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Prepared by L. A. Linden Levy, University of Colorado, for the DNP web page
Scientists from over 26 countries have been working diligently at the relativistic heavy ion collider (RHIC) accelerator facility at Brookhaven National laboratory (BNL) to quantify the properties of the quark gluon plasma produced in ultra-relativistic heavy ion collisions. The idea that charmonium states should melt (or never form) in hot dense matter was originally proposed by Matsui and Satz  and may provide a model dependent method for extracting the temperature of the plasma. The idea is that the color screening length in a deconfined plasma of quarks and gluons would be smaller than the binding radius of a charm anti-charm pair. The pair, would be screened and therefore not able to bind (much like Debye screening in electromagnetic plasmas). In addition the different states have different binding radii and thus melt at different temperatures, a process termed "sequential melting" (Figure 1).
However this simple prediction poses a very serious experimental challenge. First one has to know the baseline for quarkonium production in a binary (proton-proton) collision, which can then be scaled up by the number of binary collisions in a nucleus-nucleus collision and compared to measurement. However the problem becomes more complicated when one looks at the spectroscopy of quarkonium (e.g Figure 2 for charmonium) and sees that there are transitions between the different states. This process is known as "feed down" . Therefore it is also important to measure the feed down fraction of different states in p-p collisions, especially into the J/Ψ which is second to lowest energy and thus an easily produced charmonium state. It is also believed that at the RHIC energies the mechanism for charmonium production is mostly gluon fusion, thus one needs to account for the shadowing of parton distributions in nuclei. The term shadowing refers to the modification of parton distribution functions in nuclei when compared to those measured in nucleons . From lower energy fixed target experiments it was also realized that the charmonium states may have some suppression beyond that coming from nuclear shadowing of the gluons. This is typically parameterized as a constant "breakup cross section" that describes the magnitude of charmonium suppression that comes from traversing the remnant of a nucleus.
courtesy of A. Mocsy
Figure 1: Cartoon representing the charmonium states as a thermometer for the quark gluon plasma.
Figure 2: The spectrum and so called "feed-down" transitions of the charmonium family . A similar spectroscopic diagram can be found in the reference for bottomonium.
In order to measure the baseline, disentangle the cold nuclear matter (CNM) effects and determine the hot nuclear matter effects RHIC collides three different species-configurations. First proton-proton (p-p) collisions of symmetric beams of 100 GeV are measured to determine the baseline. Next deuteron-nucleus collisions are measured in order to extract CNM effects. In this case the deuteron is a stand in for the proton forced by accelerator constraints. Finally nucleus-nucleus collisions are measured and compared to the baseline, after taking into account CNM suppression, to discern the amount of hot nuclear matter suppression that is seen at RHIC. This straight-forward process has been hindered by lack of statistics and large systematic uncertainties in all three cases. Recently both the STAR and PHENIX experiments have made strides in reducing the systematic uncertainties and the accelerator facility has delivered a large increase in integrated luminosity.
Here we report the latest measurements from the PHENIX and STAR collaborations using the 2008 deuteron-gold run and the 2006 proton-proton run and the 2005 copper-copper run, which has recently been pushed to larger transverse momentum.
The first set of these improved measurements comes from the RHIC 2006 p-p run. In this run PHENIX recorded approximately a factor of three more integrated luminosity than in the 2005 p-p run. In addition to the increase in statistics, refinements in signal extraction techniques and methodology for applying acceptance and efficiency corrections that agree more closely with real data have led to an improvement in systematic uncertainties. Figure 3 shows the invariant yields of J/Ψ from p-p collisions as a function of rapidity and transverse momentum for the three rapidities accessible by the PHENIX detector. These improvements make these data a very powerful baseline as well as providing a challenge to theoretical calculations using different QCD inspired production mechanisms.
