Violation of Universality in Spin-Dependent Fragmentation

The fragmentation of an unpolarized quark into a transversely polarized spin-1/2 particle is studied in the framework of a simple model which, in particular, describes the gluon exchange incorporated in the gauge link of the fragmentation function. By comparing the transverse single spin asymmetry in $e^+ e^-$ annihilation and semi-inclusive deep-inelastic scattering it is shown that the universality of the corresponding fragmentation function is violated. The main reason for this result lies in the fact that a certain on-shell intermediate state, which contributes to the spin asymmetry in $e^+ e^-$ annihilation, has no counterpart in deep-inelastic scattering.