PHY578 Effective Field Theories for Particle Physics
General Information
| Lecturer: | Prof. Peter Stoffer ( Y15 H82D and PSI ) |
| Assistants: | David Radic ( PSI ) |
| Lecture: | Tuesday, 13:45 - 15:30, room HCI D 2 at ETH |
| Exercises: | Tuesday, 15:45 - 16:30, room HCI D 2 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.
Lecture details
|
Lecture |
Date |
Topics covered |
Lecture notes |
|
Lecture 1 |
16.09.2025 |
Introduction, general principles |
Sects. 1, 2.1, 2.2 |
|
Lecture 2 |
23.09.2025 |
Operator bases, EOM |
Sect. 2.3 |
|
Lecture 3 |
30.09.2025 |
Renormalization, running, tree-level matching |
Sects. 2.4, 2.5.1 |
|
Lecture 4 |
07.10.2025 |
Off-shell matching, matching at one-loop |
Sects. 2.5.2, 2.6 |
|
Lecture 5 |
14.10.2025 |
Q&A Sect. 2; Fermi theory |
Sects. 3.1, 3.2, 3.3 |
|
Lecture 6 |
21.10.2025 |
Fierz relations, operator mixing, scheme dependence |
Sects. 3.4, 3.5 |
|
Lecture 7 |
28.10.2025 |
Q&A Sect. 3; Chiral symmetry, SSB, Goldstone's theorem |
Sects. 4.1, 4.2 |
|
Lecture 8 |
04.11.2025 |
CCWZ, explicit symmetry breaking, spurions |
Sects. 4.3, 4.4 |
|
Lecture 9 |
11.11.2025 |
Chiral power counting, chiral Lagrangian at NLO |
|
|
Lecture 10 |
18.11.2025 |
ChPT at one loop |
|
|
Lecture 11 |
25.11.2025 |
SMEFT |
|
|
Lecture 12 |
02.12.2025 |
SMEFT/LEFT; nonlinear realization of EW symmetry |
|
|
Lecture 13 |
09.12.2025 |
Unitarity and analyticity |
|
|
Lecture 14 |
16.12.2025 |
Dispersion relations and EFTs |
Problem sets
| Problem sheet | Topics | Discussed on | Solutions |
|---|---|---|---|
Dimensional regularization, renormalization |
16./23.09.2025 |
||
| Sheet 2 (PDF, 123 KB) | Operator bases | 30.09.2025 | Solutions 2 (PDF, 7 MB) |
| Sheet 3 (PDF, 192 KB) | Renormalization-group equations | 07.10.2025 | Solutions 3 (PDF, 4 MB) |
| Sheet 4 (PDF, 157 KB) | Matching | 14.10.2025 | Solutions 4 (PDF, 6 MB) |
| Sheet 5 (PDF, 203 KB) | EFT below the weak scale | 21.10.2025 | Solutions 5 (PDF, 5 MB) |
| Sheet 6 (PDF, 150 KB) | EFT below the weak scale: operator mixing | 28.10.2025 | Solutions 6 (PDF, 4 MB) |
| Sheet 7 (PDF, 177 KB) | Linear sigma model, current algebra | 04.11.2025 | Solutions 7 (PDF, 4 MB) |
| Sheet 8 (PDF, 184 KB) | Nonlinear realization, soft-pion theorem | 11.11.2025 | Solutions 8 (PDF, 4 MB) |
| Sheet 9 (PDF, 181 KB) | Pion decay constant, isospin breaking | 18.11.2025 |
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
- A. Manohar, Introduction to Effective Field Theories, Les Houches Lect. Notes 108 (2020).
- A. Manohar, Effective field theories, Lect. Notes Phys. 479 (1997) 311.
- D. Kaplan, Five lectures on effective field theory
- S. Scherer, M. R. Schindler, A Primer for Chiral Perturbation Theory, Lect. Notes. Phys. 830 (2012).
- A. Pich, Effective Field Theory with Nambu–Goldstone Modes
- A. Pich, Chiral Perturbation Theory
- G. Colangelo and G. Isidori, An Introduction to ChPT
- A. Manohar, Effective Field Theories
- I. Stewart, MIT web course on Effective Field Theory
- R. Contino, The Higgs as a Composite Nambu-Goldstone Boson