QCD analysis of the semi - inclusive DIS data with modified Jacobi polynomial expansion method

It is proposed the modification of the Jacobi polynomial expansion method (MJEM) which is based on the application of the truncated moments instead of the full ones. This allows to reconstruct with a high precision the local quark helicity distributions even for the narrow accessible for measurement Bjorken x region using as an input only four first moments extracted from the data in NLO QCD. It is also proposed the variational procedure allowing to reconstruct the distributions outside the accessible Bjorken x region using the distributions obtained with MJEM in the accessible region. The numerical calculations encourage one that the proposed variational procedure could be applied for estimation of the full first (especially important) quark moments. The extraction of the quark helicity distributions is one of the main tasks of the semi-inclusive deep inelastic scattering (SIDIS) experiments with the polarized beam and target. At the same time it was argued [1] that to obtain the reliable distributions at comparatively low average Q 2 available to the modern SIDIS experiments 4 , the leading order (LO) analysis is not sufficient and next to leading order analysis (NLO) is necessary. In ref. [3] the procedure allowing the direct extraction from the SIDIS data of the first moments of the quark helicity distributions in NLO QCD was proposed. However, in spite of the special importance of the first moments 5 , it is certainly very desirable to have the procedure of reconstruction in NLO QCD of the polarized densities themselves. However, it is extremely difficult to ask to extract the local in Bjorken x distributions directly, because of the double convolution product entering the NLO QCD expressions for semi-inclusive asymmetries (see [3] and references therein). Fortunately, operating just as in ref. [3], one can directly extract not only the first moments, but the Mellin moments of any required order. Let us stress that though one can do it for any types of SIDIS asymmetries, in this paper we will apply the method with respect to particular example of pion difference asymmetries 6. The simple extension of the procedure proposed in ref. [3] gives for the n-th moments ∆ n q ≡