Quasinormal modes for quarkonium in a plasma with magnetic fields

Abstract

Heavy vector mesons detected after a heavy ion collision are important sources of information about the quark gluon plasma. The fraction of such particles that survive the plasma phase and reach the detectors is related to the dissociation degree inside the thermal medium. A consistent picture for the thermal behavior of charmonium and bottomonium quasi-states in a thermal medium was obtained recently using a holographic bottom up model. This model captures the heavy flavour spectroscopy of masses and decay constants in the vacuum (zero temperature) and is consistently extended to finite temperature. The spectral functions that emerge provide a description of the dissociation process in terms of the broadening of the quasi-state peaks with temperature. The holographic approach makes it possible to determine also the quasinormal modes. They are gravity solutions representing the quasi-particle states in the thermal medium, with complex frequencies related to the thermal mass and width. The quasinormal modes for charmonium and bottomonium have been studied very recently and a consistent description of the dissociation process was found. An additional factor can affect the dissociation process: strong magnetic fields are expected to be present when the plasma is formed by non-central heavy ion collisions. So, it is important to understand the effect of such fields on the heavy meson dissociation scenario. Here we extend the holographic determination of quasinormal modes for the case when magnetic fields are present. The real and imaginary parts of the mode frequencies are determined for different values of background $e B$ field. The associated dispersion relations for heavy quarks moving inside the plasma are also investigated for both $ c \bar c$ and $ b \bar b \, $.