Two-loop electroweak Sudakov logarithms for massive fermion scattering

TL;DR

This paper analyzes the dominant two-loop electroweak logarithmic corrections in high-energy fermion scattering, demonstrating factorization of photon singularities and the cancellation of symmetry-breaking effects, supporting resummation methods.

Contribution

It provides a diagrammatic derivation of leading and next-to-leading logarithmic terms for massive and massless fermion scattering at high energies, clarifying the role of symmetry breaking.

Findings

Photon soft and collinear singularities can be factorized into a QED-like term.

Symmetry-breaking effects cancel up to logarithms of the Z-W mass ratio.

Results support resummation approaches based on a symmetric electroweak theory.

Abstract

We study the asymptotic behaviour of two-loop electroweak corrections at energies Q >> M_W, where logarithms of the type ln(Q/M_W) become dominant. The calculation of the leading and next-to-leading logarithmic terms for massless and massive fermion-scattering processes is summarized. The derivations are performed diagrammatically within the spontaneously broken electroweak theory. We find that the soft and collinear singularities resulting from photons can be factorized into a QED-like term and that, up to logarithms of the Z-W mass ratio, the effects of symmetry breaking cancel. This result supports resummation prescriptions that are based on a symmetric SU(2)xU(1) theory matched with QED at the electroweak scale.