Quark-Parton Fragmentation Functions

The distributions of ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ produced in the current fragmentation region are analysed in the framework of the quark-parton model. Motivated by experimental results on deep-inelastic neutrino scattering, we have neglected antiquark (and strange quark) contributions whenever the Bjorken scaling variable $x$ is not close to zero. This approximation enables us to extract the quark fragmentation functions ${{D}_{u}^{\ensuremath{\pi}}}^{+}(z)$ and ${{D}_{d}^{\ensuremath{\pi}}}^{+}(z)$. The $\frac{{\ensuremath{\pi}}^{+}}{{\ensuremath{\pi}}^{\ensuremath{-}}}$ asymmetry is then calculated as a function of ${Q}^{2}$. This tests the factorization properties of the quark-parton model as a whole range of $x$ values is involved. Agreement with existing data is found. Predictions for future experiments are also presented.