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

TL;DR

This paper derives all-order analytic results for the dominant threshold logarithms in inclusive DIS and semi-inclusive e+e- annihilation, improving understanding of soft-gluon effects in these processes.

Contribution

It introduces a unified approach to threshold resummation using Bernoulli functions, providing new all-order expressions for splitting and coefficient functions.

Findings

Small corrections for splitting functions; large for coefficient functions.

More threshold expansion terms are needed for precise predictions.

Results enhance theoretical precision in QCD calculations.

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.