Excitation function Analysis for Charmonium Production in Heavy-Ion Collisions

Both color screening and regeneration are hot medium effects on charmonium production in heavy ion collisions. While they affect in an opposite way the charmonium yield, their competition in transverse dynamics bring sensitivity to the ratio of averaged transverse momentum square for charmonium, which thus can reveal more nature of the QCD medium created from the collisions. We make an excitation analysis based on transport approach to illustrate such a picuture. Since 1986 and firstly in light of color screening argument for the initial proposing [1], J/Ψ has long been considered as an effective probe to the hot and dense QCD matter created from heavy ion collisions. A suppression for their production in A+A compared with in p+p collisions is motivated and extensively studied both in experiment and theory. Along with more released experimental data, it’s realized that apart from color screening, many other medium effects come into play during the collision evolution, which make the picture for charmonium production complicated. Before any hot medium effects acting, the cold nuclear matter also impacts the J/Ψ production through nuclear absorption, Cronin effect and nuclear shadowing effect. After entering the created partonic medium, the color screening will alter the binding inside the bound state. Different suppression mechanism availably works here at different temperature domain. When the temperature is higher than the charmonium dissociation temperature, no bound states survive based on spectral analysis where no peak signal is left due to color screening, thus they will melt into the medium. Below this melting threshold, the partons inside the medium can break-up the quarkonium bound states through collisions, like the gluon dissociation and quasi-free dissociation, which respectively correspond to Singlet-to-Octet transition and Landau damping in terms of EFT (effective field theory). Another important concept that arises here is regeneration [2], thus the recombination to bound state from those uncorrelated charm and anticharm quark pairs being in favor of their more abundant hard production along with increasing collision energy. Through regeneration, the hot medium effects on heavy quarks would also leave a mark on heavy quarkonium production. Actually from the theoretical point of view it’s still not clear enough about the quarkonium evolution inside QGP. Like, which suppression mechnism works dominantly? Which is the proper potential, free energy F or internal energy U, for quarkonium in medium? Also, in a rapidly cooling QGP medium, a potential analysis might not possess enough validity since a bound state would hardly always lie in a fixed eigenstate of the evolving Hamiltonian describing in medium quarkonium. Even further, if a seperate treatment for heavy quarkonia evolution taking the 15th International Conference on Strangeness in Quark Matter (SQM2015) IOP Publishing Journal of Physics: Conference Series 668 (2016) 012100 doi:10.1088/1742-6596/668/1/012100 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 QGP medium only as background really works is somehow questionable, as recently pointed out in Ref. [3]: according to the associated large entropy for heavy quarkonium in medium observed from Lattice QCD study (especially near Tc) [4], the coupling between medium constituent and quarkonium interquarks is stronger even than the binding between the interquarks inside the bound state. This makes it unjustifiable to treat the bound state as a color neutral entity to be influenced by the surrounding medium, since actually each of their interquarks are strongly entangled with the medium to be consistent with the Lattice results [4]. Nevertheless, in the present proceeding we provide a transport model based analysis for the medium effects on charmonium production, and we especially focus on their excitation function to illustrate the picture given by kinetic approach. We now start with a brief introduction to the transport model we adopted in the analysis. Since a charmonia is heavy and can hardly reach equilibrium with the surronding medium, its phase space distribution function, fΨ(x,p, t), is governed by the following Boltzmann-type transport equation [5], ∂fΨ ∂t + vΨ · ∇fΨ = −αΨfΨ + βΨ, (1) where the loss and gain terms α and β are the main hot medium effects describing dissociation and regeneration, while the cold matter effects are reflected in the initial condition. Taking gluon dissociation as the dominant suppression mechanism, α is the momentum integration of the dissociation cross section multiplied by the thermal gluon distribution. The color screening induced melting is also considered, where the melting temperature Td is evaluated from potential approach. Using detailed balance the regeneration cross section can be got from the gluon dissociation cross section. By convoluting it with the in-medium charm quarks’s distribution we obtain the continuous regeneration rate β(x,pΨ, t). Considering the experimentally observed large quench factor [6] and anisotropic flow [7] of open charm mesons, we here approximate the charm quarks’ distribution to be kinetically thermalizaed which is a strong interaction limit. On the level of kinetic approach, the medium information is then encoded in the loss and gain term through the distribution function, thus the appeared local temperature T (x, t) and fluid velocity uμ(x, t) those being controled by ideal hydrodynamics in the present model analysis. Using the above transport model, we have studied the nuclear modification factor RAA and transverse momentum distribution and also the anisotropic flow for charmonium production [5]. Along with increasing collision energy, the medium becomes hotter and we naturally expect stronger J/Ψ suppression to be observed. However, it’s found that in mid-rapidity the suppression magnitude of J/Ψ at RHIC is similar to that at SPS and smaller than that at LHC. To make the advantages protruded in explaining these phenomenon from transport model, here we turn to analyze their collision energy dependence thus the excitation function. As the collision becomes more violent, more charm quark pairs are produced through hard process, the regeneration component gradually dominate the charmonium production. The fraction of the regenerated J/Ψs, gAA = N reg AA/NAA, calculated from our transport model, is shown in the left of Fig. 1 as a function of collision energy, where N reg AA is J/Ψ yield from regeneration. At lower energy collisions like at SPS, only very few charm quarks are produced initially, then almost no regeneration happens. At RHIC, the initial production is still dominant but the regeneration becomes equally important especially in mid-rapidity. At LHC, the final charmonium yield is dominated by regeneration in both mid and forward rapidiy. The lower fraction in forward rapidity merely reflects the rapidity distribution of charm quarks. Since the transverse motion in heavy ion collisions which is developed during the dynamical evolution of the system can directly reflect the multiple scattering and also parton density in the medium, as has been well documented in light quarks sector [8], for charmonium production, the transverse momentum distribution also can reveal more information about their evolution and be more sensitive to the medium effects. We propose the following new defined nuclear 15th International Conference on Strangeness in Quark Matter (SQM2015) IOP Publishing Journal of Physics: Conference Series 668 (2016) 012100 doi:10.1088/1742-6596/668/1/012100