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

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.

Version accepted for publication in JHEP; 38 pages, 5 figures, 2 tables

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Cited by in corpus (3)

• One-loop analysis of the interactions between doubly charmed baryons and Nambu-Goldstone bosons
• Chiral extrapolation of the doubly charmed baryons magnetic properties
• The axial-vector form factor of the nucleon in a finite box