Relativistic correction to color-octet J/ψ production at hadron colliders

The relativistic corrections to the color-octet J/psi hadroproduction at the Tevatron and LHC are calculated up to O(v(2)) in nonrelativistic QCD factorization frame. The short distance coefficients are obtained by matching full QCD with NRQCD results for the partonic subprocess g + g -> J/psi(S-1(0)[8], S-3(1)[8], P-3(J)[8]) + g, q + (q) over bar -> J/psi(S-1(0)[8], S-3(1)[8], P-3(J)[8]) + g and g + q((q) over bar) -> J/psi(S-1(0)[8], S-3(1)[8], P-3(J)[8]) + q((q) over bar). The short distance coefficient ratios of relativistic correction to leading order for color-octet states S-1(0)[8], S-3(1)[8], P-3(J)[8] at large p(T) are approximately -5/6, -11/6, and -31/30, respectively, for each subprocess, and it is 1/6 for color-singlet state S-3(1)[1]. If the higher order long distance matrix elements are estimated through velocity scaling rule with adopting v(2) = 0.23 and the lower order long distance matrix elements are fixed, the leading order cross sections of color-octet states are reduced by about a factor of 20-40% at large p(T) at both the Tevatron and the LHC. Comparing with QCD radiative corrections to color-octet states, relativistic correction is ignored along with p(T) increasing. Using long distance matrix elements extracted from the fit to J/psi production at the Tevatron, we can find the unpolarization cross sections of J/psi production at the LHC taking into account both QCD and relativistic corrections are changed by about 20-50% of that considering only QCD corrections. These results indicate that relativistic corrections may play an important role in J/psi production at the Tevatron and the LHC.