Validation of the finite-volume quantization condition 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 = 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.

Analytic expansions of multi-hadron finite-volume energies. I. Two-particle states

“…The question of how the value of E n (L) converges as a function of max has also recently been studied in ref. [42]. We comment in more detail on each of these points in the conclusion.…”