Quark mass dependence of light resonances and phase shifts in elastic π π and π к scattering

Abstract

We study the light quark mass dependence of the π π scattering phase shifts in standard one and two-loop SU(2) Chiral Perturbation Theory (ChPT). We then repeat the study with unitarized ChPT and; furthermore, we extend the analysis to SU(3) and generate the elastic f_0(600), к(800) ρ(770) and K*(892) resonances from unitarization. The quark masses are varied up to values of interest for lattice studies. We find that the SU(2) π π phase shifts both in standard and unitarized ChPT depend very softly on the pion mass and that our results are in fair agreement with lattice results in the I=2, J=0 channel. In the SU(3) amplitudes, the mass and width of the ρ (770) and K*(892) present an analogous and smooth quark mass dependence. In contrast, both scalars present a similar non-analyticity at high quark masses. We also confirm the lattice assumption of independence of the vector two-meson coupling on the quark mass, that is, nevertheless, violated for scalars.