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arXiv · 2408.07062

Discretization effects in finite-volume $2\to2$ scattering

Maxwell T. Hansen·Toby Peterken
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Abstract

We incorporate non-zero lattice-spacing effects into L\"uscher's finite-volume scattering formalism. The new quantization condition takes lattice energies as input and returns a version of the discretized scattering amplitude whose definition is transparent in the context of Symanzik Effective Theory. In contrast to the standard formalism, this approach uses single-hadron discretization effects to define modified versions of the finite-volume zeta functions. The new formalism requires two sets of angular-momentum indices, which encode the ultraviolet mixing of angular momentum states (due to the lattice spacing), in addition to the well-known infrared mixing (due to the finite volume).

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Maxwell T. Hansen, Toby Peterken. 2024-08-13. Discretization effects in finite-volume $2\to2$ scattering. https://arxiv.org/abs/2408.07062

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