First Measurement of the J/psi Azimuthal Anisotropy in PHENIX at Forward Rapidity in Au+Au Collisions at sqrt s(NN) = 200 GeV

The PHENIX experiment has shown that J/psis are suppressed in central Au+Au collisions at a center of mass energy per nucleon-nucleon collision sqrt s(NN) = 200 GeV, and that the suppression is larger at forward than at mid-rapidity. Part of this difference may be explained by cold nuclear matter effects but the most central collisions suggest that regeneration mechanisms could be at play. In 2007, PHENIX collected almost four times more Au+Au collisions at this energy than used for previous published results. Moreover, the addition of a new reaction plane detector allows a much better analysis of the J/psi behavior in the azimuthal plane. Since a large elliptic flow has been measured for open charm, measuring J/psi azimuthal anisotropies may give a hint if J/psi are recombined in the expanding matter. First PHENIX results of J/psi elliptic flow as a function of transverse momentum at forward rapidity are presented in this article. The analysis is detailed and results are compared to mid-rapidity PHENIX preliminary results as well as to predictions.


Introduction
A non-central collision creates a spatial anisotropy of the overlap region. In a thermodynamical picture, the asymmetric distribution of the initial energy density causes a pressure gradient larger in the shortest direction of the ellipsoidal medium. An azimuthal anisotropic emission of particles indicates a rapid thermalization of the system. It is quantified by measuring the second Fourier coefficient, v 2 , of the produced particles in the φ direction, with respect to the reaction plane angle, ψ [1,2]: A positive flow has been measured with light quarks [3], which validates a rapid thermalization of the system.
The cc that eventually forms a J/ψ can be initially produced in the first instant of the collision through gluon fusion. These are called direct J/ψs. In heavy ion collisions, their formation can be reduced for example by shadowing [4,5] or color screening [6]. In addition, interactions with comovers [7] might dissociate the mesons. On the other hand, given the large density of uncorrelated charm quarks in the hot medium at RHIC, these may recombine into J/ψs again [8,9]. A way to experimentally disentangle direct J/ψs from regenerated ones is to measure the J/ψs' elliptic flow.

Detectors
The elliptic flow is measured with respect to the collision reaction plane, estimated using a subset of parti- cles produced during the collision [2,11]. Careful attention must be taken to choose the subset so that all correlations but the elliptic flow are removed between this subset and the particle of interest. Until 2007 the collision reaction plane was measured using PHENIX Beam-Beam counters (BBC). In 2007 a new reaction plane detector (RxnP) was installed. Its acceptance coverage is |η| ∈ [1, 2.8]. This new detector allows two times better precision on the reaction plane measurement, as shown on Figure 2. The resolution by which the reaction plane angle is measured is used as a correction to the measured v 2 . At forward rapidity, J/ψs are measured through their decay into di-muons. The muon identifiers (MuID) [12] made of Iarroci tubes and steel absorbers, allow identification of the muons by matching their penetration depth with the track momentum. The cathode strip chambers (MuTr) [12] measure the particles momentum. The muon arms have a rapidity coverage for single muons of |η| ∈ [1.2, 2.2] which overlaps with the RxnP acceptance. This might induce a bias in the measurement of the collision reaction plane if the muons and particles produced by radiative gluons accompanying the J/ψ go through the RxnP detector used to estimate the reaction plane angle. In order to minimize this bias the RxnP detector opposite to the arm where the muons go is used in this analysis.

