Abstract
The relativistic corrections to the productions of double J/ψ, double , and J/ψ + at the Tevatron and the LHC were investigated within the frame of non-relativistic QCD. The ratios of short distance coefficients between relativistic correction and leading order result for color singlet and color octet states in large p T limit are approximately −1, −11/3, respectively, for pair production. And for J/ψ + process the ratio is for the J/ψ color octet channel and for the color octet channel. The K factors of next-to-leading order in v 2 for color singlet and color octet double J/ψ production are 0.77 and 0.16 at large p T region with adopting v 2 = 0.23. The contribution from the color-octet channel is depressed by the relativistic correction heavily and is negligible at the most p T region comparing with the color-singlet contribution for the J/ψ pair production. So we conclude the J/ψ pair production is no longer a nice platform to check the color-octet mechanism. On the other hand, relativistic corrections show limited to affect the coloroctet cross section for the J/ψ + process and this process can still be a probe to check color-octet mechanism. Also our results show that the single parton scattering model may be enough to explain the LHCb data for the J/ψ pair production.