Abstract
In this paper, we construct a simple model for the complex heavy quark potential which is defined through the Fourier transform of the static gluon propagator. Besides the hard thermal loop resummed contribution, the gluon propagator also includes a non-perturbative term induced by the dimension two gluon condensate. Within the framework of thermal field theory, the real and imaginary parts of the heavy quark potential are determined in a consistent way without resorting to any extra assumption as long as the exact form of the retarded/advanced gluon propagator is specified. The resulting potential model has the desired asymptotic behaviors and reproduces the data from lattice simulation reasonably well. By presenting a direct comparison with other complex potential models on the market, we find the one proposed in this work shows a significant improvement on the description of the lattice results, especially for the imaginary part of the potential, in a temperature region relevant to quarkonium studies.
Highlights
The heavy-ion experiments at RHIC and the LHC have shown very rich and interesting physics that cannot be interpreted by simple extrapolation from protonproton collisions, which indicates the formation of a new form of matter—the quark-gluon plasma (QGP) during the ultrarelativistic heavy-ion collisions
We proposed a model for the complex HQ potential which is defined as the Fourier transform of the static gluon propagators in the Keldysh representation
These propagators consist of two parts: the Coulombic term comes from the resummed hard thermal loop (HTL) perturbation theory at leading order while the string contributions are induced by the dimension two gluon condensate
Summary
The heavy-ion experiments at RHIC and the LHC have shown very rich and interesting physics that cannot be interpreted by simple extrapolation from protonproton collisions, which indicates the formation of a new form of matter—the quark-gluon plasma (QGP) during the ultrarelativistic heavy-ion collisions. The EFT was generalized to finite temperature QCD which justified the description of heavy quarkonia in terms of an in-medium potential. After analytical continuation to Minkowski space, it was found that besides a Debye screened potential as its real part, the potential contains an imaginary part which determines the decay width of a quarkonium state Such a perturbative calculation in the weak-coupling limit, is only valid when the distance r between the quark and antiquark is small. Solving the Schrödinger equation with such a complex HQ potential, the binding energies and decay widths of quarkonia have been obtained They did not make a comparison between their potential model and the corresponding lattice results. For the above mentioned purpose, the current paper aims to construct a complex HQ potential model which can be used for other phenomenological studies on the heavy quarkonia.
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