Quantum numbers and quark-parton fragmentation models

Cascade models for quark and hadron fragmentation are displayed. These models illustrate many of the predictions of the parton model for inclusive reactions. Multiplicities are constructed to go as $C_h\ln \left(\frac{s}{m^2}\right)$ in hadron-hadron collisions and as $C_{e^{+}{e}^{-}}\ln \left(\frac{Q^2}{m^2}\right)$ in $e^{+}{e}^{-}$ annihilation, implying a multiplicity in leptoproduction of $C_{e^{+}{e}^{-}}\ln \left(\frac{Q^2}{m^2}\right)+C_h\ln (\omega -1)$. However, Feynman's conjecture that quark quantum numbers are retained, on the average, in the parton fragmentation region is not necessarily true. This was first noted by Farrar and Rosner in a model with meson emission only. The conjecture (as a general principle) is shown to fail as well with baryon emission included if multiplicities grow no faster than logarithmically. In cascade models a weaker version of Feynman's conjecture is found to be true in general and this version is accessible experimentally. Also, triality is found to play a significant role, suggesting that $C_{e^{+}{e}^{-}}$ need not equal $C_h$. Other implications of cascade models are also explored for hadron-hadron collisions, $e^{+}{e}^{-}$ annihilation, and leptoproduction, for both small and large transverse momentum of the produced particles.