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.
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 |
|---|---|---|---|
|
Dimensional regularization, renormalization |
19./26.09.2023 |
||
|
Operator bases |
03.10.2023 |
||
|
RGEs in EFT, derivative interactions |
10.10.2023 |
||
|
Matching |
17.10.2023 |
||
|
Fierz relations, EFT below the weak scale |
24.10.2023 |
||
|
Operator mixing |
31.10.2023 |
||
|
Linear sigma model, current algebra |
7.11.2023 |
Solutions 07 (PDF, 3 MB) | |
|
Nonlinear realization, soft-pion theorem |
14.11.2023 |
Solutions 08 (PDF, 2 MB) | |
|
Pion decay constant, isospin breaking |
21.11.2023 |
Solutions 09 (PDF, 3 MB) | |
|
ChPT at one loop |
28.11.2023 |
Solutions 10 (PDF, 4 MB) Mathematica notebook (NB, 231 KB) |
|
|
SMEFT in the broken phase |
05.12.2023 |
Solutions 11 (PDF, 6 MB) | |
|
Neutrino masses |
12.12.2023 |
Solutions 12 (PDF, 2 MB) | |
|
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
- 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