PHY578 Effective Field Theories for Particle Physics

General Information

Lecturer:

Prof. Peter Stoffer ( Y36 H68 and PSI )

Assistants:

Felix Wilsch ( Y36 J44 )

Lecture: Tuesday, 13:45 - 15:30, room HCI H 8.1 at ETH
Exercises: Tuesday, 15:45 - 16:30, room HCI H 8.1 at ETH
Module code: PHY578, 402-0845-61L
ECTS Credits: 6

Description

This course covers the basic concepts of effective field theories (EFTs) and dispersion theory. We will start by introducing the core concept of constructing EFTs and apply them to the low-energy description of the weak interaction and the effective description of heavy physics beyond the Standard Model. We will discuss Chiral Perturbation Theory (ChPT), the low-energy effective theory of Quantum Chromodynamics (QCD). We will also briefly discuss the application of this concept to describe a class of theories beyond the SM in which the SM Higgs arises as a composite state of a new confining sector.

The last part of the course is on dispersion theory and its interplay with EFTs. We will discuss how to make use of the constraints from unitarity of the S-matrix and analyticity of scattering amplitudes, in order to extend the range of validity of the theoretical description compared to pure EFT methods. We will also discuss how to obtain constraints on EFT parameters from unitarity and analyticity.

Main topics:

  • Introduction to Effective Field Theories
  • Decoupling and matching
  • Renormalization-group resummation
  • The Standard Model Effective Field Theory (SMEFT)
  • Chiral Lagrangians
  • Unitarity of the S-matrix
  • Analyticity and dispersion relations

Lecture notes

The following lecture notes will be updated weekly in the course of the semester.

EFT lecture notes (updated 25.10.2022) (PDF, 958 KB)

Lecture details

Lecture

Date

Topics covered

Lecture notes

Lecture 1

20.09.2022

Introduction, general principles

Sects. 1, 2.1, 2.2

Lecture 2

27.09.2022

Operator bases, EOM

Sect. 2.3

Lecture 3

04.10.2022

Renormalization, running, tree-level matching

Sects. 2.4, 2.5

Lecture 4

11.10.2022

One-loop matching

Sect. 2.6

Lecture 5

18.10.2022

Fermi theory, Fierz relations

Sects. 3.1, 3.2, 3.3

Lecture 6

25.10.2022

Operator mixing, scheme dependence

Sects. 3.4, 3.5

Lecture 7

01.11.2022

Chiral symmetry, SSB, Goldstone's theorem

Sects. 4.1, 4.2

Lecture 8

08.11.2022

CCWZ, explicit symmetry breaking, spurions

Sects. 4.3, 4.4

Lecture 9

15.11.2022

Chiral power counting, chiral Lagrangian at NLO

Sects. 4.5, 4.6

Lecture 10

22.11.2022

ChPT at one loop

Sect. 4.7

Lecture 11

29.11.2022

SMEFT

 

Lecture 12

06.12.2022

LEFT; nonlinear realization of EW symmetry

 

Lecture 13

13.12.2022

Unitarity and analyticity

 

Lecture 14

20.12.2022

Dispersion relations and EFTs

 

 

Problem sets

Series Topics Discussed on Solutions

Sheet 1 (PDF, 160 KB)

Dimensional regularization, renormalization

20./27.09.2022

Solution 1 (PDF, 8 MB)

Sheet 2 (PDF, 32 KB)

Operator bases

04.10.2022

Solution 2 (PDF, 6 MB)

Sheet 3 (PDF, 52 KB)

Renormalization, Feynman rules

11.10.2022

Solution 3 (PDF, 2 MB)

Sheet 4 (PDF, 46 KB)

Tree-level and one-loop matching

18.10.2022

Solution 4 (PDF, 6 MB)

Sheet 5 (PDF, 48 KB)

Fierz identities and LEFT

25.10.2022

Solution 5 (PDF, 5 MB)

Sheet 6 (PDF, 57 KB)

Operator mixing, γ5 in D dimensions

01.11.2022

Solution 6 (PDF, 7 MB)

Sheet 7 (PDF, 45 KB) Linear sigma model 08.11.2022

Solution 7 (PDF, 4 MB)

Sheet 8 (PDF, 174 KB) Current algebra, chiral symmetry 15.11.2022

Solution 8 (PDF, 4 MB)

Sheet 9 (PDF, 64 KB)

Nucleon Pion interactions, Pion decay constant,

isospin breaking

22.11.2022 Solution 9 (PDF, 4 MB)
Sheet 10 (PDF, 59 KB) Chiral perturbation theory at one loop 29.11.2022  

Suggested references