
145
R-Hadron pairs produced and the Neutralinos in the event. Neutralinos are
neutral supersymmetric (SUSY) particles that are predicted to be the lightest
supersymmetric particle (LSP) in SUSY theory, therefore they are the canonical
dark matter candidate. The small mass splitting between these samples produces
the long-lived properties of these R-Hadrons. The resulting low-pT byproducts of
this decay will be displaced and well-selected by the PTF algorithm.
FIGURE A.1. Various jet and jet-track selections on R-Hadron samples with 0.1 ns
(left) and 10 ns (right) lifetimes. The timing selection refers to a selection on the
offline jet timing, the d0 selection refers to a selection with a cut on the highest d0
track associated to the jet, and the inverse pT cut is the PTF algorithm applied
with varying cofactors in front of the resolution function.
The emerging jets trigger is therefore expected to have good sensitivity to
these signal types.
A.1.2. GRLs and Configurations
GRLs used in data selection:
data15_13TeV.periodAllYear_HEAD_
DQDefects-00-02-02_PHYS_StandardGRL_All_Good_25ns
data16_13TeV.periodAllYear_DetStatus-v89-pro21-01_DQDefects-
00-02-04_PHYS_StandardGRL_All_Good_25ns
146
data17_13TeV.periodAllYear_HEAD_
Unknown_PHYS_StandardGRL_All_Good_25ns_ Triggerno17e33prim
data18_13TeV.periodAllYear_HEAD_Unknown_
PHYS_StandardGRL_All_Good_25ns_ Triggerno17e33prim
A.1.3. Pythia Model Generation
The software tags used for the generation are the following: Event
Generation: e8381 Event Simulation: s3126 Event Reconstruction: r9364 (mc16a)
r10201 (mc16d) r10724 (mc16e) Derivation Production: p4432
The overlaid pileup samples were: mc16_13TeV.361239.Pythia8EvtGen_
A3NNPDF23LO_minbias_inelastic_high.simul.HITS.e4981_s3087_s3111
mc16_13TeV.361238.Pythia8EvtGen_A3NNPDF23LO
_minbias_inelastic_low.simul.HITS.e4981_s3087_s3111
The following is the configuration used within Athena for the event
generation.
###########################################################
# Emerging Jets Event Generation
# Pythia 8: Zd --> Qd Qd_bar --> 2EJ
# contact: Aaron Kilgallon (aaron.joseph.kilgallon@cern.ch)
#==========================================================
evgenConfig.description = "emerging jets from pair-produced dark quarks"
evgenConfig.keywords = ["exotic", "hiddenValley", "4jet"]
evgenConfig.process = "p p --> Zd --> Qd Qd_bar --> 2EJ"
evgenConfig.contact = ["aaron.joseph.kilgallon@cern.ch"]
147
include("Pythia8_i/Pythia8_A14_NNPDF23LO_EvtGen_Common.py")
# set sample / model parameters automatically based on jo name
print("ARGS: ", runArgs.jobConfig[0])
print("JO ARGS: ", jofile.rstrip(’.py’).split(’_’))
m_Xd = float(jofile.rstrip(’.py’).split(’_’)[3])
ctau_pi_d = float(jofile.rstrip(’.py’).split(’_’)[4])
print("SCALAR MEDIATOR MASS: %f " % m_Xd)
print("DARK PION LIFETIME: %f " % ctau_pi_d)
mod = jofile.rstrip(’.py’).split(’_’)[2]
print("MODEL: %s " % mod)
if mod == "ModelA":
m_pi_d = 5.0
elif mod == "ModelB":
m_pi_d = 2.0
elif mod == "ModelC":
m_pi_d = 10.0
elif mod == "ModelD":
m_pi_d = 20.0
elif mod == "ModelE":
m_pi_d = 0.8
print("DARK PION MASS: %f " % m_pi_d)
print("DARK RHO MASS: %f " % (m_pi_d*4))
148
print("LAMBDA / DARK QUARK MASS: %f " % (m_pi_d*2))
print("PT MIN FSR: %f " % (m_pi_d*2*1.1))
# show 5 events for testing
genSeq.Pythia8.Commands += ["Next:numberShowEvent = 1"]
