Higher order finite volume quantization conditions for two spinless particles

Abstract

Lattice QCD calculations of scattering phaseshifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed Lüscher'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.

Comments: 55 pages, 9 figures, 45 tables, 1 supplement. This update matches the published version in PRD