m_pi and N_c dependence of resonances from Unitarized Chiral Perturbation Theory

TL;DR

This paper investigates how rho and sigma resonances depend on pion mass and number of colors using Unitarized Chiral Perturbation Theory, revealing their quark content and comparing with lattice results.

Contribution

It provides a detailed analysis of resonance properties' dependence on $m_$ and $N_c$, clarifying the quark composition of rho and sigma resonances.

Findings

The rho resonance behaves as a typical $ar qq$ state with $1/N_c$ scaling.

The sigma resonance does not follow $ar qq$ behavior, indicating a different dominant component.

The rho-pi-pi coupling is independent of $m_$, unlike the sigma-pi-pi coupling.

Abstract

We review our studies on the rho and sigma resonances properties 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 $\bar qq$ states, which is neatly satisfied by the $\rho$ but not by the sigma, showing that its dominant component is not $\bar qq$. 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.