Strange and non-strange quark mass dependence of elastic light resonances from SU(3) Unitarized Chiral Perturbation Theory to one loop

TL;DR

This study uses unitarized one-loop Chiral Perturbation Theory to analyze how light and strange quark masses affect the properties of certain meson resonances, providing insights relevant for lattice QCD.

Contribution

It demonstrates a comprehensive fit to experimental and lattice data, revealing the different quark mass dependencies of scalar and vector meson resonances.

Findings

Vector meson masses scale with decay constants.

Scalar mesons show non-analytic quark mass dependence.

Vector widths are well approximated by the KSRF relation.

Abstract

We study the light quark mass dependence of the f_0(600), kappa(800), rho(770) and K*(892) resonance parameters generated from elastic meson-meson scattering using unitarized one-loop Chiral Perturbation Theory. First, we show that it is possible to fit simultaneously all experimental scattering data up to 0.8-1 GeV together with lattice results on decay constants and scattering lengths up to a pion mass of 400 MeV, using chiral parameters compatible with existing determinations. Then, the strange and non-strange quark masses are varied from the chiral limit up to values of interest for lattice studies. In these amplitudes, the mass and width of the rho(770) and K*(892) present a similar and smooth quark mass dependence. In contrast, both scalars present a similar non-analyticity at high quark masses. Nevertheless, the f_0(600) dependence on the non-strange quark mass is stronger than for the kappa(800) and the vectors. We also confirm the lattice assumption of quark mass independence of the vector two-meson coupling that, in contrast, is violated for scalars. As a consequence, vector widths are very well approximated by the KSRF relation, and their masses are shown to scale like their corresponding meson decay constants.