Analysis Method
The integrated luminosity analysed to get the present results is 537 µb −1 (611 µb −1 ) at backward (forward) rapidity, which is almost four times more than used in the previous publications [13]. The sample is Level-2 filtered, which means that it has been online filtered based on a fast tracking in the MuID.
The method to measure the elliptic flow chosen for this analysis is the most straight forward. It uses of the maximum statistics in each φ − ψ bin by dividing the sample in only two bins in φ − ψ (the separation between the two bins being set at φ − ψ = π/4). The v 2 is measured by forming the ratio of the number of J/ψs that belong to the bin which contains the reaction plane, N in , with the number of J/ψs that belong to the bin which does not contain the reaction plane N out , leading to: v meas 2 , σ in being the error on N in and σ out being the error on N out . The v meas 2 is corrected by the RxnP resolution to get the true J/ψ v 2 [11].
In order to get maximum control over the background which is critical for the v 2 measurement, the background subtraction is improved. In previous analysis, a mixed event subtraction technique was used to extract the J/ψ signal in a high background environment [13]. This method accounts for the fact that the MuTr acceptance differs for like-sign (like) and unlike-sign (+−) muon pairs and improves the statistical errors for bins where the signal over background is poor. The invariant mass distribution using the mixed-background subtraction for the [20-60]% centrality region is shown on Figure 3. The signal fit seems to be accurate, but some distortions at mass below 2.6 GeV are visible. They come from a bias introduced by the online filtering which creates a difference in the mixed-event (M ixed) and same-event (F G) distributions. To account for this bias, the mixed-event and like-sign distributions are combined as follow: Mixed like . The mass spectra obtained with the combined subtraction is shown on Figure 4. The distortions at mass below 2.6 GeV are highly reduced. The residual background possibly sitting below the J/ψ peak should also be reduced by this procedure, which is crucial for the v 2 measurement. On the other hand, this method results in larger statistical errors by about √ 2 due to the additional use of the unlike-sign same-event distributions.    ure 5 for negative (positive) rapidity in black circles (red squares). The physics at positive and negative rapidity being the same for symmetric collisions, the measurements are averaged in magenta closed circles on Figure 6, leading to smaller uncertainties. The error bars on the two figures account for statistical and point to point uncorrelated errors. They come from the statistical uncertainty on the number of signal counts [13], and the systematic uncertainty on the signal and background line-shape. Boxes refer to point to point correlated errors. They account for the error on the average RxnP detector resolution and the error on the J/ψ φ angle measurement that is less accurate at p T < 1. An additional global error of 3% is written on the figures. It accounts for the error on the technique used to determine the reaction plane angle and resolution [2,11]. It is a relative error that allows points to move together by 3% of their value.  Also shown in Figure 6 are PHENIX measurements at mid-rapidity (|y| < 0.35) as open circles, which are detailed in [14]. Forward and mid rapidity measurements are independent measurements since they use different detectors, triggers, and methods to get the v 2 (and thus the error bars and boxes are not estimated the same way). The two measurements show a similar trend, with a neg-  It is not clear whether the result at forward rapidity should differ from the result at mid-rapidity or not, especially since the forward measurement only reaches y = 2: the underlying physics related to collective behavior might not differ much over such a rapidity range. Given this hypothesis, one may combine the two rapidity measurements and test their statistical compatibility with a positive v 2 . This results in only 10% probability of the v 2 to be positive for the bin [0,5] GeV/c in p T . However due to the p T distribution of the measure J/ψ this value is dominated by the [1,2] GeV/c bin, for which the probability of having a positive v2 is only of 6.3%. Knowing if the v 2 is positive is more interesting for p T > 2 GeV/c since it is where the v 2 is expected to increase in coalescence models. The statistical probability for the combined v 2 measurements to be positive in the bin [2,5] GeV/c is of 41.9%, and the probability for this combined measurement to be above 0.01 is of 15.4%. However additional mid-rapidity measurements at higher p T would give more statistical importance to this number.
The theoretical curves on Figure 6 are for mid-rapidity, and most of them have no centrality selection, although the authors believe that predictions at [20,60]% should not differ a lot from other centralities predictions. They predict a higher v 2 when more recombination is at play, and almost no v 2 for direct J/ψs, even when including comover interactions ( [15,16,17,18,19,20]). No predictions at forward rapidity are yet available. However models do not expect much difference in v 2 as a function of p T at forward rapidity for direct J/ψ, whereas for J/ψ produced from regeneration, a little less flow could be expected at forward rapidity than at mid (although this is still to be quantified by theorists).
Experiments performed at lower energies have recently measured the J/ψ v 2 . NA60 measured a positive J/ψ v 2 of 7 ± 3% in In+In non-central collisions [21] with no selection in p T . At the SPS in In+In, only cold nuclear matter (CNM) effects are expected to affect the J/ψ. The positive flow could be due to geometrical nuclear absorption even though theorists have always thought that this effect would be negligible. In any case, models should include this v 2 from CNM effects and extrapolate it to heavier nuclei and higher energy so that the measurements can distinguish such effects from the flow induced by a QGP. On the other hand, NA50 measured a small J/ψ v 2 in Pb+Pb collisions [22] with a maximum of 3.5 ± 1.5 ± 1.3% for p T = 2 GeV/c. This result has no binning in centrality, and since the v 2 for central collisions should be close to zero, their measurement could correspond to slightly larger values for non-central collisions. Interpretations of these results could help to shed light on higher energy measurements done at RHIC. It would also help if experiments could measure the same binning in centrality and p T in order to compare the results directly.

Outlook
PHENIX has measured J/ψ azimuthal anisotropy at forward rapidity for centrality [20,60]% using all the statistics from the 2007 data taking, and the online filtered sample. Forward and mid-rapidity results show similar trends. For each measured p T bin, the value is compatible with both zero and maximal flow, appearing slightly negative for p T ∈ [0, 5] GeV/c. The current precision on the measurements does not allow firm conclusions.
The forward rapidity statistical significance may improve for our final results. These results will use the minimumbias sample, which will gain 10% in statistics that are lost in the present analysis given the online filter inefficiency. In addition, there will be no need to use the combined background subtraction described above and thus the statistical uncertainty will be reduced by √ 2. However, all these changes will probably not be enough to allow discrimation between models. A much larger data sample is needed and is expected at RHIC in 2010.