Configuration entropy and stability of bottomonium radial excitations in a plasma with magnetic fields

Abstract

Heavy vector mesons produced in a heavy ion collision are important sources of information about the quark gluon plasma (QGP). For instance, the fraction of bottomonium states observed in such a collision is altered by the dissociation effect caused by the plasma. So, it is very important to understand how the properties of the plasma, like temperature $(T)$, density and the presence of background magnetic fields $(eB)$, affect the dissociation of bottomonium in the thermal medium. AdS/QCD holographic models provide a tool for investigating the properties of heavy mesons inside a thermal medium. The meson states are represented by quasinormal modes in a black hole geometry. In this work we calculate the quasinormal modes and the associated complex frequencies for the four lowest levels of radial excitation of bottomonium inside a plasma with a magnetic field background. We also calculate the differential configuration entropy (DCE) for all these states and investigate how the dissociation effect produced by the magnetic field is translated into a dependence of the DCE on $eB$. An interesting result obtained in this study is that the DCE increases with the radial excitation level $n$. Also, a nontrivial finding of this work is that the energy density associated with the bottomonium quasinormal modes presents a singularity near the black hole horizon for some combination of values of $T,eB$ and $n$. As we show here, it is possible to separate the singular factor and define a square integrable quantity that provides a DCE that is always finite. In addition, we discovered that, working with the potentially singular energy density, one finds a very interesting way to use the DCE as a tool for determining the dissociation temperature of the meson quasisates.

22 pages, 2 tables and 10 figures with 26 subfigures in total. In version 2, we show an original result concerning the use of the differential configuration entropy to characterize the dissociation temperature of the physical system studied. Some clarifications were also included

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• Configurational entropy and shape complexity of strange vector kaons in AdS/QCD
• Holography and the internal structure of charmonium
• Deformed AdS/QCD, mesonic mass spectra, and DCE: Still a margin for heavier resonances
• Landau-Zener-Stückelberg-Majorana dynamics of magnetized quarkonia
• Quarkonium spectra with magnetically induced anisotropic confinement