Non-extensive Hard Thermal Loop Resummation and Its Applications: Analysis in Zero and Finite Magnetic Fields

Abstract

The impact of non-extensive statistics on the hard thermal loop (HTL) resummation technique is investigated, in the absence and presence of a magnetic field. By utilizing the non-extensive bare propagators in the real-time formalism of finite temperature field theory, we determine the non-extensive deformations of both HTL gluon self-energies and resummed gluon propagators at the one-loop order. We observe that the introduction of non-extensivity results in distinct shifts in the Debye masses for the retarded/advanced and symmetric gluon self-energies. Applying the non-extensive modified resummed gluon propagators to obtain the dielectric permittivity of a quark-gluon plasma (QGP), we thereby derive the static heavy quark potential, which incorporates both short-range Yukawa and long-range string-like interactions between heavy quarks and the QGP medium. The real part of the potential exhibits increased screening as the non-extensive parameter $q$ ($q \geq 1$) increases, reducing the binding energies of heavy quarkonia. Furthermore, including non-extensivity enhances the magnitude of the imaginary part of the potential, causing a broadening in the decay widths of heavy quarkonia. Based on these observations, we estimate the melting temperatures of heavy quarkonia. Our results indicate that non-extensivity lowers the melting temperatures of heavy quarkonia, thus facilitating their dissociation, whereas the presence of a magnetic field inhibits this dissociation.