Charmonium-hadron interactions from QCD

The heavy quark system is an excellent probe to learn about the QCD dynamics at finite density. First, we discuss the properties of the J/ψ and D meson at finite nucleon density. We discuss why their properties should change at finite density and then introduce an exact QCD relation among these hadron properties and the energy momentum tensor of the medium. Second, we discuss attempts to calculate charmonium-hadron total cross section using effective hadronic models and perturbative QCD. We emphasize a recent calculation, where the cross section is derived using QCD factorization theorem. We conclude by discussing some challenges for SIS 200. 1. J/ψ and D mesons at finite density In the heavy quark system, the heavy quark massmH provides a natural normalization scale μ, which makes the perturbative QCD approach possible even for calculating some bound state properties of the heavy quarks. This implies that the heavy quark system is an excellent probe to learn about the QCD dynamics at finite density and/or temperature. Here, we will highlight some calculations which explicitly demonstrate the relations between the changes of the properties of the heavy quark system and the QCD dynamics at finite density. 1.1. J/ψ mass at finite density Let us first start with the J/ψ meson mass at finite density. The interaction between the J/ψ and a hadron h can be perturbatively generated by multiple gluon exchanges. This implies that the mass shift of the J/ψ in nuclear medium can be estimated if the gluon distribution is known in nuclear medium [1]. In fact, in the heavy quark mass limit mc → ∞, the mass shift can be calculated exactly to leading order in QCD [2] and is given as ∆mJ/ψ = c1 ×∆〈E 〉matter, (1) where c1 is a calculable constant and the matrix element is taken with respect to the nuclear matter. To the leading order in density, the matrix element is known from the trace anomaly relation and the gluon distribution function of the nucleon [3]. For a more realistic charm quark mass, there are some model dependence on how to treat the bound state part. So far, there are potential model approaches [1, 4] and QCD sum rule approaches [5, 6]. In all cases, similar relation to Eq. (1) holds with slightly different expressions for c1, such that the mass shift at nuclear matter density ranges Charmonium-hadron interactions from QCD 2 from −4 to −7 MeV. The mass shift is small at nuclear matter density and one doubts whether such a small mass shift can be observed. However, one can turn the argument around and claim that if any mass shift for J/ψ is observed, it will tell us about the changes of gluon field configuration at finite density through Eq. (1). 1.2. D meson mass at finite density In the D meson, the heavy quark acts as a source for the light quark, which surrounds the heavy quark and probes the QCD vacuum. This is the basic picture of the constituent quark in the heavy-light meson system within the formulation based on the heavy quark symmetry [7]. Therefore, if the vacuum properties are changed at finite temperature or density, the light quark should be sensitively affected and be reflected in the changes of the D meson properties in matter. For the D meson, there does not exist a formal limit where one can calculate the mass change in matter. Nevertheless, model calculations suggest [8, 9, 10] that it is dominantly related to the change in the chiral condensate. In fact, in both the quark-meson coupling model [9] and in the QCD sum rule approach [10], the average mass shift of the D mesons at normal nuclear matter density were found to be around −50 MeV. The D meson mass shift has several importance in the J/ψ suppression phenomena in relativistic heavy ion collisions (RHIC). First, it leads to subthreshold production and the change of the DD̄ threshold for the J/ψ system in matter [11]. Second, a change of the averaged D mass might lead to level crossings of the D̄D threshold with the ψ and χ mass [10, 12], which leads to a step-wise J/ψ suppression [10, 13]. Unfortunately, for the D meson mass shift, there are large model dependence and nontrivial splitting between the D and D mesons [14]. 1.3. Exact sum rule from QCD The D meson mass and the DD̄ threshold have important phenomenological consequences. Unfortunately, only model-dependent calculation could be made. Here, we will introduce an exact QCD equality, which can be used to link the DD̄ threshold to J/ψ suppression. The exact sum rules in QCD at finite temperature and/or density were first introduced to the correlation functions between light hadrons [15] and the derivation goes as follows. Let us consider the correlation function between two meson currents and its dispersion relation, ∆Π(Q, T, ρ) = i ∫ dxe∆〈q̄Γq(x)q̄Γq(0)〉