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arXiv · 2110.03750

Higher order 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 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 formulae. We derive quantization conditions up to $\ell=5$ partial waves in both cubic and elongated geometries, and for states with zero and non-zero total momentum. All 45 quantization conditions we include here (22 in cubic box, 23 in elongated box) pass our cross-check test.

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Frank X. Lee, Andrei Alexandru, Ruairí Brett. 2021-10-07. Higher order quantization conditions for two spinless particles. https://doi.org/10.22323/1.396.0235

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