PHY 7097 "High Energy Theory"
Class Diary for Spring 2023 (tentative)

 

Date Notes
Tuesday 01/10 Introductions, course policies. Syllabus.

Career discussions:
APS statement on Career Options for Physicists
Physics Careers: the Myths, the Data and Tips for Success; invited talk at the Career Forum of the Pheno 2020 conference.
HET faculty job rumors.
Statistics of new faculty hires by PhD institution.

Artificial Intelligence:
AI in particle physics.
NSF AI Research Institutes.
New AI job openings: AI fellows.
Major ML conferences: NeurIPS and ICML.
28 ML topics at the APS March meeting.

AI Initiative at UF:
AI@UF; UF AI Initiative; UF first US university to acquire world's most advanced AI system.
UF Informatics Institute
Inspirational message from your course instructor.
Graduate Machine Learning Certificate from ECE.
Machine Learning course in the Physics Department.
What is data science?
A map of AI topics from a blog by a former physicist.

Programming:
Introduction to Google Colab.
Python cheatsheets: Python, Jupyter, NumPy, Scikit-Learn, Matplotlib, Seaborn, SciPy. Skip: Pandas, Bokeh.

PHY 7097 Special Topics course:
Multi-faculty option: CMT; Biophysics.
Single faculty option: Dark Matter, Cosmology, Supersymmetry, String Theory, Group Theory.
My previous teachings on HET-related topics:

Thursday 01/12 Lectures on Physics Beyond the Standard Model at Colliders, TASI 2014.
Tuesday 01/17 Overview of the available simulation tools in collider phenomenology.
Standard Model: symmetries, particle representations, gauge structure.
Thursday 01/19 Standard Model: interactions and parameters.
An overview of collider phenomenology.
Tuesday 01/24 Overview of CalcHEP. The SM particles and their quantum numbers. Interactions in the SM. Calculating a decay rate and branching fractions with CalcHEP. Decays and branching fractions of the Z boson.
Extracting analytical results from CalcHEP and CompHEP. Example: e+e- -> mu+mu-.
Implementing a higher-dimensional operator in CalcHEP. One-loop mediated Higgs couplings. Radiative correction to the Higgs mass. Hierarchy problem.
Thursday 01/26 Continue overview of CalcHEP. Setting up the initial state for cross-section calculations. Calculating cross-sections with CalcHEP and plotting distributions. Using Regularization for faster convergence.
Continue overview of CalcHEP. Numerical precision on the cross section calculations.
Tuesday 01/31 Tree-level versus loop calculations.
Cancellation of soft and colinear divergences.
CalcHEP example: e+e- -> mu+ mu- gamma. Imposing cuts. Regularization.
Using CalcHEP for calculations at hadron colliders. Single W production (W+ and W-) at the LHC. Comparing the contributions from different subprocesses.
Thursday 02/02 Groundhog Day Quiz: CalcHEP data challenge.
String Theory Essay discussion and awards.
Mathematical Capabilities of ChatGPT
Article on string theory and a certain string theorist.
Tuesday 02/07 Implementing a new model in CalcHEP: Z'. Implementing a user function in CalcHEP. Higgs to 4 leptons at the LHC.
CalcHEP-PYTHIA interface: generating events in CalcHEP and feeding them into PYTHIA.
Final CalcHEP tutorial. Discussion of the CalcHEP homework.
Brief overview of CompHEP.
Brief introduction to Madgraph

Introduction to BSM model building:
1) Extra gauge groups (Z', W')
2) Extra dimensions
3) Extra generations
4) Extra representations
5) Grand unification: SU(5) gauge bosons, unification of the gauge couplings, proton decay.
6) Hierarchy problem

