Large-$N_c$ naturalness in coupled-channel meson-meson scattering

TL;DR

This paper introduces a Bayesian method to incorporate large-$N_c$ constraints into meson-meson scattering analysis, reducing parameter ambiguities and improving agreement with experimental phase shifts.

Contribution

It presents a novel Bayesian approach to apply large-$N_c$ constraints in effective field theory analysis of meson-meson scattering, enhancing parameter determination.

Findings

Reduced ambiguity in low-energy constants

Improved fit to experimental phase shifts

Effective integration of large-$N_c$ constraints

Abstract

The analysis of hadronic interactions with effective field theory techniques is complicated by the appearance of a large number of low-energy constants, which are usually fitted to data. On the other hand, the large-$N_c$ limit imposes natural short-distance constraints on these low-energy constants, providing a parameter reduction. A Bayesian interpretation of the expected $1/N_c$ accuracy allows for an easy and efficient implementation of these constraints, using an augmented $\chi^2$. We apply this approach to the analysis of meson-meson scattering, in conjunction with chiral perturbation theory to one loop and coupled-channel unitarity, and show that it helps to largely reduce the many existing ambiguities and simultaneously provide an acceptable description of the available phase shifts.