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

TL;DR

This paper advances the precision of soft-gluon resummation in semi-inclusive e^+e^- annihilation to N^3LL accuracy, enabling more accurate theoretical predictions in perturbative QCD.

Contribution

It derives third-order soft and virtual contributions, extending resummation accuracy and revealing the equivalence of resummation exponents with deep-inelastic scattering.

Findings

N^3LL resummation is achieved for semi-inclusive e^+e^- annihilation.

The resummation exponent matches that of deep-inelastic scattering.

Numerical impact of N^3LL terms is negligible at LEP energies.

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.