Towards a formalism for $\pi\pi$ scattering from staggered lattice QCD

TL;DR

This paper develops methods to extract $c0c0$ scattering amplitudes from staggered lattice QCD data, addressing unitarity violations and taste-splitting effects inherent in the discretization.

Contribution

It introduces the first one-loop calculations using Rooted Staggered Chiral Perturbation Theory and generalizes the formalism to include taste-splitting and rooting effects.

Findings

Calculated one-loop $c0c0$ scattering amplitudes with staggered fermions.

Proposed a generalized formalism to incorporate taste-splitting and rooting effects.

Discussed prospects for applying the methods to other scattering channels.

Abstract

Scattering processes featuring the strong interactions can be studied using lattice QCD by means of the L\"uscher formalism. This approach relies on analyticity and unitarity of the $S$-matrix to relate infinite-volume scattering amplitudes to finite-volume energy levels. However, lattice QCD simulations employing rooted staggered fermions manifest unitarity violation as an $\mathcal{O}(a^2)$ lattice artifact. Moreover, the meson sector of this theory contains multiple non-mass-degenerate pions (due to the so-called taste splitting), which only reduce to the physical pion in the continuum limit. These features restrict the applicability of the L\"uscher formalism to staggered lattice data at non-zero lattice spacing. Hence, in this work, we discuss two complementary approaches to deal with the challenges of extracting $\pi\pi$ scattering amplitudes from lattice QCD with staggered quarks: (1) using the corresponding effective theory, Rooted Staggered Chiral Perturbation Theory, to calculate one-loop amplitudes for the first time. These amplitudes can be used to explicitly check the validity of the quantization condition. And (2) generalizing the formalism to incorporate taste-splitting as well as fourth-rooting effects. We focus on the simpler case of $\pi\pi$ scattering in the isospin-2 channel, and discuss prospects for other channels.