ABOUT THE COURSE:Particle physics is the study of nature at the most fundamental level. Its aim is to discover new principles of physics in the form of symmetries, laws, and concepts: the program of reductionism inaugurated by Isaac Newton. The course will explore phenomena that arise from uniting quantum mechanics and special relativity, often expressed in the language of field theory. Emphasis will be on theoretical aspects in the first half, and experimental observables in the second half.INTENDED AUDIENCE:4th year undergraduates, Masters, IntPhD, PhD students.PREREQUISITES: Bachelor’s level quantum mechanics and special relativity must be completed.
Overview
Syllabus
Week 1:
Week 3:
- What is a particle? Why particle physics? Noether's Theorem.
- Standard Model at 3 scales: sub-Fermi, sub-QCD, above QCD. Flavour puzzle and eightfold way.
- Long-lived and stable particles vis-a-vis symmetries/conservation laws, parity in electromagnetic and strong forces. Intrinsic parity. Parity, charge conjugation, CP and CP violation in weak forces.
- Strong CP problem. CPT Theorem & proof. Tests of CP and T violation. Angular momenta, spins, spinors in quantum mechanics. Spinor rotations. Introduction to group theory. Isospin. Epilogue: Introduction to Feynman diagrams.
Week 3:
- Relativistic field equations and quantization. Spin 0: Klein-Gordon equation, Lagrangian construction, the Hamiltonian, and the cosmological constant problem. Mass dimensions of fields.
- Spin 1: Proca equation & Lagrangian, and Lorenz gauge; free photon Lagrangian, gauge-fixing in Coulomb gauge.
- Spin 1/2: Dirac equation. Lagrangian in 4-spinor and 2-spinor forms.
- Lorentz group and generators in SO(1,3) representation. Spinor [SU(2)L x SU(2)R] representation. Chiral theory.Gauge invariance. Quantum electrodynamics. Yang-Mills theories. Gauge boson self interactions and asymptotic freedom.
- Field content and Yang-Mills Lagrangians of the Standard Model, gauge invariance and the masslessness of fermions & gauge bosons, Higgs Yukawa terms.
- Electroweak symmetry breaking, round 1: dynamical breaking of chiral symmetry and explicit breaking of electroweak.
- Electroweak symmetry breaking, round 2: spontaneous breaking of electroweak symmetry. Goldstone's theorem and the Higgs mechanism.
- Higgs boson and its mass. Fermions in the bases of Yukawa interactions, masses, and charged current interactions. CKM matrix, counting observable rotation angles and complex phases, CP violation.
- Flavour changing neutral currents. Unitarity triangles and Jarlskog invariant. PMNS matrix and neutrino oscillations: 2-flavour approximation. Baselines, oscillation lengths, and atmospheric neutrinos.
- Fast oscillation regime, solar neutrinos and matter potential. Neutrino mass ordering and mass scale.
- Relativistic kinematics and particle collisions: fixed target and centre-of-momentum configurations.
- Scattering cross sections: projectile in medium, beam on target. Generalization to 2 -> n scattering; S-matrix and transition amplitude. Decay rates and branching fractions.
- Muon and beta decays. Proton decay: Super-Kamiokande and Goldhaber's lethal radiation dose estimate.
- QED cross section for e+e- --> \mu+\mu- with spinor helicity & photon polarization states.
- Forward-backward asymmetry, chronology of Z boson discovery.
- Deep inelastic scattering of protons. Bjorken x and infinite momentum frame. Quark parton model. Momentum sum rule. Effect of the gluon and DGLAP evolution. Bjorken scaling and scaling violations.
- Quark number sum rules, PDF-fitting processes and colliders, Drell-Yan PDF factorization. Fifth-force searches in deep inelastic scattering.
- Dark matter: particle properties inferable from astronomy.
- Epilogue 1: charged pion decay to the muon and helicity flip.
- Epilogue 2: The dimensionality of time and particle decays to lighter daughters.
- Particle cosmology. Big Bang nucleosynthesis. Recombination and cosmic microwave background.
Taught by
Prof. Nirmal Raj
