Lattice determination of $I= 0$ and 2 $\pi\pi$ scattering phase shifts with a physical pion mass

TL;DR

This study calculates $s$-wave $$ and 2 $$ $ ext{-}$ $$ scattering phase shifts using lattice QCD with a physical pion mass, providing insights into $$ and 2 $$ interactions relevant for CP violation studies.

Contribution

It presents a novel lattice QCD calculation of $$ and 2 $$ $ ext{-}$ scattering phase shifts at physical pion mass, including multiple momenta and systematic error analysis.

Findings

Phase shifts determined for multiple total momenta.

Results support previous CP violation studies.

Systematic errors carefully analyzed.

Abstract

Phase shifts for $s$-wave $\pi\pi$ scattering in both the $I=0$ and $I=2$ channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of $32^3\times 64$. These results support our recent study of direct CP violation in $K\to\pi\pi$ decay \cite{Abbott:2020hxn}, improving our earlier 2015 calculation \cite{Bai:2015nea}. The phase shifts are determined for both stationary and moving $\pi\pi$ systems, at three ($I=0$) and four ($I=2$) different total momenta. We implement several $\pi\pi$ interpolating operators including a scalar bilinear "$\sigma$" operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem (GEVP) method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.