Polarized Heavy Quarkonium Production At S^1/2=510 GeV At RHIC

The problem of proton spin has been concerned by physicists for a long time.In the1980s the CERN muon collaboration collide high-energy polarized muon to proton,and found that the total spin of the quark in the proton did not equal to the spin of proton.Which was called“proton spin crisis”.Subsequent experiments found that the contribution of quarks to proton spin between 20%to 30%.In recent years,experiments at Relativistic Heavy Ion Collider?RHIC?have shown that,the contributions of the gluon in the proton are compared with that of the three quarks of the proton to the proton's total spin.While the remaining spin is provided by the orbital angular momentum of the quarks and gluons.In this paper,we calculate the double spin asymmetry through J/?hadron production process and compared the result with PHENIX experimental data at RHIC.Charmonium hadron production have three sub-process gluon-gluon fusion,gluon-quark and quark-antiquark?We use the NNPDF parton distribution function,centre-of-mass energy^?s=510 GeV,and select the two pseudo-range:1.2<?<2.2?|?|<0.6.We calcu-late the production cross section and the double spin asymmetric of charmonium.We found that in the the region of large transverse momentum region the³S₁^[8]channel has main con-tribution to J/?hadron production process at leading order.In the region of 3<p_T<20GeV,we get the value of double-spin asymmetric between 1.6×10^-4and 2.3×10^-3.This is different with the recent experimental data on PHENIX.The experimental data is slightly larger than the theoretical calculation We choose different long-distance matrix elements to calculate the double-spin asymmetries and get different value,the difference is about 20%.However,the experimental data at RHIC is limited and more data is needed to study the contribution of gluon to the spin of proton.