Higher-order threshold resummation for semi-inclusive e^+e^- annihilation
Abstract
The complete soft-enhanced and virtual-gluon contributions are derived for the quark coefficient functions in semi-inclusive e^+e^- annihilation to the third order in massless perturbative QCD. These terms enable us to extend the soft-gluon resummation for the fragmentation functions by two orders to the next-to-next-to-next-to-leading logarithmic (N^3LL) accuracy. The resummation exponent is found to be the same as for the structure functions in inclusive deep-inelastic scattering. This finding, together with known results on the higher-order quark form factor, facilitates the determination of all soft and virtual contributions of the fourth-order difference of the coefficient functions for these two processes. Unlike the previous (N^2LL) order in the exponentiation, the numerical effect of the N^3LL contributions turns out to be negligible at LEP energies.
Keywords
Cite
@article{arxiv.0908.2746,
title = {Higher-order threshold resummation for semi-inclusive e^+e^- annihilation},
author = {S. Moch and A. Vogt},
journal= {arXiv preprint arXiv:0908.2746},
year = {2009}
}
Comments
13 pages, LaTeX, 1 eps-figure