## OVERRIDE STANDARD ATLAS TAU0 LIMIT ##
genSeq.Pythia8.Commands += ["ParticleDecays:limitTau0 = off"]
# settings for dark sector
genSeq.Pythia8.Commands += ["HiddenValley:spinFV = 0",
"HiddenValley:Ngauge = 3",
# n dark QCD colors
"HiddenValley:alphaFSR = 0.7"]
# dark coupling
# Model settings
genSeq.Pythia8.Commands += ["4900101:m0 = " + str(m_pi_d*2),
# qd mass
"4900111:m0 = " + str(m_pi_d),
# pi_d mass
"4900113:m0 = " + str(m_pi_d*4),
# rho_d mass
"4900211:m0 = " + str(m_pi_d),
# pi_d off-diag
"4900213:m0 = " + str(m_pi_d*4),
# rhod offdiag
149
"HiddenValley:Lambda = " + str(m_pi_d*2),
"HiddenValley:pTminFSR = "
+ str(m_pi_d*2*1.1)]
# pT cutoff for dark shower
# dark pion lifetime
genSeq.Pythia8.Commands += ["4900111:tau0 = " + str(ctau_pi_d)]
# pi_d lifetime -- variable
# off-diagonal dark pion lifetime
genSeq.Pythia8.Commands += ["4900211:tau0 = " + str(ctau_pi_d)]
# non-model dependent settings
genSeq.Pythia8.Commands += ["PartonLevel:MPI = on",
"PartonLevel:ISR = on"]
# emerging jet event processes
genSeq.Pythia8.Commands += ["HiddenValley:ffbar2Zv = on"]
genSeq.Pythia8.Commands += ["4900023:m0 = " + str(m_Xd)]
genSeq.Pythia8.Commands += ["4900023:tau0 = 1E-20",
"4900023:mWidth=10",
"4900023:isResonance = on",
"4900023:mayDecay = on",
"4900023:0:bRatio = 1",
"4900023:0:meMode = 102"]
genSeq.Pythia8.Commands += ["4900023:onMode = off",
"4900023:offIfAny 1 2 3 4 5 6 -1 -2 -3 -4 -5
150
-6 7 8 9 10 11 12 13 14 15 16 -7 -8 -9 -10
-11 -12 -13 -14 -15 -16",
"4900023:onIfAny 4900101 -4900101",
"4900023:oneChannel 1 0.999 102 4900101
-4900101",
"4900023:addChannel 1 0.001 102 1 -1"]
# dark meson decays
genSeq.Pythia8.Commands += ["4900111:0:all on 1.0 102 1 -1",
\newline # dark pion to down quarks
"4900113:0:all on 0.999 102 4900111 4900111",
# dark vector to dark pions 99.9%
"4900113:addchannel on 0.001 102 1 -1"]
# dark vector to down quarks 0.1%
# dark meson off-diagonal decays
genSeq.Pythia8.Commands += ["4900211:oneChannel on 1.0 91 1 -1",
# dark pion to down quarks
"4900213:oneChannel on 0.999 102 4900211
4900211",
# dark vector to dark pions 99.9%
"4900213:addchannel on 0.001 102 1 -1"]
# dark vector to down quarks 0.1%
# dark QCD coupling (alphaHV) running
genSeq.Pythia8.Commands += ["HiddenValley:alphaOrder = 1",
"HiddenValley:nFlav = 7"]
151
# HV parton shower settings
genSeq.Pythia8.Commands += ["HiddenValley:FSR = on",
"HiddenValley:fragment = on"]
genSeq.Pythia8.Commands += ["Main:timesAllowErrors = 500"]
genSeq.Pythia8.Commands += ["ProcessLevel:all = on",
"ProcessLevel:resonanceDecays = on",
"PartonLevel:all = on",
"PartonLevel:ISR = on",
"HadronLevel:all = on",
"PhaseSpace:useBreitWigners = on"]
# workarounds for TestHepMC
testSeq.TestHepMC.MaxVtxDisp=5000000.
testSeq.TestHepMC.MaxTransVtxDisp = 5000000.
## JET FILTERING ##
include ("GeneratorFilters/FindJets.py")
CreateJets(prefiltSeq, 0.4)
if not hasattr( filtSeq, "TruthJetFilter" ):
152
from GeneratorFilters.GeneratorFiltersConf import TruthJetFilter
filtSeq += TruthJetFilter()
pass
filtSeq.TruthJetFilter.TruthJetContainer = "AntiKt4TruthJets"
filtSeq.TruthJetFilter.Njet = 2
filtSeq.TruthJetFilter.NjetMinPt = 125*GeV
filtSeq.TruthJetFilter.NjetMaxEta = 2.4
A.2. Appendix B
The following are the full set of signal sample efficiencies.
