Quark "fragmentation" in a field-theoretic model of composite hadrons and $e^{+}{e}^{-}$ annihilation

We consider here a dynamical mechanism for the "fragmentation" of quarks with a field-theoretic model of composite hadrons with quarks as constituents, and with a phenomenological interaction of quarks mediated by vector mesons. In the present model the bounded nature of the transverse momentum of quark jets arises from the momentum localization of the wave functions of the hadrons. In the lowest-order contribution the kinematics becomes such that for the quark-antiquark pair, there is hardly any change in the four-momentum of one, whereas the four-momentum of the other gets shared between a quark and a meson with limited transverse momentum corresponding to the quark "fragmentation." As an example, the harmonic-oscillator wave functions for the mesons are used for the calculation of the quark-fragmentation functions which has been used throughout. Different signals for quark jets and for $e^{+}{e}^{-}$ annihilation are then examined. The model automatically includes a transverse-momentum distribution which is discussed. This transverse momentum depends on the scaling variable giving rise to an energy-dependent sea-gull effect. It appears that the harmonic-oscillator wave functions, though adequate for the gross features of quark-fragmentation processes with practically no free parameter, as expected, fail regarding some details. Also, the mechanism for the recombination of the final quark and antiquark after repeated fragmentation becomes relevant for the analysis of data at low energies, an illustration of which has been given. The possibility that the above phenomenological interaction may be that of quantum chromodynamics is noted.