Navigation auf uzh.ch

Suche

Physik-Institut

PHY578 Effective Field Theories for Particle Physics

General Information

Lecturer:

Prof. Peter Stoffer ( Y36 H68 and PSI )

Assistants:

Luca Naterop ( Y36 H70 and PSI )

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 13.02.2024) (PDF, 972 KB)

Lecture details

Lecture

Date

Topics covered

Lecture notes

Lecture 1

19.09.2023

Introduction, general principles

Sects. 1, 2.1, 2.2

Lecture 2

26.09.2023

Operator bases, EOM

Sects. 2.2, 2.3

Lecture 3

03.10.2023

Renormalization, running, tree-level matching

Sects. 2.4, 2.5

Lecture 4

10.10.2023

One-loop matching

Sect. 2.6

Lecture 5

17.10.2023

Q&A section 2; Fermi theory

Sects. 3.1, 3.2

Lecture 6

24.10.2023

Fierz relations, operator mixing

Sects. 3.3, 3.4

Lecture 7

31.10.2023

Scheme dependence; chiral symmetry, SSB, Goldstone's theorem

Sects. 3.5, 4.1, 4.2

Lecture 8

07.11.2023

CCWZ, explicit symmetry breaking, spurions

Sects. 4.3, 4.4

Lecture 9

14.11.2023

Chiral power counting, chiral Lagrangian at NLO

Sects. 4.4, 4.5, 4.6

Lecture 10

21.11.2023

ChPT at one loop

Sects. 4.6, 4.7

Lecture 11

28.11.2023

ChPT; SMEFT

Sects. 5.1.1, 5.1.2

Lecture 12

05.12.2023

SMEFT/LEFT; nonlinear realization of EW symmetry

Sects. 5.1.3, 5.1.4, 5.2, 5.3

Lecture 13

12.12.2023

Unitarity and analyticity

Sects. 5.3, 6.1, 6.2

Lecture 14

19.12.2023

Dispersion relations and EFTs

Sects. 6.2, 6.3, 6.4

 

Problem sets

Series Topics Discussed on Solutions

Sheet 1 (PDF, 160 KB)

Dimensional regularization, renormalization

19./26.09.2023

Solutions 01 (PDF, 3 MB)

Sheet 2 (PDF, 134 KB)

Operator bases

03.10.2023

Solutions 02 (PDF, 2 MB)

Sheet 3 (PDF, 175 KB)

RGEs in EFT, derivative interactions

10.10.2023

Solutions 03 (PDF, 1 MB)

Sheet 4 (PDF, 157 KB)

Matching

17.10.2023

Solutions 04 (PDF, 6 MB)

Sheet 5 (PDF, 188 KB)

Fierz relations, EFT below the weak scale

24.10.2023

Solutions 05 (PDF, 5 MB)

Sheet 6 (PDF, 148 KB)

Operator mixing

31.10.2023

Solutions 06 (PDF, 6 MB)

Sheet 7 (PDF, 156 KB)

Linear sigma model, current algebra

7.11.2023

Solutions 07 (PDF, 3 MB)

Sheet 8 (PDF, 184 KB)

Nonlinear realization, soft-pion theorem

14.11.2023

Solutions 08 (PDF, 2 MB)

Sheet 9 (PDF, 181 KB)

Pion decay constant, isospin breaking

21.11.2023

Solutions 09 (PDF, 3 MB)

Sheet 10 (PDF, 221 KB)

ChPT at one loop

28.11.2023

Solutions 10 (PDF, 4 MB)
Mathematica notebook (NB, 231 KB)

Sheet 11 (PDF, 185 KB)

SMEFT in the broken phase

05.12.2023

Solutions 11 (PDF, 6 MB)

Sheet 12 (PDF, 263 KB)

Neutrino masses

12.12.2023

Solutions 12 (PDF, 2 MB)

Sheet 13 (PDF, 195 KB)

Analyticity and dispersion relations

05.12.2023

Solutions 13 (PDF, 2 MB)

Recordings

The course is organized as on-campus lecture only, without remote option. Recordings of the fall 2021 lectures can be found on SWITCHcast.

Suggested references