153
Z ′m cτ Model DAOD Analysis Eff. 10% NN Eff. 1% NN
[GeV] [mm]
1500.0 1.0 A 96.4 29.2 23.6 8.0
1500.0 1.0 B 96.1 23.1 26.2 15.0
1500.0 1.0 C 96.2 35.1 21.6 2.4
1500.0 1.0 D 96.3 35.6 15.3 0.6
1500.0 1.0 E 96.4 25.1 36.1 19.3
1500.0 2.0 A 96.3 32.5 34.9 16.6
1500.0 2.0 B 96.1 26.9 40.4 21.9
1500.0 2.0 C 96.4 38.9 33.6 16.7
1500.0 2.0 D 96.3 39.7 32.6 6.0
1500.0 2.0 E 96.2 29.2 36.0 25.1
1500.0 5.0 A 96.3 34.4 43.2 27.0
1500.0 5.0 B 96.3 28.6 45.9 27.5
1500.0 5.0 C 96.5 40.0 41.2 22.8
1500.0 5.0 D 96.3 42.9 42.0 9.4
1500.0 5.0 E 96.3 29.5 29.1 16.4
1500.0 10.0 A 96.1 32.8 46.2 27.4
1500.0 10.0 B 95.9 26.4 33.1 23.6
1500.0 10.0 C 96.1 39.7 39.0 26.2
1500.0 10.0 D 96.1 43.8 50.1 24.5
1500.0 10.0 E 95.6 25.7 29.4 3.8
1500.0 25.0 A 95.8 29.2 39.3 21.6
1500.0 25.0 B 95.2 19.6 14.1 1.1
1500.0 25.0 C 95.9 37.8 48.2 26.0
1500.0 25.0 D 95.3 44.2 46.6 20.0
1500.0 25.0 E 95.9 16.4 5.9 1.2
1500.0 50.0 A 94.3 22.5 20.9 4.8
1500.0 50.0 B 93.9 12.5 4.9 0.3
1500.0 50.0 C 93.9 34.5 48.9 27.2
1500.0 50.0 D 93.6 43.1 55.1 30.7
1500.0 50.0 E 95.4 7.3 2.9 0.0
1500.0 100.0 A 91.9 13.3 4.5 0.8
1500.0 100.0 B 92.8 4.9 8.3 1.7
1500.0 100.0 C 90.9 25.6 19.3 5.7
1500.0 100.0 D 88.9 38.2 43.6 13.7
1500.0 100.0 E 94.7 1.5 16.7 0.0
TABLE A.1. Signal efficiencies for 1.5 TeV samples.
154
Z ′m cτ Model DAOD Analysis Eff. 10% NN Eff. 1% NN
[GeV] [mm]
2000.0 1.0 A 95.9 31.3 35.9 12.3
2000.0 1.0 B 96.2 26.7 36.3 16.8
2000.0 1.0 C 96.3 35.3 33.7 18.3
2000.0 1.0 D 96.0 35.7 30.7 11.3
2000.0 1.0 E 96.0 28.0 48.3 24.3
2000.0 2.0 A 96.0 34.0 44.5 22.7
2000.0 2.0 B 96.3 30.4 45.9 23.8
2000.0 2.0 C 96.1 38.9 44.7 21.9
2000.0 2.0 D 95.9 39.8 42.9 19.2
2000.0 2.0 E 95.8 31.2 48.1 24.1
2000.0 5.0 A 95.5 35.2 48.1 23.7
2000.0 5.0 B 96.1 31.0 44.8 23.2
2000.0 5.0 C 95.9 40.6 55.3 22.4
2000.0 5.0 D 95.8 42.2 48.9 23.1
2000.0 5.0 E 95.9 31.0 37.8 14.3
2000.0 10.0 A 95.8 33.9 53.3 26.2
2000.0 10.0 B 95.7 28.1 35.8 23.0
2000.0 10.0 C 96.2 40.2 51.7 21.3
2000.0 10.0 D 95.9 42.9 51.1 23.2
2000.0 10.0 E 95.5 27.9 31.3 7.0
2000.0 25.0 A 95.0 30.1 44.1 16.2
2000.0 25.0 B 94.9 21.8 15.7 2.3
2000.0 25.0 C 95.4 38.3 50.3 23.0
2000.0 25.0 D 95.3 42.8 45.2 28.0
2000.0 25.0 E 95.1 20.1 12.7 1.4
2000.0 50.0 A 92.4 25.3 17.0 2.8
2000.0 50.0 B 94.5 16.3 2.3 0.3
2000.0 50.0 C 94.1 34.9 38.2 13.5
2000.0 50.0 D 94.4 41.9 49.4 26.9
2000.0 50.0 E 95.0 12.6 2.9 0.4
2000.0 100.0 A 91.7 17.3 11.3 2.5
2000.0 100.0 B 92.8 8.4 6.5 0.8
2000.0 100.0 C 90.1 28.4 17.7 3.0
2000.0 100.0 D 89.5 38.3 36.3 21.4
2000.0 100.0 E 93.3 3.9 12.7 1.8
TABLE A.2. Signal efficiencies for 2 TeV samples.
