Clustering and hadronization of quarks: A treatment of the low-pTproblem

The low-$p_T$ problem of hadron fragmentation is treated in the framework of the quark model. The basic mechanism of hadronization of quarks is recombination, which is formulated here on a firm basis. Clustering of quarks in a hadron is discussed in detail. The quark and antiquark joint distribution is derived systematically with incorporation of quantum-chromodynamics ideas wherever possible. Parameters describing the distribution are determined by fitting low-$Q^2$ electroproduction data. No free parameters are therefore involved in the calculation of the pion inclusive distribution in the fragmentation region. The result agrees well with data in both shape and normalization. The formalism can be applied to calculate inclusive distributions of all nucleon- and pion-initiated reactions, while for kaon-initiated reactions it can be used to extract from low-$p_T$ data the quark distributions in kaons.