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Within the framework of the constituent quark model, it is shown that thesingle hadron fragmentation function of a parton can be expressed as aconvolution of shower diquark or triquark distribution function and quarkrecombination probability, if the interference between amplitudes of quarkrecombination with different momenta is neglected. The recombinationprobability is determined by the hadron's wavefunction in the constituent quarkmodel. The shower diquark or triquark distribution functions of a fragmentingjet are defined in terms of overlapping matrices of constituent quarks andparton field operators. They are similar in form to dihadron or trihadronfragmentation functions in terms of parton operator and hadron states.Extending the formalism to the field theory at finite temperature, weautomatically derive contributions to the effective single hadron fragmentationfunction from the recombination of shower and thermal constituent quarks. Suchcontributions involve single or diquark distribution functions which in turncan be related to diquark or triquark distribution functions via sum rules. Wealso derive QCD evolution equations for quark distribution functions that inturn determine the evolution of the effective jet fragmentation functions in athermal medium.Comment: 23 pages in RevTex with 8 postscript figure

Modified fragmentation function from quark recombination