Two-loop electroweak next-to-leading logarithmic corrections to massless fermionic processes

Abstract

We consider two-loop leading and next-to-leading logarithmic virtual corrections to arbitrary processes with external massless fermions in the electroweak Standard Model at energies well above the electroweak scale. Using the sector-decomposition method and alternatively the strategy of regions we calculate the mass singularities that arise as logarithms of Q^2/MW^2, where Q is the energy scale of the considered process, and 1/\epsilon poles in D=4-2\epsilon dimensions, to one- and two-loop next-to-leading logarithmic accuracy. The derivations are performed within the complete electroweak theory with spontaneous symmetry breaking. Our results indicate a close analogy between the form of two-loop electroweak logarithmic corrections and the singular structure of scattering amplitudes in massless QCD. We find agreement with the resummation prescriptions that have been proposed in the literature based on a symmetric SU(2) \times U(1) theory matched with QED at the electroweak scale and provide new next-to-leading contributions proportional to ln(MZ^2/MW^2).