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

TL;DR

This paper investigates how magnetic fields and temperature affect bottomonium mesons in a quark-gluon plasma using holographic models, revealing how dissociation correlates with configuration entropy and identifying a method to determine dissociation temperatures.

Contribution

It introduces a novel approach to analyze bottomonium dissociation in magnetic fields via holographic quasinormal modes and differential configuration entropy, including handling singularities in energy density.

Findings

DCE increases with radial excitation level n.

Energy density exhibits singularity near the black hole horizon for certain parameters.

DCE can be used to estimate the meson dissociation temperature.

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.