Analytic result for the one-loop scalar pentagon integral with massless propagators

Understand

The method of dimensional recurrences proposed by one of the authors [1,2] is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines.

• For the first time, an analytic result valid for arbitrary space-time dimension d and five arbitrary kinematic variables is presented.
• An explicit expression in terms of the Appell hypergeometric function F_3 and the Gauss hypergeometric function_2F_1, both admitting one-fold integral representations, is given.
• In the case when one kinematic variable vanishes, the integral reduces to a combination of Gauss hypergeometric functions_2F_1.