Quark mass dependence of $\pi \pi$ scattering in isospin 0, 1, and 2 from lattice QCD

TL;DR

This study uses lattice QCD to analyze how varying quark masses affect pion-pion scattering in different isospin channels, revealing resonance behaviors and the transition of the sigma state.

Contribution

It provides new lattice QCD results on pion scattering amplitudes at different quark masses, especially near the sigma resonance region, and discusses methods to improve resonance parameter extraction.

Findings

Confirmed weak repulsion in isospin-2 channel.

Identified a narrow rho resonance in isospin-1.

Observed the sigma state transition near the studied pion masses.

Abstract

Using lattice QCD we extract $\pi\pi$ scattering amplitudes with isospin--0,1,2 in low partial-waves at two values of the light quark mass corresponding to $m_\pi \sim 283$ and $330$ MeV. We confirm expectations of weak repulsion in isospin--2, and the presence of a narrow $\rho$ 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 $\sigma$ 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 $\sigma$ 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.