Dependence on the quark masses of elastic phase shifts and light resonances within standard and unitarized Chiral Perturbation Theory

TL;DR

This paper investigates how light quark masses influence pion-pion scattering phase shifts and light resonances using standard and unitarized Chiral Perturbation Theory, providing insights relevant for lattice QCD studies.

Contribution

It offers a detailed analysis of quark mass dependence of phase shifts and resonances within ChPT, including unitarized SU(3) extensions, highlighting differences between scalar and vector resonances.

Findings

Pion-pion phase shifts show a soft dependence on quark mass at one loop.

Vector resonances depend smoothly on quark mass, scalar resonances show non-analytic behavior.

Lattice assumption of quark mass independence of vector couplings is confirmed, scalar couplings are not independent.

Abstract

We study the dependence of the pion-pion scattering phase shifts on the light quark mass in both standard and unitarized SU(2) Chiral Perturbation Theory (ChPT) to one and two loops. We then use unitarized SU(3) ChPT to study the elastic f_0(600), kappa(800), rho(770) and K*(892) resonances. The quark masses are varied up to values of interest for lattice studies. We find a very soft dependence on the light quark mass of the pion-pion phase shifts at one loop and slightly stronger at two loops and a good agreement with lattice results. The SU(3) analysis shows that the properties of the rho(770) and K*(892) depend smoothly on the quark mass whereas the scalar resonances present a non-analyticity at high quark masses. We also confirm the lattice assumption of quark mass independence of the vector two-meson coupling that, however, is violated for scalars.