Resummation of double logarithms in electroweak high energy processes

TL;DR

This work develops a unified, gauge-invariant framework to resum double logarithms in high-energy electroweak processes via an infrared evolution equation. It demonstrates exact exponential exponentiation of Sudakov-type DL corrections for both non-radiative and soft-emission amplitudes in unbroken and broken gauge theories, and extends the analysis to Regge-like DL in forward/backward kinematics. The approach provides explicit DL exponents for QED, non-Abelian theories, and the Standard Model, including region-mapped treatments across the electroweak scale and semi-inclusive cross sections. It also explores Regge kinematics with Mellin-transform techniques, revealing exact DL asymptotics and reggeization phenomena, and discusses implications for precision predictions and potential New Physics inputs. The framework connects to broader RG-like structures in high-energy QCD and EW processes and highlights methodological debates with recent competing approaches.

Abstract

At future linear $e^+e^-$ collider experiments in the TeV range, Sudakov double logarithms originating from massive boson exchange can lead to significant corrections to the cross sections of the observable processes. These effects are important for the high precision objectives of the Next Linear Collider. We use the infrared evolution equation, based on a gauge invariant dispersive method, to obtain double logarithmic asymptotics of scattering amplitudes and discuss how it can be applied, in the case of broken gauge symmetry, to the Standard Model of electroweak processes. We discuss the double logarithmic effects to both non-radiative processes and to processes accompanied by soft gauge boson emission. In all cases the Sudakov double logarithms are found to exponentiate. We also discuss double logarithmic effects of a non-Sudakov type which appear in Regge-like processes.

Figures (3)

• Figure 1: Feynman diagrams contributing to the infrared evolution equation (\ref{['eq:vem']}) for a process with $n$ external legs. In a general covariant gauge the virtual gluon with the smallest value of ${\hbox{\boldmath $k$}}_{\perp}$ is attached to different external lines. The inner scattering amplitude is assumed to be on the mass shell.
• Figure 2: Schematic Feynman diagrams contributing to the real gauge boson emission for a process with $n$ external legs. For $\hbox{\boldmath $k$}_\perp^2 \ll \mu^2$ the diagram on the left corresponds to the non-Abelian generalization of Gribov's theorem (\ref{['eq:rem']}). The diagram on the right leads to an additional term, (\ref{['eq:f1']}), in the kernel of the evolution equation in the case when $\hbox{\boldmath $k$}_\perp^2 \gg \mu^2$.
• Figure 3: Two-loop 'rainbow' Feynman diagrams contributing to DL corrections in an axial gauge. The photon contribution has DL corrections in both the regions $\mu^2 \ll M^2$ and $M^2 \ll \mu^2 \ll s$. Taken together with the $W$- and $Z$-contributions, it yields the exponentiation of the Sudakov DL terms in the electroweak theory. In the region $M^2 \ll \mu^2$, the spontaneously broken gauge symmetry is restored and omitting the photon contributions would lead to a non-gauge invariant result.