Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD

TL;DR

This paper presents a lattice QCD study of two-pion scattering at physical pion mass in isospin channels 0 and 2, employing all-to-all propagators and GEVP to extract phase shifts and excited states, with results consistent with theoretical predictions.

Contribution

It introduces the use of all-to-all propagators and GEVP in lattice QCD to analyze two-pion scattering at physical masses, including excited states, which was challenging before.

Findings

Phase shifts agree with Roy Equation and chiral perturbation theory.

Successful extraction of two-pion excited states at physical mass.

Method enables future studies of K→ππ decay processes.

Abstract

A study of two-pion scattering for the isospin channels, $I=0$ and $I=2$, using lattice QCD is presented. M\"obius domain wall fermions on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions are used for the lattice computations which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of $L=4.63$ and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states, two pions with a non-zero relative momentum as well as two pions at rest. Our results for phase shifts for both $I=0$ and $I=2$ channels are consistent with and the Roy Equation and chiral perturbation theory, though at this preliminary stage our errors for $I=0$ are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying $K\to\pi\pi$ decay, on physical-mass ensembles using GEVP.