Master integrals with one massive propagator for the two-loop electroweak form factor

We compute the master integrals containing one massive propagator entering the two-loop electroweak form factor, i.e., the process f (f) over bar --> X, where f (f) over bar is an on-shell massless fermion pair and X is a singlet particle under SU(2)(L) x U(1)(Y), such as a virtual gluon or an hypothetical Z'. The method used is that of the differential equation in the evolution variable x = -s/m(2) where s is the c.m. energy squared and m is the mass of the W or Z bosons (assumed to be degenerate). The 1/epsilon poles and the finite parts are computed exactly in terms of one-dimensional harmonic polylogarithms of the variable x, H((w) over bar; x), with c = 2 - D/2 and D the space-time dimension. We present large-momentum expansions of the master integrals, i.e., expansions for \s\ much greater than m(2) which are relevant for the study of infrared properties of the Standard Model. We also derive small-momentum expansions of the master integrals, i.e., expansions in the region \s\ much less than m(2), related to the threshold behaviour of the form factor (soft probe). Comparison with previous results in the literature is performed finding complete agreement. (C) 2003 Elsevier B.V. All rights reserved.