Next-to-leading mass singularities in two-loop electroweak singlet form factors

TL;DR

The paper computes one- and two-loop virtual electroweak corrections to massless chiral-fermion form factors coupled to a singlet gauge boson in the high-energy regime $s \gg M_W^2$, using sector decomposition to extract mass singularities in $D=4-2\epsilon$ up to next-to-leading logarithms. It shows that the two-loop leading and next-to-leading mass singularities can be organized in a Catani-like formula, generalizing the massless QCD structure to the electroweak theory and highlighting the interplay between gauge mixing, mass gaps, and symmetry breaking. The results demonstrate exponentiation of the one-loop LL/NLL terms plus additional contributions proportional to the one-loop beta-function coefficients, and reveal that mass-gap effects largely reduce to QED-like corrections that must be subtracted at the appropriate scale. The analysis also clarifies how proper treatment of $A$–$Z$ mixing and the $Z$–$W$ mass gap, together with the vacuum expectation value, ensures cancellations that preserve infrared behavior, providing a robust framework for high-energy EW resummations with potential applications to precision collider phenomenology.

Abstract

We consider virtual electroweak corrections to the form factors for massless chiral fermions coupling to an SU(2)xU(1) singlet gauge boson in the asymptotic region $s\gg M_W^2$, where the invariant mass $s$ of the external gauge boson is much higher than the weak-boson mass scale. Using the sector-decomposition method we compute mass singularities, which arise as logarithms of $s/M_W^2$ and $1/ε$ poles in $D=4-2ε$ dimensions, to one- and two-loop next-to-leading logarithmic accuracy. In this approximation we include all contributions of order $α^l ε^{k} log^{j+k}(s/M_W^2)$, with $l=1,2$ and $j=2l,2l-1$. We find that the electroweak two-loop leading- and next-to-leading-logarithmic mass singularities can be written in a form that corresponds to a generalization of Catani's formula for massless QCD.