Discretization effects in finite-volume $2\to2$ scattering

TL;DR

This paper extends L"uscher's finite-volume scattering formalism to include non-zero lattice-spacing effects, providing a more accurate framework for analyzing lattice QCD data by accounting for discretization artifacts.

Contribution

It introduces a new quantization condition incorporating lattice-spacing effects into the scattering amplitude, using Symanzik Effective Theory and modified zeta functions.

Findings

New formalism explicitly includes discretization effects

Defines modified zeta functions for lattice artifacts

Requires additional angular-momentum indices for UV mixing

Abstract

We incorporate non-zero lattice-spacing effects into L\"uscher's finite-volume scattering formalism. The new quantization condition takes lattice energies as input and returns a version of the discretized scattering amplitude whose definition is transparent in the context of Symanzik Effective Theory. In contrast to the standard formalism, this approach uses single-hadron discretization effects to define modified versions of the finite-volume zeta functions. The new formalism requires two sets of angular-momentum indices, which encode the ultraviolet mixing of angular momentum states (due to the lattice spacing), in addition to the well-known infrared mixing (due to the finite volume).