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arXiv · 2107.04430

Higher order finite volume quantization conditions for two spinless particles

Frank X. Lee·Andrei Alexandru·Ruairí Brett
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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.

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Frank X. Lee, Andrei Alexandru, Ruairí Brett. 2021-07-09. Higher order finite volume quantization conditions for two spinless particles. https://doi.org/10.1103/physrevd.105.054517

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