Resonance saturation of the chiral couplings at NLO in 1/Nc

TL;DR

This paper examines the validity of the resonance saturation hypothesis at next-to-leading order in 1/Nc within Resonance Chiral Theory, showing that chiral couplings can be expressed in terms of resonance parameters under QCD constraints.

Contribution

It extends the resonance saturation hypothesis to NLO in 1/Nc, providing a formulation that accounts for scale dependence and QCD constraints in resonance chiral theory.

Findings

Chiral couplings depend on resonance masses and couplings, not on chiral operator coefficients.

Imposing QCD short-distance constraints links LECs to resonance parameters.

The approach controls the renormalization scale dependence of LEC estimates.

Abstract

The precision obtainable in phenomenological applications of Chiral Perturbation Theory is currently limited by our lack of knowledge on the low-energy constants (LECs). The assumption that the most important contributions to the LECs come from the dynamics of the low-lying resonances, often referred to as the resonance saturation hypothesis, has stimulated the use of large-Nc resonance lagrangians in order to obtain explicit values for the LECs. We study the validity of the resonance saturation assumption at the next-to-leading order in the 1/Nc expansion within the framework of Resonance Chiral Theory (RChT). We find that, by imposing QCD short-distance constraints, the chiral couplings can be written in terms of the resonance masses and couplings and do not depend explicitly on the coefficients of the chiral operators in the Goldstone boson sector of RChT. As we argue, this is the counterpart formulation of the resonance saturation statement in the context of the resonance lagrangian. Going beyond leading order in the 1/Nc counting allow us to keep full control of the renormalization scale dependence of the LEC estimates.