Logarithmic expansion of electroweak corrections to four-fermion processes in the TeV region

TL;DR

This paper analyzes the high-energy behavior of electroweak corrections in four-fermion processes within the Standard Model, highlighting the dominance of Sudakov-type logarithmic terms at TeV energies and proposing an effective parametrization for future collider predictions.

Contribution

It provides a detailed analysis of electroweak corrections at high energies and introduces a simple effective parametrization for observables in the TeV region.

Findings

Logarithmic electroweak corrections dominate at TeV energies.

Sudakov-type logarithms grow with energy, reaching 10% at 1 TeV.

Proposed an effective parametrization valid for future collider energies.

Abstract

Starting from a theoretical representation of the electroweak component of four-fermion neutral current processes that uses as theoretical input the experimental measurements at the Z peak, we consider the asymptotic high energy behaviour in the Standard Model at one loop of those gauge-invariant combinations of self-energies, vertices and boxes that contribute all the different observables. We find that the logarithmic contribution due to the renormalization group running of the various couplings is numerically overwhelmed by single and double logarithmic terms of purely electroweak (Sudakov-type) origin, whose separate relative effects grow with energy, reaching the 10% size at about one TeV. We then propose a simple "effective" parametrization that aims at describing the various observables in the TeV region, and discuss its validity both beyond and below 1 TeV, in particular in the expected energy range of future linear electron-positron (LC) and muon-muon colliders.