Higher order finite volume quantization conditions for two spinless particles

TL;DR

This paper derives and validates higher-order finite volume quantization conditions for two spinless particles in lattice QCD, enabling more precise extraction of scattering parameters beyond the lowest order.

Contribution

It presents a comprehensive validation of quantization conditions up to =5 partial waves in various geometries and momentum states, confirming their accuracy for lattice QCD calculations.

Findings

Perfect agreement for all 45 quantization conditions tested

Validated conditions up to =5 partial waves in multiple geometries

Supports higher-order analysis in lattice QCD scattering studies

Abstract

Lattice QCD calculations of scattering phaseshifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed L\"uscher's formula for extracting these quantities at lowest order. As the calculations become more ambitious, higher-order relations are required. In this study we present a way to validate the higher-order quantization conditions. This is an important step given the involved derivations of these formulae. We derive and validate quantization conditions up to $\ell=5$ partial waves in both cubic and elongated geometries, and for states zero and non-zero total momentum. For all 45 quantization conditions we considered (22 in cubic box, 23 in elongated box) we find perfect agreement.