Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory

TL;DR

This paper investigates how the masses and couplings of the rho and sigma mesons depend on quark mass using Chiral Perturbation Theory and dispersion relations, revealing a stable rho coupling and a non-analytic sigma mass behavior.

Contribution

It combines one-loop Chiral Perturbation Theory with dispersion methods to analyze quark mass effects on meson resonances, providing new insights into their mass dependence.

Findings

Rho-pion-pion coupling is nearly quark mass independent.

Rho mass varies smoothly with quark mass.

Sigma mass exhibits strong non-analytic behavior.

Abstract

We use the one-loop Chiral Perturbation Theory pion-pion scattering amplitude and dispersion theory in the form of the inverse amplitude method, to study the quark mass dependence of the two lightest resonances of the strong interactions, the f_0(600) (sigma) and the rho-meson. As main results we find that the rho-pion-pion coupling constant is almost quark mass independent and that the rho mass shows a smooth quark mass dependence while that of the sigma shows a strong non-analyticity. These findings are important for studies of the meson spectrum on the lattice.