# David Tong: Lectures on the Standard Model

This is a course on the Standard Model, given to Part III (i.e. masters level) students. It assumes a basic knowledge of quantum field theory and describes the structure of the Standard Model, as well as a number of important, underlying aspects of field theory. Please do email me if you find any typos or mistakes.

# Content

**1. Symmetries: PDF**

Introduction. Spacetime symmeries, the Lorentz group and Poincare group and their representations. Spinors, Dirac spinors vs Weyl spinors. Gauge invariance, Maxwell theory, Lie algebras, Yang-Mills theory. Parity, time reversal, charge conjugation, and CPT invariance.**2. Broken Symmetries: PDF**

Spontaneous symmetry breaking. Discrete symmetries and quantum tunnelling. Continuous symmetries, the Mexican hat potential, the O(N) model, Goldstone bosons and Goldstone's theorem. The Coleman-Mermin-Wagner theorem. The Higgs mechanism. Superconductivity, the London equations, magnetic vortices and confinement of magnetic monopoles. The non-Abelian Higgs mechanism.**3. The Strong Force: PDF**

Quantum chromodynamics (QCD), asymptotic freedom, anti-screening and paramagnetism, the mass gap, confinement. Chiral symmetry breaking, the quark condensate, pions as Goldstone bosons, the chiral Lagrangian, phases of massless QCD. Hadrons, mesons, baryons, isospin, the eightfold way, lifetimes, heavy quarks. The theta term and the strong CP problem, instantons.**4. Anomalies: PDF**

The anomaly: the path integral measure is not invariant. Gauge anomalies, the Witten anomaly. Chiral anomalies, or ABJ anomalies, the theta term, neutral pion decay. 't Hooft anomalies. Confinement implies chiral symmetry breaking.**5. Electroweak Interactions: PDF**

The structure of the Standard Model, anomaly cancellation, Yukawa interactions, three generations, baryon and leption number and B-L, the gauge group of the Standard Model. Electroweak symmetry breaking, unification, fermion masses. Weak decays, electroweak currents, beta decay, 4-Fermi theory.**6. Flavour: PDF**

The flavour basis and mass eigenbasis. The CKM matrix, Counting parameters, the Cabibbo angle, the Wolfenstein parameterisation, the unitarity triangle. Flavour changing neutral currents, the GIM mechanism. CP violation, the Jarlskog invariant, the strong CP problem, neutral kaon mixing.**7. Neutrinos: PDF**

Neutrino masses and mass differences, Dirac vs Majorana masses, the dimension 5 operator, neutrinoless double beta decay, neutrino mixing angles and the PMNS matrix, CP violation; neutrino oscillations, oscillations in matter and the MSW effect, neutrino detection experiments.

# Problem Sheets

**Problem Sheet 1: PDF**The Basics**Problem Sheet 2: PDF**Symmetry Breaking and QCD**Problem Sheet 3: PDF**Anomalies**Problem Sheet 4: PDF**Standard Model

# The Standard Model on the Web

**Particle Physics Booklet**by the Particle Data Group**Part III Standard Model**by Fernando Quevedo**Part III Standard Model**by Hugh Osborn-
**Lectures on Field Theory and the Standard Model**by Luis Alvarez-Gaume and Miguel Vazquez-Mozo **Just a Taste: Lectures on Flavor Physics**by Yuval Grossman and Flip Tanedo-
**Lectures on CP violation**by P. Kooijman and N. Tuning -
**TASI Lectures on Neutrino Physics**by Andrea de Gouvea