J/$\psi$ production measurements by the PHENIX experiment at RHIC

Measurements of J/$\psi$ production by the PHENIX experiment in p+p, d+Au, Cu+Cu and Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV are reviewed. The results show a suppression beyond what can be explained by cold nuclear matter effects in the most central Au+Au and to a lesser extent in Cu+Cu collisions. In addition, the suppression observed at mid rapidity in Au+Au is smaller than at forward rapidity, a tendency opposite to what is expected from the higher energy density at mid rapidity. Regeneration, a possible explanation, can be tested by measuring the elliptic flow parameter v$_2$ of J/$\psi$.


Introduction
J/ψ suppression is considered to be one of the key probes of the Quark Gluon Plasma (QGP) formation in heavy ion collisions. Color screening was proposed 1 as a mechanism leading to anomalous suppression beyond normal hadronic absorption if J/ψs are created in a deconfined medium. The CERN SPS experiments NA38, NA50 and NA60 were the first to investigate this phenomenon by measuring J/ψ suppression in a variety of colliding systems and energies. The results show a statistically significant anomalous suppression in central Pb+Pb 2 and In+In 3 collisions, that can be interpreted in terms of melting in the QGP.
The PHENIX experiment at RHIC has also measured the production of J/ψ in a variety of colliding systems, and provided further insights by exploring this phenomenon at higher energies. J/ψs are detected in PHENIX through their dielectron decay at mid rapidity (|y| < 0.35) and through their dimuon decay at forward rapidity (1.2 < |y| < 2.4). J/ψ suppression is characterized by a ratio called the nuclear modification factor, obtained by normalizing the J/ψ yields in heavy ion collisions (dN AB ) by the J/ψ yields in p+p collisions at the same energy (dN pp ) times the average number of binary inelastic nucleon-nucleon collisions (< N coll >): If the heavy ion collision is a superposition of independent N coll inelastic nucleon-nucleon collisions, R AB will be equal to unity, whereas it will be larger than one in case of enhancement and lower than one in case of suppression. At typical RHIC energies ( √ s N N = 19.6 -200 GeV), J/ψs are dominantly produced through gluon fusion. The J/ψ yield is therefore sensitive to gluon shadowing a . Part of the ground state charmonia yield also comes from feed down of excited states (ψ ′ and χ c ), and can contribute up to ∼ 40% to the total J/ψ yield. In subsequent stages of the collision involving heavy ions, there are a number of competing mechanisms that can enhance or suppress the J/ψ yield. The two major contributors to the suppression are absorption by nuclear fragments from incident nuclei, and an eventual melting in the QGP. Finally it is not impossible that a pair of uncorrelated c andc quarks that are close enough in phase space recombine to form a bound charmonium state and enhance the J/ψ yield.

Baseline and cold nuclear matter effect measurements
The differential cross section of J/ψ in p+p collisions as a function of rapidity measured by PHENIX is shown in Fig. 1 (left) 4 . In addition to providing normalization cross sections essential for the calculation of R AA as in Eq. 1, J/ψ measurements in p+p collisions constrain the poorly understood J/ψ production mechanism. In the same figure, predictions from various LO and NLO calculations are shown. The current precision does not discriminate between the models, but there is potential for improvement through better precision in cross section and additional information from J/ψ polarization measurements. Nuclear absorption and shadowing, collectively referred to as cold nuclear matter effects (CNM) can be constrained by measurements in proton (or light ion) on heavy ion collisions. In PHENIX this was performed in deuteron-gold collisions. The resulting suppression ratio R dAu is shown in Fig. 1 (right) 5 as a function of rapidity, where the positive rapidity coincides with the deuteron going direction. J/ψs detected in different rapidity regions probe specific gluon x 2 regions b . Forward rapidity corresponds to x 2 ∼ 0.002 -0.01 where the depletion due to shadowing is important whereas backward rapidity corresponds to x 2 ∼ 0.05 -0.2 where a slight enhancement due to anti-shadowing is expected. The rapidity dependence of R dA therefore reflects the gluon shadowing, whereas the global vertical scale is determined by the amount of normal absorption.
To quantitatively disentangle the shadowing component from the absorption component, a rapidity dependence using two shadowing schemes, EKS 6 and NDSG 7 was fitted to R dA leaving the overall vertical scale a free parameter to account for the absorption 5 . J/ψ absorption cross sections of 2.8 +1.7 −1.4 mb and 2.2 +1.6 −1.5 mb were obtained for EKS and NDSG schemes respectively. This is in agreement with the absorption cross section reported by the SPS of 4.2 ± 0.5 mb 8 but such a comparison should not be taken at face value because shadowing is not taken into account in the SPS c absorption cross sections evaluation.

