N_c and m_pi dependence of rho and sigma mesons from unitarized Chiral Perturbation Theory

TL;DR

This paper investigates how rho and sigma mesons' properties depend on the number of colors and pion mass using unitarized Chiral Perturbation Theory, revealing different quark compositions and coupling behaviors.

Contribution

It provides a detailed analysis of the N_c and m_pi dependence of rho and sigma mesons, clarifying their quark-antiquark nature and coupling characteristics through the Inverse Amplitude Method.

Findings

Rho meson behaves as a quark-antiquark state with N_c scaling.

Sigma meson does not follow quark-antiquark N_c behavior.

Rho-pi-pi coupling is independent of m_pi, unlike sigma-pi-pi coupling.

Abstract

We review our work on the rho and sigma resonances derived from the Inverse Amplitude Method. In particular, we study the leading 1/N_c behavior of the resonances masses and widths and their evolution with changing m_pi. The 1/N_c expansion gives a clear definition of quark-antiquark states, which is neatly satisfied by the rho but not by the sigma, showing that its dominant component is not quark-antiquark. The m_pi dependence of the resonance properties is relevant to connect with lattice studies. We show that our predictions compare well with some lattice results and we find that the rho-pi-pi coupling constant is m_pi independent, in contrast with the sigma-pi-pi coupling, that shows a strong m_pi dependence.