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.

The conventional definition of the running coupling α MS (µ) in quantum chromodynamics is based on a solution to the renormalization group equations which treats quarks as either completely massless at a renormalization scale µ above their thresholds or infinitely massive at a scale below them. The coupling is thus nonanalytic at these thresholds. In this paper we present an analytic extension of α MS (µ) which incorporates the finite-mass quark threshold effects into the running of the coupling. This is achieved by using a commensurate scale relation to connect α MS (µ) to the physical α V scheme at specific scales, thus naturally including finite quark masses. The analyticextension inherits the exact analyticity of the α V scheme and matches the conventional M S scheme far above and below mass thresholds. Furthermore just as in α V scheme, there is no renormalization scale ambiguity, since the position of the physical mass thresholds is unambiguous.

High energy photon colliders (γγ,γe) are based on e-e-linear colliders where high energy photons are produced using Compton scattering of laser light on high energy electrons just before the interaction point. This paper is a part of the Technical Design Report of the linear collider TESLA.1Physics program, possible parameters and some technical aspects of the photon collider at TESLA are discussed.