$J\mathrm{/}\psi$ production and polarization within a jet

We study the production and polarization of $J\mathrm{/}\psi$ mesons within a jet in proton-proton collisions at the LHC. We define the $J\mathrm{/}\psi$-jet fragmentation function as a ratio of differential jet cross sections with and without the reconstructed $J\mathrm{/}\psi$ in the jet. We demonstrate that this is a very useful observable to help explore the $J\mathrm{/}\psi$ production mechanism, and to differentiate between different NRQCD global fits based on inclusive $J\mathrm{/}\psi$ cross sections. Furthermore, we propose to measure the polarization of $J\mathrm{/}\psi$ mesons inside the jet, which can provide even more stringent constraints for the heavy quarkonium production mechanism.