Integration‐by‐parts identities in FDR

Abstract

Four‐Dimensionally Regularized/Renormalized (FDR) integrals play an increasingly important role in perturbative loop calculations. Thanks to them, loop computations can be performed directly in four dimensions and with no ultraviolet counterterms. In this paper I prove that integration‐by‐parts (IBP) identities based on simple integrand differentiation can be used to find relations among multi‐loop FDR integrals. Since algorithms based on IBP are widely applied beyond one loop, this result represents a decisive step forward towards the use of the FDR approach in multi‐loop calculations.