Quark-parton fragmentation functions

The distributions of ${\pi }^{+}$ and ${\pi }^{-}$ 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 ${D_u^{\pi }}^{+}\mathrm{}\left(z\right)\mathrm{}$ and ${D_d^{\pi }}^{+}\mathrm{}\left(z\right)\mathrm{}$. The $\frac{{\pi }^{+}}{{\pi }^{-}}$ 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.