Higher order finite volume quantization conditions for two spinless particles

Lattice QCD calculations of scattering phase shifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed Luscher's formula for extracting these quantities at lowest order. As the calculations become more ambitious, higher-order relations are required. In this study we derive higher-order quantization conditions and introduce a method to transparently cross-check our results. This is an important step given the involved derivations of these formulas. We derive quantization conditions up to l = 5 partial waves in both cubic and elongated geometries, and for states with zero and nonzero total momentum. All 45 quantization conditions we include here (22 in cubic box, 23 in elongated box) pass our cross-check test.