One-loop Feynman integrals with Carlson hypergeometric functions

Abstract

In this paper, we present analytic results for scalar one-loop two-, three-, four-point Feynman integrals with complex internal masses. The calculations are considered in general space-time dimension D for two- and three-point functions and D =4 for four-point functions. The analytic results are expressed in terms of the Carlson hypergeometric functions (ℛ-functions) and valid for both real and complex internal masses.