References - Bogoliubov Laboratory of Theoretical Physics - JINR

that NLO QCD corrections can be factorized and canceled out on the level of asymmetry,
is not true.
Therefore it is important to estimate the order of the NLO QCD effects in the COM-
PASS experiment analysis. In this paper corrections to PGF process are only considered.
As it was said in the Introduction the place where QCD approximation is used is the
analyzing power, aLL. The measured asymmetry is related to the gluon polarization as
follows:
A exp S
= PbPtfaLL
S + B
Δg
g
+ Abgd
where Pb,Pt and f are beam polarization, target polarization and dilution factor, respectively.
A combinatorial background asymmetry, A bgd , is extracted together with the signal
(D 0 meson reconstructed in the event). S/(S + B) is a signal purity and Δg/g is a gluon
polarization, integrated over kinematically accessible region by COMPASS measurement.
For more details the reader is referred to [2].
There are two types of the NLO QCD corrections to PGF process: virtual and soft
ones, where kinematics is the same as for LO PGF process (two into two particle kinematics)
and the corrections with extra gluon emission (two into three particle kinematics).
To guarantee the proper cancellation of the infrared and soft parts the virtual and real
corrections should be added together (after integration over unobserved gluon in the final
state) to obtain the so-called reduced cross section, free of any divergences [4]. COMPASS
is using polarized muon beam what means that virtuality of the photon, Q 2 never reach
the photoproduction limit. The smallest value of Q 2 allowed by kinematics is related to
the muon mass. Nevertheless the calculation of the aLL in the photoproduction limit is a
very good approximation and can be used in the COMPASS analysis. The collection of
the formulae for polarized and unpolarized cross sections for the finite Q 2 for PGF process
in LO QCD approximation can be found in [6]. The NLO QCD corrections are partially
listed in [4, 5] while the missing, finite parts are available by request [7]. To compute
analyzing power aLL event-by-event basis the knowledge of kinematics on of the parton
level is needed. The measurement does not allow to reconstruct kinematical variables on
the partonic level as the only one produced, charmed D 0 meson is reconstructed in the
event at COMPASS. Therefore the exact kinematics of the event have to be simulated
with the help of MC technique. 2 In the next section the MC approach for aLL calculation
in LO QCD approximation is discussed and the extension of the method including NLO
QCD corrections is proposed.
3 Monte-Carlo approach for the calculation of the
analyzing power
As the COMPASS analysis is performed in LO QCD approximation LO MC generator
AROMA [8] is used to calculate analyzing power, aLL. The COMPASS apparatus is
simulated using GEANT package and produced output is in the form of the real data.
2 In the ideal case where two charmed particles produced in the final states are reconstructed the LO
QCD PGF process could be calculated using measured kinematics of charmed mesons. If unobserved
gluons are radiated (NLO QCD corrections to PGF) the kinematics on the partonic level cannot be
reconstructed from reconstructed heavy system.
231
(1)