Renormalisation of the low-energy constants of chiral perturbation theory from loops with dynamical vector mesons

TL;DR

This paper performs a one-loop renormalisation of low-energy constants in chiral perturbation theory including vector mesons, clarifying their scale dependence and divergence structures at orders Q^2 and Q^4.

Contribution

It provides the first detailed calculation of divergence structures and renormalisation-scale dependence for low-energy constants with dynamical vector mesons in chiral perturbation theory.

Findings

Divergent structures at chiral orders Q^2 and Q^4 identified.

Renormalisation-scale dependence of low-energy constants determined.

Results applicable to both pseudoscalar octet and nonet in large N_c limit.

Abstract

Starting from a relativistic Lagrangian for pseudoscalar Goldstone bosons and vector mesons in the antisymmetric tensor representation, a one-loop calculation is performed to pin down the divergent structures that appear for the effective low-energy action at chiral orders Q^2 and Q^4. The corresponding renormalisation-scale dependences of all low-energy constants up to chiral order Q^4 are determined. Calculations are carried out for both the pseudoscalar octet and the pseudoscalar nonet, the latter in the framework of chiral perturbation theory in the limit of a large number of colours.