Quark mass dependence of light resonances and phase shifts in elastic ππ and πK scattering

Abstract

We study the light quark mass dependence of the ππ 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 f0(600), κ(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) ππ 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.