Reduction of $\epsilon$-expanded Feynman integrals

Abstract

Since Feynman integrals (FIs) at higher spacetime dimensions are free of infrared and collinear divergence--and their ultraviolet divergences can be systematically subtracted--this allows us to construct a wide range of locally finite Feynman integrals. Especially, we propose a method named $\bar{R}$-operation to subtract out ultraviolet divergences that at the same time preserves infrared and collinear safety of the original FI. By expressing these locally finite FIs in terms of master integrals and imposing constraints on their $\epsilon$-expanded forms, we reduce the $\epsilon$-expanded master integrals to a minimal basis. We provide an automated package to identify such constraints, offering a tool useful for high-order perturbative computations.