Front matter
Dedication
Epigraph
Table of Contents
List of Figures
List of Tables
Acknowledgements
Vita
Abstract of the Dissertation
Introduction
I
Theoretical Background
II
Experimental Background
III
AI/ML and Statistics Background
IV
Accelerating Simulations with AI
V
Searches for High Energy Higgs Boson Pairs
VI
AI for Jets
VII
Appendix
Bibliography
⭠
⭢
Table of Contents
I
Theoretical Background
1
Introduction to the Standard Model
2
Symmetries in physics
2.1
Group theory
2.2
Lie algebras
2.3
Particles are irreps of the Poincaré group
3
Quantum field theory
3.1
Free scalar field theory
3.1.1
Classical field theory
3.1.2
Symmetries and Noether’s theorem
3.1.3
Quantization
3.1.4
Propagators and Green functions
3.2
Interactions
3.2.1
Interactions in the Lagrangian
3.2.2
S-matrix elements
3.2.3
Feynman diagrams
3.2.4
Decay rates and cross sections
3.3
Gauge theories
3.3.1
Maxwell Theory
3.3.2
Quantum electrodynamics
3.3.3
Yang-Mills Theory
3.3.4
Running couplings and asymptotic freedom
3.4
The ABEGHHK (Higgs) mechanism
3.4.1
The abelian Higgs mechanism
3.4.2
The non-abelian Higgs mechanism
4
The Standard Model of Particle Physics
4.1
Quantum chromodynamics
4.1.1
Asymptotic freedom and confinement
4.1.2
Quarks and the eightfold way
4.1.3
The parton model
4.1.4
Jets
4.2
Electroweak interactions
4.2.1
Weak interactions
4.2.2
Before electroweak symmetry breaking
4.2.3
Electroweak symmetry breaking
4.2.4
Fermion masses and flavor
4.3
The Higgs sector
4.3.1
Higgs boson production and measurements at the LHC
4.3.2
Higgs pair production in the SM
4.3.3
Experimental status of
H
H
measurements with CMS
4.3.4
BSM
X
→
H
Y
production
II
Experimental Background
5
The CERN Large Hadron Collider
5.1
The accelerator
5.2
Luminosity and timeline
6
The CMS detector
6.1
Overview
6.2
Detecting particles
6.2.1
Particle interactions with matter
6.2.2
Types of detectors
6.3
CMS detector components
6.3.1
The magnet
6.3.2
Tracker
6.3.3
ECAL
6.3.4
HCAL
6.3.5
Muon system
6.4
Detector reconstruction and performance
6.4.1
Tracker
6.4.2
ECAL
6.4.3
HCAL
6.4.4
Muon system
6.4.5
Object reconstruction and particle flow
6.5
The Phase-2 Upgrade
6.5.1
Tracker
6.5.2
Timing layers
6.5.3
Barrel calorimeters
6.5.4
HGCAL
6.5.5
Muon system
III
AI/ML and Statistics Background
7
Machine Learning for HEP
7.1
Introduction
7.1.1
Basics of ML
7.1.2
The importance of generalization and calibration
7.1.3
Artificial neural networks and deep learning
7.1.4
The importance of being physics-informed
7.2
Equivariant neural networks
7.2.1
Equivariance
7.2.2
Steerable CNNs for
E
(
2
)
-equivariance
7.2.3
Tensor-field networks for
E
(
3
)
-equivariance
7.2.4
Lorentz-group-equivariant networks
7.3
Autoencoders and generative models
7.3.1
Autoencoders and anomaly detection
7.3.2
Generative models
7.3.3
Previous work
8
Data Analysis and Statistical Interpretation
8.1
Introduction or: What is an analysis?
