Quark and gluon decay functions in quantum chromodynamics and recombination model

Inclusive longitudinal-momentum distributions of pions in jets initiated by quarks and gluons are determined in perturbative quantum chromodynamics and the recombination model. The quark and antiquark joint distributions in jets are first calculated in the leading-order approximation at high $Q^2$. Gluons in the jets are completely converted to quark pairs. From the overall distribution, $q\overline{q}$ pairs with definite quantum numbers then recombine to form pions. The recombination function for the process is well determined in the valon model. No adjustable parameters are involved in these calculations, and no data at low $Q^2$ are used as phenomenological input. The result for the quark decay functions can be compared with data on $e^{+}{e}^{-}$ annihilation, and the agreement is very good in both shape and normalization. Predictions for the gluon decay functions are presented, but they cannot yet be checked by experiments. The $x$ and $Q^2$ depesndences of both type of decay functions have been parametrized in simple form suitable for use in theoretical and experimental applications.