Impact of $η_c$ hadroproduction data on charmonium production and polarization within NRQCD framework

Abstract

With the recent LHCb data on $η_c$ production and based on heavy quark spin symmetry, we obtain the long-distance matrix elements for both $η_c$ and $J/ψ$ productions, among which, the color-singlet one for $η_c$ 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 $η_c$ and $J/ψ$ hadroproduction measurements. Our predictions on $J/ψ$ polarization are in good agreement with the LHCb data and pass through the two sets of CDF measurements in medium $p_t$ region. Considering all the possible uncertainties carefully, we obtained quite narrow bands of the $J/ψ$ polarization curves.