Introduction to Effective Field Theories

TL;DR

This lecture collection provides a cohesive, technique-focused tour of effective field theories in high-energy physics, starting from foundational ideas of locality and scale separation and proceeding through concrete constructions such as Fermi theory, HQET, chiPT, SCET, and SMEFT. It develops a rigorous framework for organizing calculations via power counting, renormalization, and matching, and demonstrates how RG running and operator mixing enable reliable predictions across widely separated energy scales. The notes emphasize the practical toolkit of EFTs: dimensional regularization, systematic inclusion of higher-dimension operators, and the interplay between UV completions and low-energy observables. The SMEFT and LEFT sections underscore EFTs’ central role in probing new physics, enabling model-independent constraints on BSM effects while preserving gauge and Lorentz invariance. Overall, the work highlights EFTs as a unifying, predictive language for connecting experimental data to fundamental theory across scales, with substantial implications for precision tests and new-physics searches.

Abstract

Lecture notes from the 2017 Les Houches Summer School on Effective Field Theories. The lectures covered introductory material on EFTs as used in high energy physics to compute experimentally observable quantities. Other lectures at the school covered a wide range of applications in greater depth.

Figures (17)

• Figure 1: The electric field and potential lines for two point charges of the same sign. The right figure is given by zooming out the left figure.
• Figure 2: A charge distribution with two intrinsic scales: $d$, the size of each clump, and $a$, the distance between clumps.
• Figure 3: The left figure is the QED contribution to the $\gamma\gamma$ scattering amplitude from an electron loop. The right figure is the low-energy limit of the QED amplitude treated as a local $F_{\mu \nu}^4$ operator in the Euler-Heisenberg Lagrangian.
• Figure 4: Tree-level diagram for semileptonic $b \to c$ decay.
• Figure 5: $b \to c$ vertex in the Fermi theory.