New Insights into the Perturbative Structure of Electroweak Sudakov Logarithms
W. Beenakker, A. Werthenbach
TL;DR
The paper tackles large electroweak Sudakov corrections at TeV energies by developing a Coulomb-gauge framework that localizes these logs to external-fermion self-energies. It performs one- and two-loop calculations for the process $e^+e^- \to f\bar{f}$, clarifying how the photon–$Z$ mass gap affects exponentiation. The main result is that the two-loop Sudakov correction factor exponentiates, i.e., $\delta^{(2)}_f = \tfrac{1}{2}(\delta^{(1)}_f)^2$, with cancellations among various diagram topologies ensuring consistency with unbroken theories at high energy. This supports the use of Sudakov resummation in SM predictions and extends the understanding to real-emission processes as well. The work provides a concrete, gauge-consistent method to quantify EW Sudakov logs for precision phenomenology at future colliders.
Abstract
To match the expected experimental precision at future linear colliders, improved theoretical predictions beyond next-to-leading order are required. At the anticipated energy scale of sqrt(s)=1 TeV the electroweak virtual corrections are strongly enhanced by collinear-soft Sudakov logarithms of the form log^2(s/M^2), with M being the generic mass scale of the W and Z bosons. By choosing an appropriate gauge, we have developed a formalism to calculate such corrections for arbitrary electroweak processes. As an example we consider in this letter the process e^+e^- --> f fbar and study the perturbative structure of the electroweak Sudakov logarithms by means of an explicit two-loop calculation. In this way we investigate how the Standard Model, with its mass gap between the photon and Z boson in the neutral sector, compares to unbroken theories like QED and QCD. In contrast to what is known for unbroken theories we find that the Sudakov logarithms are not exclusively given by the so-called rainbow diagrams, owing to the mass gap and the charged-current interactions. In spite of this, we nevertheless observe that the two-loop corrections are consistent with an exponentiation of the one-loop corrections. In this sense the Standard Model behaves like an unbroken theory at high energies.