Chiral perturbation theory

TL;DR

Chiral perturbation theory is an effective field theory that describes low-energy QCD phenomena by exploiting chiral symmetry breaking and Goldstone bosons, allowing systematic perturbative analysis of hadronic interactions.

Contribution

This paper reviews the formulation and applications of chiral perturbation theory, highlighting its systematic loop expansion and inclusion of matter fields for low-energy QCD studies.

Findings

Systematic perturbative expansion in momenta and meson masses.

Handling of ultraviolet divergences via contact interactions.

Inclusion of baryons extends phenomenological applicability.

Abstract

In the limit of vanishing up, down and strange quark masses, QCD exhibits a chiral symmetry. This symmetry is broken spontaneously to its vector subgroup, giving rise to Goldstone bosons. These acquire a small mass through the explicit chiral symmetry breaking for non-vanishing quark masses. The consequences of these broken symmetries can be investigated in a suitably tailored effective field theory called chiral pertubation theory. It admits a perturbative expansion in the external momenta and the Goldstone boson masses and can be systematically analyzed in terms of a loop expansion. The appearing ultraviolet divergences in loop diagrams can be dealt with order-by-order through the Goldstone boson contact interactions. Matter fields like the lowest-lying baryons can also included, leading to a rich and testable phenomenology of low-energy QCD.