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Joint CATHIE-INT Mini-Program "Quarkonium in Hot Media: From QCD to Experiment"

By Peter Petreczky and Ramona Vogt

CATHIE (Center of Analysis and Theory for Heavy-Ion Experiments) was proposed a year ago to foster collaboration between theorists and experiments to focus on realistic calculations of: three-dimensional hydrodynamical simulations of heavy-ion collisions; jet production and in-medium energy loss; and heavy flavor (open charm and J/ψ), thermal photon, and dilepton production.  An advisory board representing major groups involved in theory and experiment at RHIC and the LHC was formed to oversee CATHIE's activities, including collaborative development of a quantitative approach to heavy-ion theory and center-sponsored workshops and programs at BNL and elsewhere.  See the CATHIE website, http://quark.phy.bnl.gov/www/cathie.html, for more information.

One such CATHIE mini program ``Quarkonium in Hot Media: from QCD to Experiment'', sponsored jointly with the INT, Seattle, took place in Seattle June 16-26, 2009 with 32 participating researchers.  The program focused on different topics relevant for quarkonium production in a hot medium, including the properties of quarkonium at high temperatures; the role of cold nuclear matter effects on quarkonium production in heavy-ion (A+A) collisions; and the interpretation of the available experimental data in heavy-ion collisions.

A major goal of this program was to enhance the exchange of ideas between theorists studying quarkonia in a high-temperature environment using different approaches, e.g. ab-initio calculations (lattice QCD and pQCD) and phenomenological models (potential models, sum rules, etc.). The applicability of potential models to screening has been extensively discussed and scrutinized with an emphasis on the importance of thermal broadening of the quarkonium states. In particular, it has become clear that, in the weak-coupling limit, the dominant effect is thermal broadening rather than the screening suggested by Matsui and Satz. There were several fruitful discussions on how to understand the temperature dependence of the Euclidean correlators calculated in lattice QCD in terms of effective theories (pNRQCD) and weak-coupling expansion in the short-distance regime.  An understanding of these issues is crucial for quantitative results on quarkonium properties in a thermal deconfined medium.  In the past the weak temperature dependence of quarkonium correlators in Euclidean time was interpreted as evidence for survival of the quarkonium states. It is now clear that significant broadening or even dissolution of the quarkonium states will not result in large changes of the Euclidean correlation functions.  This is illustrated in Fig. 1 where the S-wave charmonium spectral functions are depicted at different temperatures, along with the corresponding normalized Euclidean correlators (inset). These results show that direct lattice calculations of the quarkonium spectral functions are very challenging and realistic potential model calculations are needed.

Figure 1

Figure 1: Charmonium spectral functions at different temperatures calculated in a  potential model approach (Á. Mocsy and P. Petrezky, Phys. Rev. D {\bf 77}, 014501 (2008)).  A lattice calculation of the spectral function is also shown. In the inset, the corresponding  Euclidean correlation functions calculated in the potential model (lines), normalized by the reference correlators Grec, are compared to lattice data. The reference correlator is constructed from the zero temperature spectral function.  Note that the lines and labels in the main figure have the same color coding as the points and lines in the inset.

It is important to understand the role of cold nuclear matter (CNM) effects to interpret the quarkonium yields in heavy-ion collisions. In the past, CNM effects were studied in terms of the nuclear absorption cross section σabs extracted from proton-nucleus (p+A) data. The absorption was interpreted as resulting from interactions of the small Q-Qbar pair with nuclear fragments after the collision. Recently it has become clear, however, that there are other CNM effects, including shadowing and initial-state energy loss. Therefore the analysis of CNM effects in terms of σabs should be considered as only an effective description. The absorption cross section depends on kinematic variables such as √s, xF etc.

Figure 2

Figure 2: The J/ψ nuclear absorption cross section as a function of ycms.  Figure courtesy of H. Wöhri.

Its value also strongly depends on the nuclear parton distribution functions (nPDF)  used in the analysis. Clearly a more differential approach in studying CNM effects should be adopted.

Figure 2 shows the σabs extracted from a wide range of center-of-mass energies, from the CERN SPS to RHIC, as a function of the center-of-mass rapidity, ycms, using the EKS98 shadowing parameterisation.  At ycms ~ 0, σabs tends to decrease with increasing √sNN.  The absorption cross section rises at forward rapidities with the onset occurring at increasing ycms as energy grows.  Such an increase in the effective σabs could be a manifestation of energy-loss effects.

A further aim of the mini-program was the clarification of some outstanding production-related issues, including separation of initial- and final-state CNM effects.  Several data-driven analyses were presented.  In particular, the interplay of different effects was studied by H. Wöhri, C. Lourenco, R. Vogt and P. Faccioli during the workshop.  One outcome was the determination of σabs using the newest nuclear shadowing parametrization, EPS09.  The kinematic dependence of σabs was discussed by H. Wöhri and C. Lourenco. The question of which part of the CNM effects extracted from p+A data should be used in the analysis of heavy-ion data was discussed.

The physical interpretation of the cold nuclear matter effects strongly depends on the quarkonium production mechanism which is still not yet well understood. Therefore, the
role of polarization in constraining the quarkonium production mechanism was discussed by J.-P. Lansberg, P. Faccioli and C. Lourenco.

Figure 3

Figure 3: The nuclear modification factor for the J/ψ yield relative to that for CNM at RHIC and the SPS as a function of ετ.  The EKS98 results are obtained from the recent d+Au run.  Figure courtesy of M. Leitch.

Another significant outcome of the program was the development of a comparative measure of anomalous J/ψ suppression (relative nuclear modification), taking cold nuclear matter effects into account, at both RHIC and the SPS.  This new comparison arose from a collaborative effort during the workshop by M. Leitch, A.D. Frawley, R. Granier de Cassagnac, A. Linden Levy,  C. Lourenco, H. Satz,  R. Vogt and H. Wöhri. In addition, R. Arnaldi and E. Scomparin from Torino University, members of the NA60 Collaboration measuring J/ψ at the SPS, remotely join ed this effort. The suppression factor can be presented in a number of ways, including as a function of the number of nucleons participating in the collision, Npart, and the energy density ε of the resulting fireball. It was found that the most suitable variable for comparing the relative anomalous suppression at RHIC and the SPS is instead ετ, where τ is an effective thermalization time. In terms of ετ, while the suppression patterns are qualitatively similar, there is clearly more anomalous suppression at RHIC than at the SPS, as shown in Fig. 3.

To find out more about the mini-program or CATHIE itself, visit the CATHIE web page and the group Wiki pages: http://quark.phy.bnl.gov/www/cathie.html and https://wiki.bnl.gov/qpg/index.php/Quarkonia.

The work of R. Vogt was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344
(http://www.llnl.gov/disclaimer.html) and NSF PHY-0555660.