Fragmentation functions from semi-inclusive DIS pion production and implications for the polarized parton densities

By combining recent HERMES data on semi-inclusive DIS ${\pi }^{\pm }$-production with the singlet fragmentation function $D_{\mathrm{\Sigma }}^{{\pi }^{+}}$, which is well determined from $e^{+}{e}^{-}$ data, we are able to extract, for the first time, the flavoured fragmentation functions $D_u^{{\pi }^{+}}$, $D_d^{{\pi }^{+}}$ and $D_s^{{\pi }^{+}}$ without making any assumptions about favoured and unfavoured transitions. Whereas $D_u^{{\pi }^{+}}$ and $D_d^{{\pi }^{+}}$ are very well determined, the accuracy of $D_s^{{\pi }^{+}}$ is limited by the uncertainty in evolving $D_{\mathrm{\Sigma }}^{{\pi }^{+}}$ from the $Z^0$ pole down to the SIDIS scale of a few $(GeV{)}^2$. We discuss how the precision on $D_s^{{\pi }^{+}}$ could be improved. Knowledge of the $D_{q=u,d,s}^{{\pi }^{+}}$ will permit the extraction of the polarized parton densities from future polarized SIDIS asymmetry measurements. We study the precision that can be expected in such an extraction.