Resummation of small- x double logarithms in QCD: semi-inclusive electron-positron annihilation
Abstract
We have derived the coefficients of the highest three1/ x-enhanced small- x logarithms of all timelike splitting functions and the coefficient functions for the transverse fragmentation function in one-particle inclusive e + e - annihilation at (in principle) all orders in massless perturbative QCD. For the longitudinal fragmentation function we present the respective two highest contributions. These results have been obtained from KLN-related decompositions of the unfactorized fragmentation functions in dimensional regularization and their structure imposed by the mass-factorization theorem. The resummation is found to completely remove the huge small- x spikes present in the fixed-order results, allowing for stable results down to very small values of the momentum fraction and scaling variable x. Our calculations can be extended to (at least) the corresponding α s n ln2 n-ℓ x contributions to the above quantities and their counterparts in deep-inelastic scattering.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- October 2011
- DOI:
- 10.1007/JHEP10(2011)025
- arXiv:
- arXiv:1108.2993
- Bibcode:
- 2011JHEP...10..025V
- Keywords:
-
- Jets;
- Renormalization Group;
- QCD;
- High Energy Physics - Phenomenology
- E-Print:
- 27 pages, LaTeX, 6 eps-figures