$\pi\pi$ scattering in partially-quenched twisted-mass chiral perturbation theory

TL;DR

This paper analyzes pion-pion scattering in partially-quenched twisted-mass lattice QCD, focusing on discretization and unitarity errors, and proposes methods to systematically subtract some errors while highlighting challenges in reducing others.

Contribution

It provides a detailed study of discretization and unitarity errors in pion-pion scattering within partially-quenched twisted-mass chiral perturbation theory, including systematic subtraction techniques.

Findings

Discretization errors can be as large as 100%.

Unitarity violation errors are estimated at around 25%.

Systematic subtraction of discretization errors is possible using $I=2$ scattering amplitude calculations.

Abstract

We study pion-pion scattering in partially-quenched twisted-mass lattice QCD using chiral perturbation theory. The specific partially-quenched setup corresponds to that used in numerical lattice QCD calculations of the $I=0$ scattering length. We study the discretization errors proportional to $a^2$, with $a$ the lattice spacing, and the errors that arise due to the use of L\"uscher's two-particle quantization condition in a theory that is not unitary. We argue that the former can be as large as $\sim 100\%$, but explain how they can be systematically subtracted using a calculation of the $I=2$ scattering amplitude in the same partially-quenched framework. We estimate the error from the violation of unitarity to be $\sim 25\%$, and argue that this error will be difficult to reduce in practice.