Analytic result for the one-loop scalar pentagon integral with massless propagators
Abstract
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. For the case when one scalar invariant is large compared to the others, the asymptotic values of the integral in terms of Gauss hypergeometric functions_2F_1 are presented in d = 2 - 2 epsilon, 4 - 2 epsilon, and 6 - 2 epsilon dimensions. For multi-Regge kinematics, the asymptotic value of the integral in d = 4 - 2 epsilon dimensions is given in terms of the Appell function F_3 and the Gauss hypergeometric function_2F_1.
Cite
@article{arxiv.1001.3848,
title = {Analytic result for the one-loop scalar pentagon integral with massless propagators},
author = {Bernd A. Kniehl and Oleg V. Tarasov},
journal= {arXiv preprint arXiv:1001.3848},
year = {2015}
}
Comments
21 pages, 1 figure; discussion extended, several equations, appendix and references added, references updated; accepted for publication in Nucl. Phys. B