QCD corrections to J/psi polarization of hadronproduction at Tevatron and LHC

The next to leading order (NLO) QCD corrections to J/psi polarization of hadronproduction at Tevatron and LHC are calculated. The results show that the J/psi polarization is extremely changed from more transversal polarization at leading order (LO) into more longitudinal polarization at NLO. Although it gives more longitudinal polarization than the recent experimental result on the J/psi polarization at Tevatron. It sheds light on the solution to the large discrepancy of J/psi polarization between theoretical predication and experimental measurement, and suggests that the next important step is to calculate the NLO correction for color octet state J/psi^{(8)} hadronproduction. Our calculations are performed in two ways where the polarizations are summed analytically or not, and they are checked with each other. It also gives a K factor for total cross section (ratio of NLO to LO) of about 2 and shows that the NLO corrections boost the J/psi production for about 2 order of magnitude in high transverse momentum p_t region of J/psi, which confirms the calculation by Campbell, Maltoni and Tramontano.