8.2
Frequentist statistics at the LHC
8.2.1
The likelihood function and test statistics
8.2.2
Hypothesis testing
8.2.3
Confidence intervals and limits
8.2.4
Expected significances and limits
8.3
Asymptotic formulae
8.3.1
Asymptotic form of the MLE
8.3.2
Asymptotic form of the profile likelihood ratio
IV
Accelerating Simulations with AI
9
Introduction and the JetNet Dataset
9.1
Simulating jets
9.2
JetNet
10
Generative models for fast particle-cloud simulations
10.1
Message passing GANs
10.1.1
Evaluation
10.1.2
Architecture
10.1.3
Experiments on MNIST handwritten digits
10.1.4
Experiments on jets
10.1.5
Summary
10.2
Generative adversarial particle transformers
10.2.1
GAPT
10.2.2
iGAPT
10.2.3
Experiments
10.2.4
Summary
11
Validating and comparing fast simulations
11.1
Evaluation metrics for generative models
11.2
Experiments on gaussian-distributed data
11.3
Experiments on jet data
11.4
Demonstration on particle cloud GANs
11.5
Summary
12
Conclusion and impact
V
Searches for High Energy Higgs Boson Pairs
13
Boosted Higgs identification
13.1
ParticleNet for
b
b
¯
-jet tagging and mass regression
13.2
GloParT for
H
∕
Y
→
V
V
classification
13.3
Calibrating
H
∕
Y
→
V
V
taggers
14
High energy
H
H
searches in the all-hadronic bbVV channel
14.1
Introduction
14.2
Overview of analysis strategy
14.3
Event Selection
14.3.1
Triggers
14.3.2
Nonresonant offline selection
14.3.3
Resonant offline selection
14.4
Background estimation
14.5
Systematic uncertainties
14.6
Results
14.6.1
Nonresonant
H
H
search
14.6.2
Resonant
X
→
H
Y
search
14.7
Summary and Outlook
VI
AI for Jets
15
Introduction and the JetNet Package
15.1
JetNet
16
Lorentz-group equivariant autoencoders
16.1
Introduction
16.2
LGAE architecture
16.2.1
LMP layers
16.2.2
Encoder
16.2.3
Decoder
16.3
Experiments
16.3.1
Dataset
16.3.2
Models
16.3.3
Reconstruction
16.3.4
Anomaly detection
16.3.5
Latent space interpretation
16.3.6
Data efficiency
16.4
Conclusion
VII
Appendix
A
Supplementary Material for Chapter 2
A.1
Symmetries in physics
A.1.1
Derivation of the Poincaré algebra
B
Supplementary Material for Chapter 3
B.1
Classical field theory
B.1.1
Lagrangian mechanics
B.1.2
Solutions to the Klein-Gordon equation
B.1.3
Hamiltonian mechanics
B.2
Quantization
B.2.1
Canonical quantization
B.2.2
The Hamiltonian and the vacuum catastrophe
B.2.3
Particles
B.2.4
The complex scalar field and antiparticles
B.3
Interactions
B.3.1
The interaction picture and Dyson’s formula
B.3.2
First-order examples and the matrix element
M
B.3.3
Feynman diagrams
B.4
Spinor field theory
B.4.1
The Dirac equation
B.4.2
Spinors
B.4.3
The Dirac Lagrangian
B.4.4
Quantizing the Dirac field
B.4.5
Interactions and Feynman rules
B.4.6
CPT Symmetries
B.5
Gauge theories
B.5.1
Why gauge invariance?
C
Supplementary Material for Chapter 10
C.1
MPGANs
C.1.1
Point Cloud Generative Models
C.1.2
Training and Implementation Details
C.1.3
Masking Strategies
C.2
GAPTs
C.2.1
Results on 150-particle jets
D
Supplementary Material for Chapter 11
D.1
Further Discussion on IPMs vs.
f
-Divergences
D.2
Further Discussion on Gaussian Dataset Experiments
D.3
Alternative Jet Distributions
E
Supplementary Material for Chapter 16
E.1
Model details
E.1.1
LGAE
E.1.2
GNNAE
E.1.3
CNNAE
E.2
Training details
E.3
Equivariance tests
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