Thursday 02/09 SUPERSYMMETRY - part I.
Superfield formalism. Particle content of the MSSM. Quantum numbers and representations. SUSY nomenclature. The need for 2 Higgs doublets. Anomaly cancellation. Gauge invariant terms in the superpotential.
Flavor models and Froggatt-Nielsen mechanism.
Tuesday 02/14 SUPERSYMMETRY - part II. Supersymmetry transformations: component formalism. Superspace. Superpotential. Deriving the SUSY interactions from the superpotential. R-parity. Proton decay constraints. Cancellation of quadratic divergencies. Hierarchy problem.
SUPERSYMMETRY - part III. Gauge interactions and collider phenomenology. Gauge interactions of superpartners. Main SUSY production processes at the LHC. Production of colored superpartners at the LHC.
Thursday 02/16 SUPERSYMMETRY - part IV. Gauge coupling unification. SUSY breaking. Soft terms. RGEs. Mass spectrum. RGE's and beta functions for the gauge couplings in the SM and MSSM. SU(5) GUTs. Doublet-triplet splitting problem. Solving the RGE's for the gauge couplings. Predictions from grand unification: M_susy. The SUSY soft breaking Lagrangian: soft mass parameters. Counting input parameters. Constraints from flavor and CP violating processes. Computing the SUSY mass spectrum in a given model of SUSY breaking. Gaugino mass RGE and its solution. Consequences from the assumption of gaugino mass universality. Solving the scalar RGEs in the MSSM. Qualitative features of the mass spectrum.
Tuesday 02/21 SUPERSYMMETRY - part V. The MSSM mass spectrum: chargino, neutralino, squark and slepton mass matrices. Solving the third generation RGEs. Radiative electroweak symmetry breaking in the MSSM. Main SUSY discovery signatures. Squark and gluino production (multuijets plus missing energy).
Thursday 02/23 Yukawa couplings in a two-Higgs doublet model. tan(beta). B-tau unification. SU(5) and SO(10) grand unification. SUSY GUTs.
High energy colliders: e+e-, pp-bar, pp, mu+mu-.
Collider phenomenology. Signatures: bump hunt, counting experiments, exotic signatures. Missing transverse momentum vs missing transverse energy.
Example: top quark pair production at a hadron collider. Dilepton, single lepton, all hadronic channels.
SUSY signatures at the LHC. Direct LSP production (monojets, single photons).
Tuesday 02/28 GROUP THEORY I. Part I of Group Theory in a Nutshell for Physicists
Symmetry of an object. Symmetries in physics. Formal definition of a group. Group axioms. Examples of groups: Z2, Z3, ZN, U(1), SO(2), SO(3). Subgroups. Direct products of groups. Multiplication tables of finite groups. Homomorphisms and isomorphisms. Lie algebras. Three methods to define the group of rotations: 1. Define what a rotation does. 2. Define what a rotation preserves. 3. Define the algebra of generators of rotations. Finite rotations. Reflections. Infinitesimal rotations in two dimensions and in three dimensions. Commutation relations and structure constants. Rotations in higher dimensions. Exercise: show that the algebra of SO(4) can be represented as a direct sum of two SO(3) algebras.
Thursday 03/02 GROUP THEORY II. Part II of Group Theory in a Nutshell for Physicists
Representations. Character is a function of class. Trivial representation. Reducible and irreducible representations. Unitary representations. Unitary groups U(n) and SU(n). The group SU(2) and its algebra. Pauli matrices. The group SU(3). Gell-Mann matrices. Structure constants of SU(3). Rank of the algebra. I-spin, U-spin and V-spin for SU(3). Raising and lowering operators.
Tuesday 03/07 GROUP THEORY III. Part V of Group Theory in a Nutshell for Physicists
Review: Contrasting Lie groups and their elements versus Lie algebras and generators. The U(1) factor. U(n)=SU(n)xU(1). Semisimple groups.
The effect of the raising and lowering operators on the states of definite isospin and hypercharge. Root vectors. Weight diagrams. The SU(3) flavor group. The baryon octet. Recipe for finding the root vectors. Positive roots. Simple roots. Rules for constructing Dynkin diagrams.
Thursday 03/09 GROUP THEORY IV. Part VI of Group Theory in a Nutshell for Physicists
Explicit derivation and construction of the Dynkin diagrams for SU(3), SO(4) and SO(5). Root systems: axioms. Examples of root systems. The group Sp(4). The group G2. Subalgebras and subgroups from Dynkin diagrams.
Tuesday 03/14 Spring break
Thursday 03/16 Spring break
Tuesday 03/21 Complete classification of Lie algebras in terms of Dynkin diagrams.
GROUP THEORY GROUP CHALLENGE: Accidental isomorphisms. Examples of subgroups.
Thursday 03/23 MONTE CARLO SIMULATIONS. The need for Monte Carlo simulations: integration, sampling, density estimation. Buffon's needle problem. Riemann integration, Monte Carlo integration, rejection method.
Tuesday 03/28 MONTE CARLO SIMULATIONS. Importance sampling. Simple random variables: uniform distribution (mean and variance). Random number generators. How to sample arbitrary distributions.
PROBABILITY AND STATISTICS: Expectation value, variance, moments (algebraic and central). Marginal distributions. Covariance, correlation. Deterministic versus non-deterministic processes. Examples from physics. Standard simulation chain. Prediction versus inference. Various definitions of probability.
Thursday 03/30 PROBABILITY AND STATISTICS. Bayes' theorem. Taxi color problem. Bayesian hypothesis testing. Inference and measurement. Parameter measurement. Likelihood. Log-likelihood. Frequentist inference. Confidence intervals. Bayesian inference. Prior and posterior distribution. Example: Gaussian measurement of a parameter. Use of different priors. Jeffreys prior.
Statistical methods in particle physics by Harrison Prosper.
Tuesday 04/04 COMPUTER TUTORIAL: Monte Carlo Integration. Riemann method. Crude Monte Carlo. Rejection (hit or miss) method. Importance sampling: choosing a good sampling distribution, how to sample from a given distribution. Accuracy of the result. HOMEWORK EXERCISES: 1) importance sampling example; 2) multi-dimensional integration.
Thursday 04/06 Review of Statistics 102:
2. Data and sampling distributions.
2.1. Random sampling and sample bias. Population. Sample. Random and stratified sampling. Bias. Random selection. Sampling with replacement. Sampling without replacement. Sample mean versus population mean. Sample size versus sample quality.
2.2. Selection bias. Vast search effect. Data snooping. Regression to the mean.
2.3. Sampling distribution of a statistic. Sample statistic. Data distribution. Sampling distribution. Central limit theorem. Standard error.
Useful online simulator: Sampling distributions

