Landau damping in a strong magnetic field: Dissociation of quarkonia

Abstract

In this article we have investigated the effects of strong magnetic field on the properties of quarkonia immersed in a thermal medium of quarks and gluons and then studied the quasi-free dissociation of quarkonia due to the Landau-damping. Thermalising the Schwinger propagator for quarks in the lowest Landau levels and the Feynman propagator for gluons in real-time formalism, we have calculated the resummed retarded and symmetric propagators, which in turn give the real and imaginary components of dielectric permittivity, respectively. Finally the inverse Fourier transform of the permittivities encrypt the effect of hot QCD medium in the presence of strong magnetic field into both real and imaginary parts of heavy quark potential. We have found that the magnetic field largely affects the large-distance interaction, as a result, the real part of potential becomes more attractive and the magnitude of imaginary part too becomes larger, compared to its counterpart in the absence of magnetic field. The real part of the potential is thereafter solved numerically by the Schrödinger equation to obtain the energy eigenvalues and energy eigenfunctions of the charmonium states. We have noticed that in the presence of strong magnetic field, the size (r2) of J/ψ and ψ′ are swelled whereas χc gets shrunk, unless the temperature is very high. Similarly the magnetic field affects the binding of J/ψ and χc differently, i.e. it decreases the binding of J/ψ but increases for χc. On contrary the magnetic field increases the width of the resonances, unless the temperature is sufficiently high. We have finally studied the dissociation due to the Landau damping and found that the dissociation temperatures become higher in the presence of magnetic field. For example, with eB=6mπ2 the J/ψ is dissociated at 2Tc, and with eB=4mπ2 the χc is dissociated at 1.1Tc in comparison, with eB = 0 the J/ψ is dissociated at T=1.6Tc and χc is dissociated at T=0.8Tc. However, with the further increase of magnetic field the dissociation temperatures decrease.