A semi-classical picture of the charmonium-hadron interaction

Abstract

In this work, we present calculations for the charmonium-hadron cross section. The hadron is represented by an external color field and the charmonium is represented by a small color dipole. Using high-energy approximations we compute the relevant cross sections, which agree with results obtained with other methods.In the near future, data on charmonium production in heavy ion collisions at RHIC will be available. In order to understand them, a crucial ingredient is a good knowledge of the charmonium -hadron cross section. In the last years much work has been done along this line [1].More than two decades ago, Peskin and Bhanot (BP) [2] showed that one could apply perturbative QCD to calculate the interactions between bound states of heavy quarks and light hadrons. The justification of their approach comes basically from the fact that the heavy quark mass provides a large energy scale. Later their results have been rederived in the context of the operator product expansion (OPE) [3] and more recently in terms of the QCD factorization theorem [4]. In all these works some nonperturbative input is needed, such as certain matrix elements involving gluon operators, the heavy quark wave function inside the bound state or moments of the gluon distribution function in the hadron. Moreover, most of the other existing calculations follow some nonperturbative approach, some of them using constituent quark wave functions [5], some others using effective lagrangians involving charm mesons in the strong coupling regime [6] (which, in many cases, need charm form factors [7]) and some others using the QCD vacuum expectation values (condensates), which appear naturally in the QCD sum rules approach [8]. All these treatments of the problem were devoted to low energy rections. However, it turns out that even at high energies ( √ s 20 GeV) nonperturbative effects play a very important role [9].In this work we calculate the charmonium -hadron cross section using the BP approach with simplifying assumptions, so as to render the calculations simple, analytic and to be able to treat more complex interactions, like those involving the χ states or the (Q − Q) 8 − g pre-resonant (or color octet) state.The starting point is the assumption that the charmonium (dipole) is small compared with the hadron (condenser). As a consequence, the Q − Q pair will interact mostly with the external color field but not with the (quark) sources. Moreover, the external color field is considered to have only low momentum components ("soft gluons") and thus is able to transfer only a small amount of energy, which will be barely enough to dissociate the bound state. The typical binding energy is 0.6 GeV. Therefore, in a first approximationwhere M is the mass of the bound state (M 3 GeV). The binding energy is also small compared to the collision energyApproximation (1) justifies the use of quantum mechanical perturbation theory (the Born approximation) and approximation (2) justifies the use of the eikonal approximation, which, in this case, implies that the h...

Chromoelectric fields and quarkonium-hadron interactions at high energies

“…To compute the transition amplitude we need to know the new wave functions, which now include both the quarkonium and the capacitor. They are i = f ( r 1 , r 2 )g( r a , r b )c n d n e m h m (20) and f = t C ( r 1 , r 2 )g( r a , r b )c i d j e l h k .…”

“…In the last step of ( 14), the integration over the phase space had to be done numerically. In [20] we made the additional assumption that the outgoing mesons are nearly at rest and we could thus simplify (10) and perform the integration over p 1 and p 2 analytically. Here we prefer to be more "exact" and perform the last integrations numerically.…”