Laurent series expansion of a class of massive scalar one-loop integrals up to O(ε2) in terms of multiple polylogarithms

Abstract

In a recent paper we have presented results for a set of massive scalar one-loop master integrals needed in the NNLO parton model description of the hadroproduction of heavy flavors. The one-loop integrals were evaluated in n=4−2ε dimension and the results were presented in terms of a Laurent series expansion up to O(ε2). We found that some of the ε2 coefficients contain a new class of functions which we termed the L functions. The L functions are defined in terms of one-dimensional integrals involving products of logarithm and dilogarithm functions. In this paper we derive a complete set of algebraic relations that allow one to convert the L functions of our previous approach to a sum of classical and multiple polylogarithms. Using these results we are now able to present the ε2 coefficients of the one-loop master integrals in terms of classical and multiple polylogarithms.