Generalized threshold resummation in inclusive DIS and semi-inclusive electron-positron annihilation

Abstract

We present analytic all-order results for the highest three threshold logarithms of the space-like and time-like off-diagonal splitting functions and the corresponding coefficient functions for inclusive deep-inelastic scattering (DIS) and semi-inclusive e^+ e^- annihilation. All these results, obtained through an order-by-order analysis of the structure of the corresponding unfactorized quantities in dimensional regularization, can be expressed in terms of the Bernoulli functions introduced by one of us and leading-logarithmic soft-gluon exponentials. The resulting numerical corrections are small for the splitting functions but large for the coefficient functions. In both cases more terms in the threshold expansion need to be determined in order to arrive at quantitatively reliable results.

20 pages, LaTeX, 3 figures (.eps). DESY address until 31 August 2013

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Cited by in corpus (10)

• On quartic colour factors in splitting functions and the gluon cusp anomalous dimension
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• High-Energy Limit of Mass-Suppressed Amplitudes in Gauge Theories
• The Soft Quark Sudakov
• Approximate NNLO QCD corrections to semi-inclusive DIS
• Light Quark Mediated Higgs Boson Threshold Production in the Next-to-Leading Logarithmic Approximation
• Fragmentation Functions Beyond Fixed Order Accuracy
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• On factorisation schemes for the electron parton distribution functions in QED
• Perturbative evolution: a different approach at small x