Effective Field Theory with Nambu-Goldstone Modes

TL;DR

This paper introduces effective field theory methods for Nambu-Goldstone modes arising from spontaneous symmetry breaking, with applications to QCD and electroweak theories, emphasizing their phenomenological relevance and potential to reveal new physics.

Contribution

It provides a detailed overview of effective field theory techniques for Nambu-Goldstone modes and compares their application in chiral perturbation theory and electroweak effective theory.

Findings

Chiral perturbation theory effectively describes low-energy QCD.

Electroweak effective theory captures symmetry-breaking effects at low energies.

Low-energy couplings encode information about high-energy dynamics.

Abstract

These lectures provide an introduction to the low-energy dynamics of Nambu-Goldstone fields, associated with some spontaneous (or dynamical) symmetry breaking, using the powerful methods of effective field theory. The generic symmetry properties of these massless modes are described in detail and two very relevant phenomenological applications are worked out: chiral perturbation theory, the low-energy effective theory of QCD, and the (non-linear) electroweak effective theory. The similarities and differences between these two effective theories are emphasized, and their current status is reviewed. Special attention is given to the short-distance dynamical information encoded in the low-energy couplings of the effective Lagrangians. The successful methods developed in QCD could help us to uncover fingerprints of new physics scales from future measurements of the electroweak effective theory couplings.