Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

S. Moch, A. Vogt

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.

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.

Paper Structure

This paper contains 29 equations, 1 figure, 1 table.

Figures (1)

  • Figure 1: Left: the LL, NLL, N$^2$LL and N$^3$LL results for the threshold resummation (\ref{['eq:cNres']}) of the SIA coefficient functions (\ref{['Cqexp']}) in $N$-space. Terms to order $\alpha_{\rm s}^{\,n\,}$ are included in $g_{\rm T,0}^{}$ for the N$^n$LL curves. Right: the convolutions of these results with a schematic large-$x$ shape for the quark fragmentation functions, using the standard 'minimal prescription' contour SoftGlue2 for the Mellin inversion.