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

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 Lüscher'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.

arXiv comment14 pages, 2 figures. v2: Minor updates to match version to appear in PRD

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Cited by in corpus (4)

• Towards a theory of hadron resonances
• Interactions of $\pi K$, $\pi \pi K$ and $KK\pi$ systems at maximal isospin from lattice QCD
• Subthreshold parameters of $\pi \pi$ scattering revisited
• The two-pion contribution to the hadronic vacuum polarization with staggered quarks