Large-Nc Properties of the rho and f0(600) Mesons from Unitary Resonance Chiral Dynamics

TL;DR

This paper constructs pi-pi scattering amplitudes respecting unitarity and chiral symmetry, analyzing how rho and sigma meson properties depend on the number of QCD colors, with robust results for the rho but inconclusive findings for the sigma.

Contribution

It introduces a unitarized chiral framework including 1/Nc effects for the lowest-lying mesons, providing insights into their large-Nc behavior.

Findings

Rho meson remains stable as Nc increases.

Uncertainty remains about the fate of the sigma (f0(600)) at large Nc.

Results support the rho as a conventional q-qbar meson.

Abstract

We construct pi-pi amplitudes that fulfill exact elastic unitarity, account for one loop Chiral Perturbation Theory contributions and include all 1/Nc leading terms, with the only limitation of considering just the lowest-lying nonet of exchanged resonances. Within such scheme, the Nc dependence of sigma and rho masses and widths is discussed. Robust conclusions are drawn in the case of the rho resonance, confirming that it is a stable meson in the limit of a large number of QCD colors, Nc. Less definitive conclusions are reached in the scalar-isoscalar sector. With the present quality of data, we cannot firmly conclude whether or not the Nc=3 f0(600) resonance completely disappears at large Nc or it has a sub-dominant component in its structure, which would become dominant for a number of quark colors sufficiently large.