MONTE CARLO SIMULATIONS: VARIANCE REDUCTION. The need for Monte Carlo simulations. The need for variance reduction. Importance sampling. Stratified sampling. Control variates. Antithetic variates.

Tuesday 04/11 COMPUTER TUTORIAL: Variance reduction.
Thursday 04/13 SIMPLIFIED MODELS
Phase space analysis. Kinematic distributions in 2-body decays. Top quark decay. Kinematic distributions in 3-body decays.
SUSY-inspired event kinematics. The squark and gluino decay chains.
Review on kinematic variables.
Tuesday 04/18 SUSY signatures with and without R-parity violation. Gauge mediated SUSY.
Traditional kinematic variables. Transverse mass. MT2.
SUSY mass measurements from kinematic endpoints.
SUSY mass measurements from kinematic constraints (polynomial method).
EVENT GENERATORS: PYTHIA.
Thursday 04/20 MINI-LECTURES (25-30 min each). Possible topics:
  • DETECTOR SIMULATION. Various types of reconstructed objects: jets, taus, heavy flavor, electrons, photons, muons, MET. ID cuts. Isolation. Fake leptons. Momentum and energy resolution. (Volunteer lecturer: SK)
  • LEPTONIC SUSY SIGNATURES AT THE LHC: Slepton pair production. Chargino pair production. Chargino-neutralino pair-production (golden channel). Like-sign dileptons. Trileptons. Mixed event subtraction. (Volunteer lecturer: MD)
  • PHASE SPACE EVENT GENERATION WITH PYTHON. Phasespace: n-body phase space generation in Python. (Volunteer lecturer: EU)
  • SYMBOLIC MATHEMATICS WITH PYTHON. SymPy: a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. (Volunteer lecturer: WO)
Tuesday 04/25 FINAL PROJECTS (20 min each).
  • BAYESIAN INFERENCE: DYNESTY. dynesty is a Pure Python, MIT-licensed Dynamic Nested Sampling package for estimating Bayesian posteriors and evidences. (Volunteer lecturer: JA)
  • EXTRA DIMENSIONS. (Volunteer lecturer: AK)
  • Using machine learning to derive the exceptional groups G2 and F4. (RF)
  • Visualization of Lie subalgebras (RB)
  • Oracle-preserving latent space flows or a secret project. (AR)