Relativistic correction to J/ψ and Υ pair production

The relativistic corrections to the productions of double J/ψ, double Υ, and J/ψ + Υ 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 + Υ process the ratio is -11/6 for the J/ψ color octet channel and -11/6 for the Υ 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 + Υ 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.