$J/\psi$ Polarization at Hadron Colliders in Nonrelativistic QCD

With nonrelativistic QCD factorization, we present a full next-to-leading order computation of the polarization observable for $J/\psi$ production at hadron colliders including all important Fock states, i.e., ${}^{3}S_1^{[1,8]}$, ${}^{1}S_0^{[8]}$, and ${}^{3}P_J^{[8]}$. We find the ${}^{3}P_J^{[8]}$ channel contributes a positive longitudinal component and a negative transverse component, so the $J/\psi$ polarization puzzle may be understood as the transverse components canceling between the ${}^{3}S_1^{[8]}$ and ${}^{3}P_J^{[8]}$ channels, which results in mainly the unpolarized (even slightly longitudinally polarized) $J/\psi$. This may give a possible solution to the long-standing $J/\psi$ polarization puzzle. Predictions for $J/\psi$ polarization at the LHC are also presented.

Figure 1

NLO results for the polarization observable ${\lambda }_{\theta }$ of $J/\psi$ production at the Tevatron. The CDF experimental data are taken from Ref. 4.

Figure 2

The $p_T$ dependence of ${\lambda }_{\theta }$ for ${}^{3}S_1^{[1]}$, ${}^{1}S_0^{[8]}$, ${}^{3}S_1^{[8]}$, and ${}^{3}P_J^{[8]}$ channels with $\sqrt{S}=1.96\mathrm{TeV}$ and $|y_{J/\psi }|<0.6$. For the NLO ${}^{3}P_J^{[8]}$ channel, the curve corresponds to the value of $(d{\widehat{\sigma }}_{11}-d{\widehat{\sigma }}_{00})/|d{\widehat{\sigma }}_{11}+d{\widehat{\sigma }}_{00}|$.

Figure 3

Cross sections of $J/\psi$ production at the LHC with the LDMEs shown in Table . The darker bands (NLO Total I) correspond to the LDMEs in the first row of Table . The lighter bands (NLO Total II) correspond to the LDMEs in the second row [$⟨\mathcal{O}({}^{1}S_0^{[8]})⟩=0$ (upper bounds)] and third row [$⟨\mathcal{O}({}^{3}S_1^{[8]})⟩=⟨\mathcal{O}({}^{3}P_J^{[8]})⟩=0$ (lower bounds)] of Table . The ATLAS data are taken from Ref. 17, and the CMS data from Ref. 18.

Figure 4

NLO predictions of the $J/\psi$ polarization observable ${\lambda }_{\theta }$ at the LHC. The uncertainty is shown by large lighter bands when varying the CO LDME $⟨\mathcal{O}({}^{1}S_0^{[8]})⟩$. The bounds of ${\lambda }_{\theta }=0$ in the lighter bands correspond to CO LDMEs in the third row of Table , while the other bounds correspond to the second row of Table . The small darker bands are the predictions using the CO LDMEs in the first row of Table .