Dimensionally regulated one-loop box scalar integrals with massless internal lines

Abstract

Using the Feynman parameter method, we have calculated in an elegant manner a set of one$-$loop box scalar integrals with massless internal lines, but containing 0, 1, 2, or 3 external massive lines. To treat IR divergences (both soft and collinear), the dimensional regularization method has been employed. The results for these integrals, which appear in the process of evaluating one$-$loop $(N\ge 5)-$point integrals and in subdiagrams in QCD loop calculations, have been obtained for arbitrary values of the relevant kinematic variables and presented in a simple and compact form.