One-loop renormalization of the chiral Lagrangian for spinless matter fields in the SU(N) fundamental representation

TL;DR

This paper calculates the one-loop renormalization of the chiral Lagrangian for spinless matter fields in the fundamental representation of SU(N), relevant for theories with spontaneous symmetry breaking and applications to QCD mesons.

Contribution

It provides the first detailed one-loop divergence analysis for the chiral Lagrangian with spinless matter fields in the fundamental representation, including counterterms up to second and third order.

Findings

Divergences are absorbed by counterterms from second and third order Lagrangians.

The method applies to QCD mesons like kaons and pseudoscalar heavy mesons.

The calculations use background field and heat kernel techniques.

Abstract

We perform the leading one-loop renormalization of the chiral Lagrangian for spinless matter fields living in the fundamental representation of SU(N). The Lagrangian can also be applied to any theory with a spontaneous symmetry breaking of $SU(N)_L\times SU(N)_R$ to $SU(N)_V$ and spinless matter fields in the fundamental representation. For QCD, the matter fields can be kaons or pseudoscalar heavy mesons. Using the background field method and heat kernel expansion techniques, the divergences of the one-loop effective generating functional for correlation functions of single matter fields are calculated up to $\mathcal{O}(p^3)$. They are absorbed by counterterms not only from the third order but also from the second order chiral Lagrangian.