Hadronization in Polarized Semi-Inclusive DIS: the Question of Independent Fragmentation

The new formalism for description of (un)polarized semi-inclusive DIS at moderate energies is developed. Hadron production is modeled as a product of distribution functions and hadronization functions (HFs) weighted by the hard scattering cross sections, as it is done in the {\tt LEPTO} event generator. The correct treatment of polarization effects shows that description of semi-inclusive DIS within this formalism includes a new nonperturbative input -- {\it polarized} HFs. It is shown that this approach does not correspond to the commonly adopted one with the independent quark fragmentation. The purity method used by the HERMES collaboration mixes up the two approaches and ignores the contributions from polarized HFs. This method cannot be considered a precise tool for the extraction of polarized quark distributions from measured SIDIS asymmetries.