  Method of polarized semi-inclusive deep inelastic scattering (SIDIS) data
analysis in the next to leading order (NLO) QCD is developed. Within the method
one first directly extracts in NLO few first truncated (available to
measurement) Mellin moments of the quark helicity distributions. Second, using
these moments as an input to the proposed modification of the Jacobi polynomial
expansion method (MJEM), one eventually reconstructs the local quark helicity
distributions themselves. All numerical tests demonstrate that MJEM allows us
to reproduce with the high precision the input local distributions even inside
the narrow Bjorken $x$ region accessible for experiment. It is of importance
that only four first input moments are sufficient to achieve a good quality of
reconstruction. The application of the method to the simulated SIDIS data on
the pion production is considered. The obtained results encourage one that the
proposed NLO method can be successfully applied to the SIDIS data analysis. The
analysis of HERMES data on pion production is performed. To this end the pion
difference asymmetries are constructed from the measured by HERMES standard
semi-inclusive spin asymmetries. The LO results of the valence distribution
reconstruction are in a good accordance with the respective leading order SMC
and HERMES results, while the NLO results are in agreement with the existing
NLO parametrizations on these quantities.
