Higher-order threshold resummation for semi-inclusive e+e- annihilation

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 Lis to extend the soft-gluon resummation for the fragmentation functions by two orders to the next-to-next-to-next-to-leading logarithmic ((NLL)-L-3) 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 ((NLL)-L-2.) order in the exponentiation, the numerical effect of the (NLL)-L-3 contributions turns Out to be negligible at LEP energies. (C) 2009 Elsevier B.V. All rights reserved.