Global analysis of light-hadron fragmentation functions with small-x improvement through soft-gluon logarithm resummation

• Applicant: Professor Dr. Bernd A. Kniehl
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2004 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5434013

Fragmentation functions (FF's) for charged light hadrons have been well determined over large and intermediate values of the hadronic momentum fraction z, where z is the variable of integration in the convolution of FF's with coefficient functions, by fitting to a wealth of experimental data. However, small x data, where x is the experimentally set kinematic variable equal to the lower bound on z in the voncolution, have always been excluded since the current fixed-order calculation of the hard part is believed to be too inaccurate in this region due to singularities that arise as x vanishes, and so FF's are not well understood at small z. However, it is possible to resum these singularities via the modified leading logarithmic approximation (MLLA), and so improve the accuracy of the hard part at smaller x. The aim of this project is to extend current analyses of FF's over a wider range of z. This will also provide a test of the MLLA in the perturbative region without using the assumptions of the local parton-hadron duality (LPHD) model as is normally the case. From the conceptual point of view, a new theoretical framework needs to be elaborated that properly combines the MLLA, appropriate for the small x region, with the conventional evolution by Dokshitser, Gribov, Lipatov, Altarelli and Parisi (DGLAP), valid at higher x, such that all leading and next-to-leading of x and energy are simultaneously resummed to all orders.

• DFG Programme: Research Grants