We study the production and polarization of J/ψ mesons within a jet in proton-proton collisions at the LHC. We define the J/ψ-jet fragmentation function as a ratio of differential jet cross sections with and without the reconstructed J/ψ in the jet. We demonstrate that this is a very useful observable to help explore the J/ψ production mechanism, and to differentiate between different NRQCD global fits based on inclusive J/ψ cross sections. Furthermore, we propose to measure the polarization of J/ψ mesons inside the jet, which can provide even more stringent constraints for the heavy quarkonium production mechanism.
Introduction.Understanding the J/ψ production mechanism is one of the most active and challenging subjects in strong interaction physics [1,2]. The most common approach to calculating the J/ψ production cross section in hadronic collisions is the non-relativistic QCD (NRQCD) factorization formalism [3]. In this approach, the heavy quark and anti-quark pair, QQ, is produced at short-distance which can be calculated perturbatively due to the large heavy quark masses. Such a QQ state will then hadronize into a physical J/ψ meson. This transition is non-perturbative, but it can be characterized through a set of universal NRQCD long-distance matrix elements (LDMEs). Global analyses of the world's data on J/ψ production with the next-to-leading order (NLO) calculations in powers of strong coupling constant α s have been performed by several groups [4][5][6][7][8]. Even though all these groups can describe the inclusive J/ψ production cross section, i.e., the p T spectrum, they have not been able to fully explain the polarization of high-p T heavy quarkonia produced at the Tevatron [9][10][11][12] and the LHC [13,14]. Despite of numerous attempts made in the past, the J/ψ polarization remains a puzzle.