Abstract
We generalize known results for heavy quarkonium in a thermal bath to the case of a finite baryonic density, and provide a number of formulas for the energy shift and decay width that hold at weak coupling for sufficiently large temperature and/or chemical potential. We find that a non-vanishing decay width requires a temperature larger than the typical binding energy, no matter how large the chemical potential is. This implies that at zero temperature the dissociation mechanism of heavy quarkonium is due entirely to screening, unlike in the finite temperature case. We use several effective theories in order to sort out the contributions of the relevant energy and momentum scales. In particular, we consider contributions of the so called quasi-static magnetic modes. The generalization to the case of a finite isospin/strangeness chemical potential is trivial. We discuss possible applications to the SIS and NICA conditions, and compare with available lattice results.
Highlights
High energy heavy-ion collision experiments (HIC) have shown the existence of collective behavior in the strong interactions, namely a new state of matter that is usually refer to as quark-gluon plasma (QGP)
The suppression of heavy quarkonium states in the products of the HIC were proposed as a signal of QGP formation long ago [2]
The QCD dynamics which is responsible for this suppression is not so easy to identify
Summary
High energy heavy-ion collision experiments (HIC) have shown the existence of collective behavior in the strong interactions, namely a new state of matter that is usually refer to as quark-gluon plasma (QGP) (see [1] for a review). These colliders will have energy enough to produce charmonium bound states [34] It is worth exploring in a solid theoretical framework, namely using QCD at weak coupling and the well-known effective field theories for heavy quarkonium, the fate of these states at nonzero baryon chemical potential. This is so even if the charm quark mass may not be high enough to apply weak coupling techniques beyond the ground state, or if the values of chemical potential attained in the experiments may not be large enough to justify a weak coupling analysis.
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