$J/\psi$ Production and Polarization within a Jet

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

Figure 1

The jet fragmentation function $F^{J/\psi }(z_h,p_T)$ as a function of $z_h$ at $\sqrt{s}=7\mathrm{TeV}$. Jets are reconstructed using the anti-${\mathrm{k}}_{\mathrm{T}}$ algorithm with $R=0.6$ and $|\eta |<1.2$. The numbers in the square brackets correspond to different jet transverse momentum $p_T$ bins.

Figure 2

The polarization of $J/\psi$ mesons in the jet (${\lambda }_F$) plotted as a function of $z_h$. The jet $p_T$ is integrated from 50 to 100 GeV.

Figure 3

The contributions to ${\lambda }_F$ from different channels: ${{}^{3}S}_1^{[1]}$, ${{}^{1}S}_0^{[8]}$, ${{}^{3}S}_1^{[8]}$, ${{}^{3}P}_J^{[8]}$ are plotted as a function of $z_h$. The NRQCD LDMEs are taken from Butenschoen et al. [4].