Modified Fragmentation Function from Quark Recombination

Within the framework of the constituent quark model, it isshown that the single hadron fragmentation function of a parton can beexpressed as a convolution of shower diquark or triquark distributionfunction and quark recombination probability, if the interference betweenamplitudes of quark recombination with different momenta is neglected.Therecombination probability is determined by the hadron's wavefunction inthe constituent quark model. The shower diquark or triquark distributionfunctions of a fragmenting jet are defined in terms of overlappingmatrices of constituent quarks and parton field operators. They aresimilar in form to dihadron or trihadron fragmentation functions in termsof parton operator and hadron states. Extending the formalism to thefield theory at finite temperature, we automatically derive contributionsto the effective single hadron fragmentation function from therecombination of shower and thermal constituent quarks. Suchcontributions involve single or diquark distribution functions which inturn can be related to diquark or triquark distribution functions via sumrules. We also derive QCD evolution equations for quark distributionfunctions that in turn determine the evolution of the effective jetfragmentation functions in a thermal medium