Figure 3: Preliminary measurement of p-p invariant J/Ψ yield multiplied by branching ratio versus rapidity (left) and transverse momentum (right). This is the baseline for comparison to heavy ion measurments. The red points are for backward rapidity (-1.2 < y < -2.2), the green points are for central rapidity (|y| < 0.35) and the blue points are for forward rapidity (1.2 < y < 2.2.) . The black points are the previous PHENIX measurement .
Using the excellent azimuthal coverage of the barrel shaped detector STAR measured J/Ψ-hadron azimuthal correlations. Then using a tuned PYTHIA Monte Carlo simulation and assuming that the J/Ψ correlations predicted from the simulation are correct, STAR can extract the feed down fraction from the B-meson to the J/Ψ. The result is a feed down fraction of 13 ± 5%.
Figure 4: Measurement of J/Ψ-hadron azimuthal correlations, used in  to extract a model based measurement of the B-meson feed-down fractions. This measurement may also be helpful in understanding the charmonium production mechanism.
Figure 7: Preliminary measurement by PHENIX of the probability distribution for different values of RAA. The 90% confident limit for the area under the curves (vertical purple line) gives RAA < 0.64 in gold-gold collisions .
Figure 5: Preliminary measurement of CNM suppression at the PHENIX experiment. The quantity shown is RCP as a function of rapidity (y) for three different centralities measured in the 2008 d-Au run. One sees a strong trend at forward rapidity that can not be accounted for with nuclear shadowing and a rapidity independent (constant) breakup cross section.
Figure 6: Preliminary measurement of invariant mass spectrum for di-electrons from the STAR detector after like sign subtraction. There is evidence for a clear upsilon peak at 9.46 GeV.
During the 2008 RHIC deuteron-gold (d-Au) run PHENIX recorded a factor of 30 higher statistics than the previous run in 2003. The data were analyzed to measure the central to peripheral ratio RCP in these collisions (Figure 5). These data have sparked much interest in the community (for details see the 2009 ECT and INT quarkonia workshops) as it is clear that a rapidity independent breakup cross section combined with nuclear shadowing cannot match the shape of the data. This has lead to the conclusion that there may be some physics missing in the models. Soon PHENIX will also release the ratio to the p-p baseline.
STAR was able to make a measurement of the upsilon production in d-Au. The clear upsilon peak is shown in Figure 6. When this is combined with their previous measurement of the p-p baseline they extract RdAu =0.98 ± 0.32 (syst.) ± 0.28 (syst.) . Measurements of the CNM suppression of higher mass states are very important when one wishes to apply the feed down fractions measured in p-p collisions to nucleus-nucleus collisions. If the higher state is completely broken up in CNM then the suppression of a lower state may not be evidence for hot nuclear matter effects.
Finally we present the most recent suppression measurement in gold-gold (Au-Au) collisions. Using the data recorded in the 2007 RHIC run PHENIX was able to extract an 90% confidence level upper limit for the suppression of upsilons. The low number of counts in the p-p and Au-Au data set was treated with Poisson statistics and a total probability distribution for RAAwas calculated (Figure 7). The result is a nuclear modification factor of 0.64. One could interpret this as evidence that the excited upsilon states (2s, 3s) are melted in the medium. However as stated above such a conclusion would be premature until the uncertainties on the CNM effects for upsilons are reduced.
In conclusion, the recent quarkonia measurements at RHIC have brought powerful new data to the community. The improved p-p baseline is beneficial to all nuclear modification measurements and may have the leverage to distinguish between different production mechanisms. The central to peripheral nuclear suppression factor measured in d-Au collisions has brought great excitement to the community and implies that simple nuclear shadowing plus breakup is not sufficient to describe the data. The upsilon measurements made by both experiments are complementary and are the first look at bottomonium so far. With luminosity improvements expected for RHIC-II these data will improve and shed more light on the temperature of the QGP.
Work supported by the U. S. Department of Energy, Principal Investigator: James Nagle, University of Colorado
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 Preliminary result shown by PHENIX collaboration at Quark Matter 2009, Knoxville, TN.
 Preliminary result shown by STAR collaboration at Quark Matter 2009, Knoxville, TN
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