References - Bogoliubov Laboratory of Theoretical Physics - JINR

Finally the COMPASS reconstruction program CORAL is used on the simulated events.
This procedure allows to take into account all effects related to real data taking as acceptance,
efficiency of the detector, reconstruction procedure efficiency etc, see [1]. The
simulated event sample after all selection criteria applied [2] are used for computing aLL
event-by-event basis. The calculated analyzing powers, aLL, are then parameterized by
set of kinematical quantities like Q 2 or pT of D 0 meson, accessible in the direct measurement
for every event. A multi-dimensional Neural Network (NN) approach for the
parameterization is used what allows to treat correctly correlations between kinematical
variables [9]. After training on the MC sample the Neural Network is run on the real
data computing aLL for every real event. Finally aLL is used to construct the statistical
weight.
In the NLO QCD approximation however the problem with Phase Space for gluon
emission processes appears. LO QCD approach in MC is not able to reproduce correctly
kinematics of the events unless the so-called Parton Shower is switched on in the generation.
The PS concept has been developed to improve the real data description by MC and
allows to simulate multi-gluon emissions in some approximation [8]. Energy of all gluons
emitted in the PS in the event can be considered as a limit of integration over unobserved
gluons associated with the NLO QCD real corrections to PGF process. This procedure
allows to calculate polarized and unpolarized cross sections in the LO and NLO QCD
approximation, where real gluon emissions are integrated out over energy allowed by PS
emissions in the event. The calculation of the analyzing power is then straightforward.
Two important problems, however, related to the method using PS concept appears.
First, the CMS energy of the simulated event can be calculated using final charmanticharm
pair, or using initial photon-gluon system. In the LO QCD approximation
there is no difference due to energy-momentum conservation but it is not longer true in
the case of PS switched on. Performing integration over unobserved gluons with CMS
energy of the event determined on the partonic level by heavy quark system the gluon
distribution should be included into integrand function because of the fact that xg, the
momentum fraction carried by initial gluon is related to the energy of the real gluon emitted
in the PS. It required the assumption about gluon distribution what is not convenient
in the ”direct” gluon polarization measurement. Therefore the CMS energy of the event
on the partonic level should be defined by initial photon-gluon system. This case is even
more similar to the real data analysis where only one charmed meson is reconstructed.
The integrand contains only calculable partonic cross sections while gluon distribution is
factorized as in the LO QCD. In the calculations presented in this paper both possibilities
have been considered to check the potential effect related to this inconsistency in the
treatment of the partonic kinematics and the three different polarized gluon distribution
models were used.
The second problem is related to the fact that PS concept is not equivalent to MC in
the NLO QCD approximation. There is still a big discussion how to use LO MC with PS to
simulate effectively correct NLO processes but the subject is difficult and the satisfactory
solutions exist only in some cases [10]. To test the correctness of the proposed method
based on the LO MC with PS for PGF process for charm muoproduction the kinematics
of the events with real gluon emission has been generated using uniformly distributed
kinematical variables and then the events were weighted by the cross section calculated
in the NLO QCD approximation (weighted MC method). This method guarantees that
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