Anomalous suppression in heavy ion systems
PHENIX has also measured J/ψ suppression in Au+Au 9 and Cu+Cu 10 collisions at √ s N N = 200 GeV. The J/ψ R AA in Au+Au collisions as a function of the number of participants N part , at forward and mid rapidity ranges is shown in Fig. 2 (left) 9 together with data points from NA38, NA50 and NA60 experiments. The R AA goes down to ∼ 0.2 for the most central Au+Au collisions (large N part ), and approaches unity for peripheral ones (small N part ). To see the extent of anomalous suppression, extrapolations of the CNM and shadowing constraints obtained from d+Au measurements were calculated using a model dependent method which assumes the above mentioned shadowing schemes as well as with a data driven method which has minimal model dependence. The result 5 from both methods is a statistically significant suppression beyond CNM extrapolation in the most central forward rapidity Au+Au collisions, less pronounced at mid rapidity Au+Au or in Cu+Cu collisions. The data show two features that contradict local density induced suppression models. The mid rapidity suppression is lower than the forward rapidity suppression (cf. Fig. 2 (left)), despite experimental evidence d that energy density is higher at mid rapidity than at forward rapidity. The same remark holds for the comparison between R AA at mid rapidity in PHENIX and R AA at SPS e (cf. Fig. 2 (left)). The two are in agreement within error bars, a surprising result considering that the energy density reached at RHIC is larger than the one reached at SPS. A number of explanations have been put forth, including sequential melting, where only ψ' and χ c are dissociated leading to a suppression of only the feed down component of the J/ψ yield 12 , and gluon saturation that leads to a lower charm quark yield at forward rapidity 13 .
c Taking into account nuclear PDF modification would increase the SPS absorption cross section, because the SPS rapidity corresponds to the anti-shadowing regime, requiring more absorption to account for the observed suppression.
d The rapidity density of charged particles which increases with the deposited energy peaks at mid rapidity 11 . e Care must be taken when comparing with SPS, because the CNM effects are not the same at the two energies.
A strong regeneration of J/ψ from uncorrelated c andc quarks is another good candidate to explain the tendency of R AA as a function of rapidity at RHIC. This is supported by the high charm quark yield measurements 14 (∼10 cc pairs are created in the most central Au+Au collisions). A number of model predictions that incorporate regeneration have been proposed 15 and all of them reproduce qualitatively the rapidity dependence of J/ψ R AA observed by PHENIX. However, important inputs to regeneration models such as the precise number of cc pairs available for recombination and the phase space conditions for recombination to take place are poorly constrained. It is thus very compelling to have a direct experimental check of regeneration. The J/ψ elliptic flow is one candidate. Elliptic flow refers to the azimuthal angle correlation of particle emission with respect to the reaction plane orientation f . It is quantified by the second Fourier coefficient v 2 of the azimuthal angle distribution of identified particles. The measured v 2 of electrons from D and B meson decays is remarkably high 16 . This is believed to originate from the elliptic flow of underlying charm and beauty quarks. J/ψs from recombination should inherit the charm quark flow, resulting in a higher v 2 than the case of direct production in hard collisions.
The first measurement of J/ψ v 2 at RHIC energy was performed by PHENIX at mid rapidity and is shown in Fig. 2 (right) as a function of transverse momentum. Predictions from models that assume various amounts of recombination from none to full coalescence at freeze out are plotted together. Data points are compatible within the error bars simultaneously with zero flow as well as with the model that predicts maximum flow. This result should therefore be seen as proof of principle of the feasibility of J/ψ v 2 measurements. There is still room for improvement using already existing data, but it is to be noted that a much larger sample will probably be needed to be able to distinguish between the different models.