 
    
    
         
Another process which can constrain the gluon helicity distribution is 
open heavy flavor production.
The cross section calculation assuming the dominance of 
 reproduces the TEVATRON 
data [10] well 
( with a K-factor of 2 ). 
Then the asymmetry for the open heavy flavor production can be formulated 
as
  reproduces the TEVATRON 
data [10] well 
( with a K-factor of 2 ). 
Then the asymmetry for the open heavy flavor production can be formulated 
as 

 
where the partonic asymmetry  is calculated as a function of partonic 
center-of-mass energy [11].
 is calculated as a function of partonic 
center-of-mass energy [11].
Open heavy flavor production could be identified with PHENIX detector system by the detection of leptons with relatively higher transverse momenta from semi-leptonic decays of heavy mesons. Studies are underway to reduce the backgrounds with e.g. coincident detection of electrons in Central Arm.
Numerical calculations with PYTHIA suggest that this 
process identified with the muon with  GeV/c will be
sensitive to the product of
 GeV/c will be
sensitive to the product of  at
 at  and
 and 
 at
 at  . This process will provide an optional 
check of existing models on
. This process will provide an optional 
check of existing models on  , although further studies of
background rejection are necessary.
, although further studies of
background rejection are necessary.
The production of heavy quarkonium has been regarded as a good probe of the gluon helicity distribution [12,13,14,15]. The production mechanism should be studied more carefully to get a access to the helicity distributions [16].
 
 
 
 
    
    
         Naohito Saito