One-loop three-point Feynman integrals with Appell $F_1$ hypergeometric functions

Abstract

New analytic formulas for one-loop three-point Feynman integrals in general space-time dimension ($d$) are presented in this paper. The calculations are performed at general configurations for internal masses and external momenta. The analytic results are expressed in terms of hypergeometric series ${}_2{F}_1$, ${}_3{F}_2$ for special cases and Appell $F_1$ for general cases. Furthermore, we cross-check our analytic results with other references which have carried out the integrals in several special cases.

22 pages, 1 figure