PHY578 Effective Field Theories for Particle Physics

General Information

Lecturer:

Prof. Peter Stoffer ( Y36 H68 and PSI )

Assistants:

Fiona Kirk ( PSI )

Dr. Jason Aebischer ( Y36 J36 )

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 23.11.2021) (PDF, 590 KB)

Lecture details

Lecture

Date

Topics covered

Lecture notes

Lecture 1

21.09.2021

Introduction, general principles

Sects. 1, 2.1, 2.2

Lecture 2

28.09.2021

Operator bases, EOM

Sect. 2.3

Lecture 3

05.10.2021

Renormalization, running, tree-level matching

Sects. 2.4, 2.5

Lecture 4

12.10.2021

One-loop matching

Sect. 2.6

Lecture 5

19.10.2021

Q&A chapter 2; Fermi theory, Fierz relations

Sects. 3.1, 3.2, 3.3

Lecture 6

26.10.2021

Operator mixing, scheme dependence

Sects. 3.4, 3.5

Lecture 7

02.11.2021

Chiral symmetry, SSB, Goldstone's theorem

Sects. 4.1, 4.2

Lecture 8

09.11.2021

CCWZ, explicit symmetry breaking, spurions

Sects. 4.3, 4.4

Lecture 9

16.11.2021

Chiral power counting, chiral Lagrangian at NLO

Sects. 4.5, 4.6

Lecture 10

23.11.2021

ChPT at one loop

Sect. 4.7

Lecture 11

30.11.2021

SMEFT

 

Lecture 12

07.12.2021

SMEFT

 

Lecture 13

14.12.2021

Dispersion relations

 

Lecture 14

21.12.2021

Dispersion relations

 

 

Problem sets

Series Topics Discussed on Solutions

Sheet 1 (PDF, 149 KB)

Dimensional regularization, renormalization 

21./28.09.2021

Solutions 1 (PDF, 3 MB)

Sheet 2 (PDF, 109 KB)

Operator bases

05.10.2021

Solutions 2 (PDF, 2 MB)

Sheet 3 (PDF, 162 KB)

Renormalization-group equations

12.10.2021

Solutions 3 (PDF, 2 MB)

Sheet 4 (PDF, 146 KB)

Matching

19.10.2021

Solutions 4 (PDF, 6 MB)

Sheet 5 (PDF, 159 KB)

EFT below the weak scale

26.10.2021

Solutions 5 (PDF, 5 MB)

Sheet 6 (PDF, 140 KB)

Operator mixing

02.11.2021

Solutions 6 (PDF, 6 MB)

Sheet 7 (PDF, 133 KB)

Linear sigma model

09.11.2021

Solutions 7 (PDF, 2 MB)

Sheet 8 (PDF, 146 KB)

Current algebra, chiral symmetry

16.11.2021

Solutions 8 (PDF, 2 MB)

Sheet 9 (PDF, 169 KB)

Pion decay constant, isospin breaking

23.11.2021

Solutions 9 (PDF, 2 MB)

Sheet 10 (PDF, 206 KB)

Chiral perturbation theory at one loop

30.11.2021

 

 

Suggested references