Azimuthal asymmetry of J/ψ suppression in non-central heavy-ion collisions

The azimuthal asymmetry of J/ψ suppression in non-central heavy-ion collisions is studied within a dynamic model of J/ψ suppression in a deconfined partonic medium. Within this model, J/ψ suppression in heavy-ion collisions is caused mainly by the initial state nuclear absorption and dissociation via gluon-J/ψ scattering in deconfined partonic medium. Only the second mechanism gives arise to azimuthal asymmetry of the final J/ψ production. We demonstrate that if there is an onset of suppression by quark-gluon plasma (QGP) in the NA50 data, it must be accompanied by the non-vanishing azimuthal asymmetry. Using the same critical density above which the QGP effect enters, we predict the azimuthal asymmetric coefficient v2 as well as the survival probability for J/ψ at the RHIC energy. PACS number(s): 12.38.Mh; 24.85.+p; 25.75.-q Typeset using REVTEX 1 In the search for quark-gluon plasma (QGP), J/ψ suppression has been proposed as one of the promising signals [1] of the deconfinement in high-energy heavy-ion collisions. Because of the color screening effect in a quark-gluon plasma, the linear confining potential in vacuum that binds two heavy quarks to form a quarkonium disappears so that it can be easily broken up causing suppression of the J/ψ production. The problem in heavy-ion collisions is however complicated by other competing mechanisms such as initial nuclear absorption [2] and hadronic dissociation [3]. While recent precision data from the NA50 [4] experiment at the CERN SPS energies clearly show anomalous suppression unexplained by the normal initial nuclear absorption, there are still much debates about the exact nature of the anomalous suppression [5,6], whether it is caused by the formation of QGP or dissociation by ordinary hadronic matter. We propose in this letter the study of azimuthal asymmetry of J/ψ production [7] as additional measurements to distinguish different competing mechanism of J/ψ suppression. Since the initial state interactions such as nuclear absorption or nuclear shadowing of gluon distribution has no preference over the azimuthal direction they will not have any contribution to the azimuthal anisotropy of the J/ψ production. Only suppression by the final state interaction with the produced medium will cause significant azimuthal anisotropy in the final J/ψ distribution in the transverse direction. If the centrality dependence of the J/ψ suppression additional to the initial nuclear absorption is caused by formation of QGP, it must be accompanied by a sudden onset of the azimuthal anisotropy. On the other hand, a hadronic absorption scenario would give a continuous centrality dependence of the azimuthal anisotropy. In this letter, we will study the centrality dependence of both the averaged J/ψ suppression factor and the azimuthal anisotropy with a model in which J/ψ suppression is caused by initial nuclear absorption and final state dissociation by QGP above a critical density. Using parameters from fitting the NA50 data, we will also give predictions for J/ψ suppression and its azimuthal anisotropy at the RHIC energies. We will quantify the azimuthal anisotropy by the second Fourier coefficient v2 of the azimuthal angle distribution of the final J/ψ distribution, similarly to the proposed elliptic 2 flow measurement [8,9]. We follow the microdynamic approach of J/ψ suppression [10], in which the J/ψ suppression is caused by gluonic dissociation. Different from a normal hadron gas, a deconfined partonic system contains much harder gluons which can easily break up a J/ψ. The perturbative calculations predict the gluon-J/ψ dissociation cross section [11,12], σψ(q ) = N0 (q0/ǫ0 − 1) (q/ǫ0) , (1) where N0 = 2π 3 ( 32 3 )( 16π 3g s ) 1 m2Q . Here gs is the strong coupling constant, mQ is charm quark mass, and q 0 is the gluon energy in the J/ψ rest frame. To break up a J/ψ, q must be larger than the binding energy ǫ0. Using similar approach, we have calculated the dissociation cross section for P -wave states by gluons, σχ(q ) = 4N0 (q0/ǫχ − 1)(9(q/ǫχ) − 20(q0/ǫχ) + 12) (q/ǫχ) , (2) where ǫχ is the binding energy of the P -wave state. For χc, it is about 0.250GeV . Because of the small value of the binding energy, the validity of the perturbative calculations for the gluonic dissociation cross section of χc might be questionable. So the above formula can only be considered more phenomenological. However, keeping this point in mind, we can see that the above expression still qualitatively reflects the fact that χc states are easier to be broken up than J/ψ, because of the much lower energy threshold and the overall larger factor of 4. Therefore, this perturbative calculation gives us a reasonable estimate and guides us to include its contribution for a more complete study of J/ψ suppression in heavy ion collisions. In the following we will consider χc contributing to about 40% of the inital J/ψ production and use the above formula to estimate its suppression in a deconfined partonic system. In the rest frame of a deconfined parton gas, the momentum distribution of thermal gluons will depend on the effective temperature T with an approximate Bose-Einstein distribution, f(k;T ) ∝ [exp(k/T ) − 1]. The velocity averaged dissociation cross sections for charmonia is defined as, 3 〈vrelσ〉(T, ~p) = ∫ d3kvrelσ(q )f(k;T )