Properties of the rho and sigma Mesons from Unitary Chiral Dynamics

TL;DR

This paper investigates the properties of rho and sigma mesons using Unitary Chiral Dynamics within SU(2) ChPT, analyzing how chiral logarithms affect their masses and widths, especially at large number of colors (NC).

Contribution

It provides a detailed analysis of rho and sigma meson behavior in the large NC limit, highlighting differences in their chiral logarithm cancellations and the limitations of the inverse amplitude method.

Findings

Chiral logarithms cancel in the rho channel but not in the sigma channel.

At large NC, the vector and scalar meson nonets become degenerate.

The scalar meson evolution at large NC may be beyond the one-loop inverse amplitude method's applicability.

Abstract

The chiral limit of the rho and sigma masses and widths is discussed. We work within the inverse amplitude method to one loop in SU(2) ChPT and analyze the consequences that all chiral logarithms cancel out in the rho-channel, while they do not cancel for the sigma case, and how they strongly influence the properties of this latter resonance. Our results confirm and explain the different behavior of the sigma and rho poles for NC not far from 3, but we extend the analysis to very large NC, where the behavior of these two resonances is re-analyzed. We note that the rather natural requirement of consistency between resonance saturation and unitarization imposes useful constraints. By looking only at the rho-channel, and within the single resonance approximation, we find that the masses of the first vector and scalar meson nonets, invoked in the single resonance approximation, turn out to be degenerated in the large NC limit. On the contrary we show that, for sufficiently large NC, the scalar meson evolution lies beyond the applicability reach of the one-loop inverse amplitude method and if the scalar channel is also incorporated in the analysis, it may lead, in some cases, to phenomenologically inconsistent results.