Abstract
Relativistic corrections to the color-singlet $J/\ensuremath{\psi}$ hadroproduction at the Tevatron and LHC are calculated up to $\mathcal{O}({v}^{2})$ in nonrelativistic QCD (NRQCD). The short-distance coefficients are obtained by matching full QCD with NRQCD results for the subprocess $g+g\ensuremath{\rightarrow}J/\ensuremath{\psi}+g$. The long-distance matrix elements are extracted from observed $J/\ensuremath{\psi}$ hadronic and leptonic decay widths up to $\mathcal{O}({v}^{2})$. Using the CTEQ6 parton distribution functions, we calculate the leading-order production cross sections and relativistic corrections for the process $p+\overline{p}(p)\ensuremath{\rightarrow}J/\ensuremath{\psi}+X$ at the Tevatron and LHC. We find that the enhancement of $\mathcal{O}({v}^{2})$ relativistic corrections to the cross sections over a wide range of large transverse momentum ${p}_{t}$ is negligible, only at a level of about 1%. This tiny effect is due to the smallness of the correction to short-distance coefficients and the suppression from long-distance matrix elements. These results indicate that relativistic corrections cannot help to resolve the large discrepancy between leading-order prediction and experimental data for $J/\ensuremath{\psi}$ production at the Tevatron.
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