Dimensionally Regulated Pentagon Integrals?

We present methods for evaluating the Feynman parameter integrals associated with the pentagon diagram in 4 − 2 dimensions, along with explicit results for the integrals with all masses vanishing or with one non-vanishing external mass. The scalar pentagon integral can be expressed as a linear combination of box integrals, up to O( ) corrections, a result which is the dimensionallyregulated version of a D = 4 result of Melrose, and of van Neerven and Vermaseren. We obtain and solve differential equations for various dimensionally-regulated box integrals with massless internal lines, which appear in one-loop n-point calculations in QCD. We give a procedure for constructing the tensor pentagon integrals needed in gauge theory, again through O( ). Research supported in part by the Department of Energy under contract DE-AC03-76SF00515 (SLAC), by the Texas National Research Laboratory Commission under grant FCFY9202 (Z.B.), and by the Direction des Sciences de la Matière of the Commissariat à l’Energie Atomique of France (Saclay).