The two-loop vector form factor in the Sudakov limit
Bernd Jantzen, Vladimir A. Smirnov
TL;DR
The paper computes the two-loop electroweak corrections to the Abelian vector form factor in a spontaneously broken SU(2) gauge theory, focusing on the Sudakov regime where Q^2 >> M^2. It develops a comprehensive evaluation using expansion by regions and Mellin–Barnes representations to reduce complex tensor integrals to scalar ones across fermionic, Abelian, non-Abelian, and Mercedes–Benz diagrams, including renormalization effects. The resulting form factor is assembled to N$^3$LL accuracy and combined with evolution equations to yield NNLL/linear-log–level corrections to four-fermion neutral current amplitudes, with robust control of the Higgs-mass dependence and an estimated theoretical uncertainty at the per-mil level. The analysis demonstrates significant cancellations among higher-order logarithms and provides explicit analytic and numerical expressions for the dominant logarithmic terms, enabling precise predictions for high-energy collider processes.
Abstract
Recently two-loop electroweak corrections to the neutral current four-fermion processes at high energies have been presented. The basic ingredient of this calculation is the evaluation of the two-loop corrections to the Abelian vector form factor in a spontaneously broken SU(2) gauge model. Whereas the final result and the derivation of the four-fermion cross sections from evolution equations have been published earlier, the calculation of the form factor from the two-loop Feynman diagrams is presented for the first time in this paper. We describe in detail the individual contributions to the form factor and their calculation with the help of the expansion by regions method and Mellin-Barnes representations.