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arXiv · 2111.13975

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

Zachary T. Draper·Stephen R. Sharpe
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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.

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Zachary T. Draper, Stephen R. Sharpe. 2021-11-27. $\pi\pi$ scattering in partially-quenched twisted-mass chiral perturbation theory. https://doi.org/10.1103/physrevd.105.034508

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