Quasinormal modes and dispersion relations for quarkonium in a plasma

Recent investigations show that the thermal spectral function of heavy ${b \bar b }$ and ${c \bar c}$ vector mesons can be described using holography. These studies consider a bottom up model that captures the heavy flavour spectroscopy of masses and decay constants in the vacuum and is consistently extended to finite temperature. The corresponding spectral functions provide a picture of the dissociation process in terms of the decrease of the quasi-state peaks with temperature. Another related tool that provides important information about the thermal behaviour is the analysis of the quasinormal modes. They are field solutions in a curved background assumed to represent, in gauge/gravity duality, quasi-particle states in a thermal medium. The associated complex frequencies are related to the thermal mass and width. We present here the calculation of quasinormal modes for charmonium and bottomonium using the holographic approach. The temperature dependence of mass and thermal width are investigated. Solutions corresponding to heavy mesons moving into the plasma are also studied. They provide the dependence of the real and imaginary parts of the frequency with the quasi-particle momenta, the so called dispersion relations.Comment: V2: enlarged version with clarifications, more comparison with previous articles and additional references included. 11 figures, 2 tables, 62 references. Version accepted for publication in JHE

Bottomonium dissociation in a finite density plasma

We present a holographic description of the thermal behavior of $b \bar b$ heavy vector mesons inside a plasma at finite temperature and density. The meson dissociation in the medium is represented by the decrease in the height of the spectral function peaks. In order to find a description for the evolution of the quasi-states with temperature and chemical potential it is crucial to use a model that is consistent with the decay constant behavior. The reason is that the height of a spectral function peak is related to the value of the zero temperature decay constant of the corresponding particle. AdS/QCD holographic models are in general not consistent with the observation that decay constants of heavy vector mesons decrease with radial excitation level. However, it was recently shown that using a soft wall background and calculating the correlation functions at a finite position of anti-de Sitter space, associated with an ultraviolet energy scale, it is possible to describe the observed behavior. Here we extend this proposal to the case of finite temperature $T$ and chemical potential $\mu$. A clear picture of the dissociation of bottomonium states as a function of $\mu$ and $T$ emerges from the spectral function. The energy scales where the change in chemical potential leads to changes in the thermal properties of the mesons is consistent with QCD expectations.Comment: In V3: errors in reference citations corrected. Version published in Physics Letters B. 15 pages, 3 figure

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

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.Comment: 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 include