Effective Field Theories

This lecture provides an introduction to the framework of low energy effective field theories. After developing the basic concepts, the method is used to analyze the electromagnetic, weak and strong interactions at low energies. The course is intended for master students, who have taken a first course in quantum field theory.

Please sign up on the ILIAS page for the course.

The handwritten lectures notes linked below were typeset in LaTeX by Jonas Haldemann in 2015 and have been revised and corrected by Martin Hoferichter in 2021. Here is the resulting PDF script (91 pages, 3MB). This script will be extended and adapted as the lecture progresses.

• Outline and some references

1. Introduction (and some introductionary slides)
2. The Wilsonian effective action
   1. Integrating out high-energy modes
   2. Classification of operators
   3. Renormalization group
3. Continuum effective theory
   1. Tree-level matching calculations
   2. Field redefinitions
   3. Matching at higher orders
   4. Power counting
   5. Renormalization group improved perturbation theory
4. The Standard Model at low energies
   1. Euler Heisenberg Theory
   2. Decoupling of heavy flavors
      1. Decoupling in QED (Figures: anomalous magnetic moment)
      2. Heavy flavors in QCD (Figures: running coupling)
   3. Effective weak Hamiltonian (Fermi Theory)
   4. The Standard Model as an EFT (slides with operators)
   5. Chiral Perturbation Theory
      1. Chiral symmetry
      2. Transformation properties of Goldstone bosons
      3. Effective Lagrangian
      4. Applications (figures)
5. Non-relativistic theories
   1. Heavy-Quark Effective Theory (HQET)
      1. Connection to quantum mechanics
      2. Applications of HQET (figures)
   2. Non-relativistic QCD and QED
6. Energetic particles and jet physics
   1. Asymptotic expansions and the method of regions
   2. Soft-Collinear Effective Theory

Appendices

1. Loop integrals in dimensional regularization
2. Feynman rules for derivative couplings
3. QCD Lagrangian and Feynman rules
4. Goldstone's theorem

1. Exercise 1 (solution)
2. Exercise 2 (solution, revised version with correction on pages 8 and 9, thanks to Noah Messerli)
3. Exercise 3 (solution). Mathematica files for the derivation of
   • the EFT Feynman rules as pdf and notebook
   • matching as pdf and notebook
   • matching with Package X as pdf and notebook (by Julian Eicher)
   • matching with FeynCalc as pdf and notebook (by Julian Eicher)
4. Exercise 4 (solution)
5. Exercise 5 (solution)
6. Exercise 6 (solution)
7. Exercise 7 (solution)
8. Exam topics