New Insights into the Perturbative Structure of Electroweak Sudakov Logarithms: Breakdown of Conventional Exponentiation

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 $e^+e^- \to f \bar{f}$. In unbroken theories like QED and QCD the Sudakov form factor, resummed to all orders in perturbation theory, simply amounts to exponentiation of the one-loop corrections. However, based on an explicit two-loop calculation we find non-exponentiating terms, originating from the mass gap between the photon and the $Z$ boson in the neutral sector of the Standard Model.