Abstract
We consider the quarkonium diffusion, dissociation and recombination inside quark-gluon plasma. We compute scattering amplitudes in potential nonrelativistic QCD for relevant processes. These processes include the gluon absorption/emission at the order $gr$, inelastic scattering at the order $g^2r$ and elastic scattering with medium constituents at the order $g^2r^2$. We show these amplitudes satisfy the Ward identity. We also consider one-loop corrections. The dipole interaction between the color singlet and octet is not running at the one-loop level. Interference between the tree-level gluon absorption/emission and its thermal loop corrections cancels the collinear divergence in the $t$-channel inelastic scattering. The inelastic scattering has no soft divergence because of the finite binding energy of quarkonium. We write out the diffusion, dissociation and recombination terms explicitly for a Boltzmann transport equation and define the dissociation and recombination rates. Furthermore, we calculate the diffusion coefficient of quarkonium. We find our result of diffusion coefficient differs from a previous calculation by two to three orders of magnitude. We explain this and can reproduce the previous result in a certain limit. Finally we discuss two mechanisms of quarkonium energy loss inside quark-gluon plasma.
Highlights
Since the early study of static screening on quarkonium [1], the bound state of a heavy quark-antiquark pair, quarkonium has been used as a probe of quarkgluon plasma (QGP) in heavy ion collisions
In addition to the static screening effect, the dynamical screening effect exists inside QGP
It is the dissociation of quarkonium caused by collisions with medium constituents
Summary
Since the early study of static screening on quarkonium [1], the bound state of a heavy quark-antiquark pair, quarkonium has been used as a probe of quarkgluon plasma (QGP) in heavy ion collisions. This leads to a dependence of the dissociation rate on the relative position of the heavy quarkantiquark pair [9,10] This maps into a dependence of the inelastic scattering on the bound-state wave function [11], as in the case of gluon absorption. To describe the transport of quarkonium inside QGP, one needs to consider the in-medium recombination from unbound QQpairs [19] This can be modeled by detailed balance and a phenomenological factor controlling how much open heavy quarks are thermalized [20]. Quarkonium can diffuse inside QGP because it is approximately a color dipole and not exactly color neutral It may elastically scatter with medium constituents.
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