Heavy quark fragmentation models

Abstract

We discuss the process of quark fragmentation placing a particular emphasise on the change of the fragmentation spectrum due to kinematical effects when light quarks are replaced by heavy ones. After investigating different methods of data extraction, we compile the data on heavy quark fragmentation from various collaborations. These data are compared with various models of heavy quark fragmentation for charm and bottom quark fragmentation. In our comparison we first separate the fragmentation models into two categories in accordance with their behaviour at large values of the fragmentation parameter. Models that are in agreement with the dimensional counting rules have a softer behaviour than some popular models which axe not in agreement. This point is crucial in the case of heavier quarks. However, due to the large errors in experimental data, it is hard to make a firm judgement about the merits of these models. We study the spin properties of heavy quark fragmentation and obtain the fragmentation functions for different polarisation states. The fragmentation function for an unpolarised state is then taken to be a combination of the longitudinal and the transverse fragmentation functions. We also give a model in which the transverse momentum of the constituent quarks is taken into account. The effect of the increase in the constituent transverse momentum is to soften the fragmentation by a limited amount, since there is a small probabability that the constituents of a bound state will have a large relative momentum. Finally we give a rather detailed Monte Carlo study of the effect of different fragmentation models on the momentum spectrum of heavy mesons, and the final state leptons resulting from heavy quark production in hadron colliders at CERN and FNAL. We find that the effect on the lepton spectrum is more significant.