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. For instance, the fraction of bottomonium states observed in a 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. Anti--de Sitter/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 the field. 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 quasistates.