Electroweak double logarithms in inclusive observables for a generic initial state

Abstract

High energy observables are characterized by large electroweak radiative corrections of infrared origin; double logarithms are present even for inclusive cross sections, thus violating the Bloch–Nordsieck theorem. This effect, related to the initial states carrying non-Abelian isospin charges, is here investigated for any inclusive cross section in the SU(2)⊗ U(1) symmetric limit, that is appropriate for energies much higher than the weak scale. We develop a general formalism allowing to calculate the all order double log resummed cross sections once the hard (tree level) ones are known. The relevant cases of fermion–fermion, fermion–boson and boson–boson scattering are discussed.