Connection between Distribution and Fragmentation Functions

Abstract

We show that the quark fragmentation function $D(z)$ and the quark distribution function $q(x)$ are connected in the $z \to 1$ limit by the approximate relation $D(z)/z \simeq q(2-1/z)$, where both quantities are in their physical regions. Predictions for proton production in inelastic $e^+ e^-$ annihilation, based on the new relation and standard parametrizations of quark distribution functions, are found to be compatible with the data.