Quark mass dependence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math> scattering in isospin 0, 1, and 2 from lattice QCD
A. Rodas, Jo Dudek, Robert G. Edwards
Abstract
Using lattice QCD we extract $\ensuremath{\pi}\ensuremath{\pi}$ scattering amplitudes with isospin 0, 1, and 2 in low partial-waves at two values of the light quark mass corresponding to ${m}_{\ensuremath{\pi}}\ensuremath{\sim}283$ and 330 MeV. We confirm expectations of weak repulsion in isospin-2, and the presence of a narrow $\ensuremath{\rho}$ resonance in isospin-1, and study the pion mass dependence of these channels. In isospin-0 we find that the two pion masses considered straddle the point at which the $\ensuremath{\sigma}$ transitions from being a stable bound state to being either a virtual bound state or a subthreshold resonance. We discuss the ability of lattice calculations like these to precisely determine the $\ensuremath{\sigma}$ pole location when it is a resonance, and propose an approach in which the full complement of amplitudes computed in this paper can be used simultaneously to provide more constraint.