Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor—planar case Original Research Article

We compute the master integrals containing 2 and 3 massive propagators entering the planar amplitudes of the 2-loop electroweak form factor. By this me mean the process image, where image is an on-shell massless fermion pair and X is a singlet under the electroweak gauge group image. This work is a continuation of our previous evaluation of master integrals containing at most 1 massive propagator. The masses of the W, Z and Higgs bosons are assumed to be degenerate. The image poles and the finite parts are computed exactly in terms of a new class of 1-dimensional harmonic polylogarithms of the variable image, with image, D the space–time dimension and s the center-of-mass energy squared. Since thresholds and pseudothresholds in image do appear in addition to the old ones in image, an extension of the basis function set involving complex constants and radicals is introduced, together with a set of recursion equations to reduce integrals with semi-integer powers. It is shown that the basic properties of the harmonic polylogarithms are maintained by the generalization. We derive small-momentum expansions image of all the 6-denominator amplitudes. Comparison with previous results in the literature is performed finding complete agreement.