  Within the framework of the constituent quark model, it is shown that the
single hadron fragmentation function of a parton can be expressed as a
convolution of shower diquark or triquark distribution function and quark
recombination probability, if the interference between amplitudes of quark
recombination with different momenta is neglected. The recombination
probability is determined by the hadron's wavefunction in the constituent quark
model. The shower diquark or triquark distribution functions of a fragmenting
jet are defined in terms of overlapping matrices of constituent quarks and
parton field operators. They are similar in form to dihadron or trihadron
fragmentation functions in terms of parton operator and hadron states.
Extending the formalism to the field theory at finite temperature, we
automatically derive contributions to the effective single hadron fragmentation
function from the recombination of shower and thermal constituent quarks. Such
contributions involve single or diquark distribution functions which in turn
can be related to diquark or triquark distribution functions via sum rules. We
also derive QCD evolution equations for quark distribution functions that in
turn determine the evolution of the effective jet fragmentation functions in a
thermal medium.
