Two-loop electroweak angular-dependent logarithms at high energies

We present results on the two-loop leading and angular-dependent next-to-leading logarithmic virtual corrections to arbitrary processes at energies above the electroweak scale. In the `t Hooft-Feynman gauge the relevant Feynman diagrams involving soft and collinear gauge bosons \gamma, Z, W^\pm coupling to external legs are evaluated in the eikonal approximation in the region where all kinematical invariants are much larger than the electroweak scale. The logarithmic mass singularities are extracted from massive multi-scale loop integrals using the Sudakov method and alternatively the sector-decomposition method in the Feynman-parameter representation. The derivations are performed within the spontaneously broken phase of the electroweak theory, and the two-loop results are in agreement with the exponentiation prescriptions that have been proposed in the literature based on a symmetric SU(2) x U(1) theory matched with QED at the electroweak scale.