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

Understand

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.