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

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