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

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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 behavior 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 1 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.