The Leading Power Regge Asymptotic Behaviour of Dimensionally Regularized Massless On-Shell Planar Triple Box

The leading power asymptotic behaviour of the dimensionally regularized massless on-shell planar triple box diagram in the Regge limit t/s → 0 is analytically evaluated. E-mail: [email protected] Systematical analytical evaluation of two-loop Feynman diagrams with four external lines within dimensional regularization [1] began three years ago. In the pure massless case with all end-points on-shell, i.e. pi = 0, i = 1, 2, 3, 4, the problem of analytical evaluation of two-loop four-point diagrams in expansion in ǫ = (4− d)/2, where d is the space-time dimension, has been completely solved in [2, 3, 4, 5, 6, 7]. The corresponding analytical algorithms have been successfully applied to the evaluation of two-loop virtual corrections to various scattering processes [8] in the zero-mass approximation. In the case of massless two-loop four-point diagrams with one leg off-shell the problem of the evaluation has been solved in [9, 10], with subsequent applications [11] to the process ee → 3jets. (See [12] for recent reviews of the present status of NNLO calculations. See [13] for a brief review of results on the analytical evaluation of various double-box Feynman integrals and the corresponding methods of evaluation.) For another three-scale calculational problem, where all four legs are on-shell and there is a non-zero internal mass, a first analytical result was obtained in [14] for the scalar master double box. The purpose of this paper is to turn attention to three-loop on-shell massless four-point diagrams. As a first step, the leading power asymptotic behaviour of the dimensionally regularized massless on-shell planar triple box diagram shown in Fig. 1 in the Regge limit t/s → 0 will be analytically evaluated. This calculation will p1 p3 p2 p4 1 2 3 4 7 5 6