Abstract
By simulating the finite temperatures magnetized background in the RHIC and LHC energies, we systematically study the characteristics of thermal widths and potentials of heavy quarkonia. It is found that the magnetic field has less influence on the real potential, but has a significant influence on the imaginary potential, especially in the low deconfined temperature. Extracted from the effect of thermal worldsheet fluctuations about the classical configuration, the thermal width of $\Upsilon(1s)$ in the finite temperature magnetized background is investigated. It is found that at the low deconfined temperature the magnetic field can generate a significant thermal fluctuation of the thermal width of $\Upsilon(1s)$, but with the increase of temperature, the effect of magnetic field on the thermal width becomes less important, which means the effect of high temperature completely exceeds that of magnetic field and magnetic field become less important at high temperature. The thermal width decreases with the increasing rapidity at the finite temperature magnetized background. It is also observed that the effect of the magnetic field on the thermal width when dipole moving parallel to the magnetic field direction are larger than that moving perpendicular to the magnetic field direction, which implies that the magnetic field tends to enhance thermal fluctuation when dipole moving parallel to the direction of magnetic field. The thermal width of $\Upsilon(1S)$ hardly changes with the increasing temperature when dipole moving perpendicular to the magnetic field. But when dipole moving parallel to the magnetic field, the thermal width at low temperature is obviously larger than that at high temperature.
Highlights
A new state of matter, so-called quark-gluon plasma (QGP), has been generated in relativistic heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the LHC [1,2,3]
By simulating the finite temperature magnetized background at the Relativistic Heavy Ion Collider and LHC energies, we systematically study the characteristics of the thermal width and potential of heavy quarkonia
It is observed that the effect of the magnetic field on the thermal width when the dipole is moving perpendicular to the magnetic field is larger than that moving parallel to the magnetic field at Tc < T < 1.5Tc, which implies that the magnetic field tends to enhance thermal fluctuation when the dipole is moving perpendicular to magnetic field, but when T > 2Tc, the effect of magnetic field on the thermal fluctuation is almost the same whether dipole moving perpendicular or parallel to the magnetic field
Summary
A new state of matter, so-called quark-gluon plasma (QGP), has been generated in relativistic heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the LHC [1,2,3]. In the study of heavy-ion collisions, besides high temperature, another important finding is the generation of a strong magnetic field of noncentral. The imaginary potential of quarkonia for N 1⁄4 4 super Yang-Mills theory was studied by Noronha and Dumitru in their seminal work [28] This imaginary contribution originates from thermal fluctuations around the bottom of the classical sagging string in the bulk that links the heavy quarks situated at the boundary in the dual gravity picture. To accurately determine the suppression of quarkonia formed in relativistic heavy-ion collisions, it is necessary to evaluate the thermal width of Υð1SÞ for moving quarkonia in the finite temperature magnetized QGP background at the RHIC and LHC energies. Reference [37] studies the charmonium dissociation in a strongly coupled chiral plasma in the presence of magnetic field and axial charge imbalance. In the supergravity limit which corresponds to a strongly coupled plasma, one can evaluate the expectation value of the Wilson loop WðCÞ by the prescription hWðCÞi ∼ e−iSNG ; ð14Þ
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