Treatment of the QCD coupling in high energy processes

The treatment of the running QCD coupling in evolution equations is discussed. It is shown that the use of the virtuality of ladder (vertical) partons as the scale for QCD coupling in every rung of ladder graphs is an approximation that holds for DIS at large x only. On the contrary, in the small x region the coupling depends on the virtuality of s -channel (horizontal) gluons. This observation leads to different results for the Regge-like processes and DIS structure functions at small x.Comment: RevTeX 6 pages, 6 figures epsf.st

QCD running coupling effects for the non-singlet structure function at small x

A generalization of the leading-order DGLAP evolution at small x is performed for the non-singlet structure function by resumming the leading-order DGLAP anomalous dimension to all orders in the QCD coupling. Explicit expressions are obtained for the non-singlet structure function of the deep inelastic scattering, taking into account both the double-logarithmic and the single-logarithmic contributions, including the running alpha_s effects. It is shown that when these contributions are included, the asymptotic small-x behaviour is power-like, with an exponent of about 0.4.Comment: Latex, 20 pages, 7 figure

Intercepts of the non-singlet structure functions

Infrared evolution equations for small-$x$ behaviour of the non-singlet structure functions $f_1^{NS}$ and $g_1^{NS}$ are obtained and solved in the next-to-leading approximation, to all orders in $\alpha_s$, and including running $\alpha_s$ effects. The intercepts of these structure functions, i.e. the exponents of the power-like small-$x$ behaviour, are calculated. A detailed comparison with the leading logarithmic approximation (LLA) and DGLAP is made. We explain why the LLA predictions for the small-$x$ dependence of the structure functions may be more reliable than the prediction for the $Q^2$ dependence in the range of $Q^2$ explored at HERA.Comment: 26 pages, LaTeX, 5 Postscript figure

Resummation of double logarithms in electroweak high energy processes

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.Comment: 26 pages, 3 figures, Latex2

How to Determine the Pion Cloud of the Constituent Quark

We calculate the differential cross section for semi-inclusive pion production in electron proton reactions using a model where the physical quark fluctuates with some probability to quark plus pion. The kinematic regions for a determination of this `pion cloud' are evaluated.Comment: 28 pages, including 10 figures; gzipped, uuencoded postscrip