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arXiv · 2207.11750

A unified formulation of one-loop tensor integrals for finite volume effects

Ze-Rui Liang·De-Liang Yao
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Abstract

A unified formulation of one-loop tensor integrals is proposed for systematical calculations of finite volume corrections. It is shown that decomposition of the one-loop tensor integrals into a series of tensors accompanied by tensor coefficients is feasible, if a unit space-like four vector $n^\mu$, originating from the discretization effects at finite volume, is introduced. A generic formula has been derived for numerical computations of all the involved tensor coefficients. For the vanishing external three-momenta, we also investigate the feasibility of the conventional Passarino-Veltmann reduction of the tensor integrals in a finite volume. Our formulation can be easily used to realize the automation of the calculations of finite volume corrections to any interesting quantities at one-loop level. Besides, it provides finite volume result in a unique and concise form, which is suited for, e.g., carrying out precision determination of physical observable from modern lattice QCD data.

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Ze-Rui Liang, De-Liang Yao. 2022-07-24. A unified formulation of one-loop tensor integrals for finite volume effects. https://doi.org/10.1007/jhep12(2022)029

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