The one-loop pentagon to higher orders in epsilon
Abstract
We compute the one-loop scalar massless pentagon integral I56-2 eps in D=6-2 dimensions in the limit of multi-Regge kinematics. This integral first contributes to the parity-odd part of the one-loop N=4 five-point MHV amplitude m5(1) at O(eps). In the high energy limit defined, the pentagon integral reduces to double sums or equivalently two-fold Mellin-Barnes integrals. By determining the O(eps) contribution to I56-2 eps, one therefore gains knowledge of m5(1) through to O(eps2) which is necessary for studies of the iterative structure of N=4 SYM amplitudes beyond one-loop. One immediate application is the extraction of the one-loop gluon-production vertex through to O(eps2) and the iterative construction of the two-loop gluon-production vertex through to finite terms which is described in a companion paper. The analytic methods we have used for evaluating the pentagon integral in the high energy limit may also be applied to the hexagon integral and may ultimately give information on the form of the remainder function.