With the recent LHCb data on ${\eta }_c$ production and based on heavy quark spin symmetry, we obtain the long-distance matrix elements for both ${\eta }_c$ and $J/\psi$ productions, among which, the color-singlet one for ${\eta }_c$ is obtained directly by the fit of experiment for the first time. Using our long-distance matrix elements, we can provide good description of the ${\eta }_c$ and $J/\psi$ hadroproduction measurements. Our predictions on $J/\psi$ polarization are in good agreement with the LHCb data, explain most of the CMS data, and pass through the two sets of CDF measurements in the medium $p_t$ region. Considering all the possible uncertainties carefully, we obtained quite narrow bands of the $J/\psi$ polarization curves.

• Received 2 December 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.092006