155
Z ′m cτ Model DAOD Analysis Eff. 10% NN Eff. 1% NN
[GeV] [mm]
3000.0 1.0 A 96.4 29.2 38.0 7.6
3000.0 1.0 B 95.4 25.2 45.7 10.7
3000.0 1.0 C 95.7 29.7 41.1 7.7
3000.0 1.0 D 95.7 29.5 44.4 8.2
3000.0 1.0 E 95.6 26.8 48.4 7.2
3000.0 2.0 A 95.9 31.0 43.0 6.3
3000.0 2.0 B 95.3 27.3 45.8 7.4
3000.0 2.0 C 95.7 32.1 45.6 7.5
3000.0 2.0 D 95.8 31.8 46.1 7.2
3000.0 5.0 A 95.8 31.0 48.6 8.3
3000.0 5.0 B 95.2 26.7 42.9 7.0
3000.0 5.0 C 96.0 33.1 46.0 6.8
3000.0 5.0 D 95.9 33.6 47.3 7.5
3000.0 5.0 E 95.8 27.3 38.9 6.7
3000.0 10.0 A 95.7 31.4 47.5 14.9
3000.0 10.0 B 95.1 25.2 39.8 5.3
3000.0 10.0 C 96.1 32.7 51.8 9.8
3000.0 10.0 D 95.8 33.7 49.9 7.5
3000.0 25.0 A 94.1 28.3 30.4 8.1
3000.0 25.0 B 94.3 22.4 22.2 5.9
3000.0 25.0 C 95.5 31.7 39.9 11.9
3000.0 25.0 D 94.7 34.1 50.6 7.3
3000.0 25.0 E 95.4 21.0 23.2 4.9
3000.0 50.0 A 93.1 24.7 18.7 4.7
3000.0 50.0 B 93.3 18.5 14.0 5.0
3000.0 50.0 C 93.1 31.0 34.6 10.8
3000.0 50.0 D 93.6 33.3 41.7 8.6
3000.0 50.0 E 95.0 16.1 7.3 1.6
3000.0 100.0 A 90.8 20.7 9.7 1.5
3000.0 100.0 B 91.5 12.9 6.6 1.2
3000.0 100.0 C 89.8 27.8 17.3 1.6
3000.0 100.0 D 88.9 31.7 29.5 5.4
3000.0 100.0 E 94.0 8.0 11.0 1.3
TABLE A.3. Signal efficiencies for 3 TeV samples.
156
Z ′m cτ Model DAOD Analysis Eff. 10% NN Eff. 1% NN
[GeV] [mm]
4000.0 1.0 A 95.8 21.5 29.2 4.6
4000.0 1.0 B 95.9 21.1 32.8 5.9
4000.0 1.0 C 96.0 22.3 31.7 5.9
4000.0 1.0 D 95.8 23.5 33.2 6.0
4000.0 1.0 E 95.9 22.0 32.4 6.0
4000.0 2.0 A 95.6 22.9 27.6 4.2
4000.0 2.0 B 96.0 22.2 35.0 5.3
4000.0 2.0 C 96.6 24.3 37.6 6.1
4000.0 2.0 D 96.2 24.7 37.1 6.2
4000.0 2.0 E 96.0 22.6 34.9 6.0
4000.0 5.0 A 95.7 22.9 34.4 6.2
4000.0 5.0 B 96.0 21.9 35.7 7.1
4000.0 5.0 C 96.2 24.7 27.6 3.6
4000.0 5.0 D 95.9 26.1 30.7 4.2
4000.0 5.0 E 95.8 22.6 29.8 5.9
4000.0 10.0 A 95.7 21.8 40.0 9.3
4000.0 10.0 B 95.7 20.5 39.6 12.7
4000.0 10.0 C 96.3 24.3 28.8 3.6
4000.0 10.0 D 96.0 26.2 23.7 3.2
4000.0 10.0 E 95.4 21.7 35.1 7.2
4000.0 25.0 A 94.7 20.9 32.3 8.0
4000.0 25.0 B 95.0 18.9 27.7 6.3
4000.0 25.0 C 95.5 23.6 33.7 7.2
4000.0 25.0 D 95.4 26.0 29.6 4.6
4000.0 25.0 E 95.3 19.1 20.4 4.9
4000.0 50.0 A 93.4 19.8 35.0 11.1
4000.0 50.0 B 93.6 17.3 16.8 4.4
4000.0 50.0 C 93.8 23.2 27.9 6.0
4000.0 50.0 D 93.8 26.4 29.7 5.5
4000.0 50.0 E 94.4 16.7 11.0 0.9
4000.0 100.0 A 91.1 17.6 11.8 2.0
4000.0 100.0 B 92.5 13.2 14.5 1.5
4000.0 100.0 C 90.7 21.8 26.9 5.1
4000.0 100.0 D 88.4 26.0 25.3 6.9
4000.0 100.0 E 94.1 10.4 8.8 0.5
TABLE A.4. Signal efficiencies for 4 TeV samples.
157
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