Determining chiral couplings at NLO

TL;DR

This paper introduces a method to estimate low-energy constants in Chiral Perturbation Theory at NLO, controlling scale dependence, and applies it to determine specific couplings related to scalar and pseudoscalar correlators.

Contribution

The paper presents a novel general method for estimating low-energy constants at NLO in the 1/N(C) expansion with full renormalization scale control, including a matching procedure.

Findings

Determined L(8) and C(38) couplings at mu_0=0.77 GeV.

Provided values with uncertainties for these couplings.

Discussed the matching procedure in effective theories.

Abstract

We present a general method that allows to estimate the low-energy constants of Chiral Perturbation Theory up to next-to-leading corrections in the 1/N(C) expansion, that is, keeping full control of the renormalization scale dependence. As a first step we have determined L(8) and C(38), the couplings related to the difference of the two-point correlation functions of two scalar and pseudoscalar currents, L(8)(mu_0) = (0.6 \pm 0.4) 10^{-3} and C(38)(mu_0) = (2 \pm 6) 10^{-6}$, with mu_0 = 0.77 GeV. As in many effective approaches, one of the main ingredients of this method is the matching procedure: some comments related to this topic are presented here.