Abstract
Based on the non-relativistic quantum chromodynamics factorization formalism, the polarization parameters $\lambda_{\theta\phi}$ and $\lambda_{\phi}$ of $J/\psi$ hadroproduction are analyzed in helicity frame and calculated at QCD next-to-leading order for the first time. For prompt $J/\psi$ production, we take into account the feeddown contributions from $\chi_{cJ}$ and $\psi(2S)$ decays. The theoretical predictions for the polarization parameters $\lambda_{\theta\phi}$ and $\lambda_{\phi}$ of $J/\psi$ are presented. With the theoretical results we have done the fit to the experimental measurements on yield and polarization for $J/\psi$ hadroproduction simultaneously, and found that the results are coincide with the experimental measurements at the LHC quite well.
Highlights
Nonrelativistic quantum chromodynamics (NRQCD) [1] is one of the most successful effective theories to describe the decay and production of heavy quarkonium
By separating the processes related to heavy quarkonium into shortdistance coefficients (SDCs) and the long-distance matrix elements (LDMEs), NRQCD allows one to organize perturbative calculations as double expansions in both the coupling constant αs and the heavy quark relative velocity v
The NLO corrections to color-singlet J=ψ hadroproduction have been investigated in Refs. [4,5], and its transverse momentum distribution was found to be enhanced by 2–3 orders of magnitude in the high-pt region and the J=ψ polarization changes from transverse to longitudinal at NLO [5]
Summary
Nonrelativistic quantum chromodynamics (NRQCD) [1] is one of the most successful effective theories to describe the decay and production of heavy quarkonium (for a review see, e.g., Refs. [2,3]). Based on the results from all of the theoretical studies, it is believed that a combined fit including pt distributions of J=ψ production rate and the polarization parameter λθ can be achived. This does not mean that the J=ψ polarization puzzle is solved: the parameters λθφ and λφ from experimental measurements still lack comparable theoretical predictions. We perform a theoretical analysis of the properties of the polarization parameters, and finish the calculation of λθφ and λφ for J=ψ and ψð2SÞ polarizations in the helicity frame based on NRQCD at QCD NLO. The last two pieces of the J=ψ polarization are successfully explained
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