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

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

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