DIMENSIONALLY-REGULATED PENTAGON INTEGRALS

We present methods for evaluating the Feynman parameter integrals asso ciated with the pentagon diagram in 4-2epsilon dimensions, along with explicit results for the integrals with all masses vanishing or with o ne non-vanishing external mass. The scalar pentagon integral can be ex pressed as a linear combination of box integrals, up to O(epsilon) cor rections, a result which is the dimensionally-regulated version of a D = 4 result of Melrose, and of van Neerven and Vermaseren. We obtain a nd solve differential equations for various dimensionally-regulated bo x integrals with massless internal lines, which appear in one-loop n-p oint calculations in QCD. We give a procedure for constructing the ten sor pentagon integrals needed in gauge theory, again through O(epsilon 0).