Thermomagnetic properties and Bjorken expansion of hot QCD matter in a strong magnetic field

Abstract

In this work we have studied the effects of an external strong magnetic field on the thermodynamic and magnetic properties of a hot QCD matter and then explored these effects on the subsequent hydrodynamic expansion of the said matter once produced in the ultrarelativistic heavy ion collisions. For that purpose, we have computed the quark and gluon self-energies up to one loop in the strong magnetic field, using the HTL approximation with two hard scales - temperature and magnetic field, which in turn compute the effective propagators for quarks and gluons, respectively. Hence the quark and gluon contributions to the free energy are obtained from the respective propagators and finally derive the equation of state (EOS) by calculating the pressure and energy density. We have found that the speed of sound is enhanced due to the presence of strong magnetic field and this effect will be later exploited in the hydrodynamics. Thereafter the magnetic properties are studied from the free energy of the matter, where the magnetization is found to increase linearly with the magnetic field, thus hints the paramagnetic behavior. The temperature dependence of the magnetization is also studied, where the magnetization is found to increase slowly with the temperature. Finally, to see how a strong magnetic field could affect the hydrodynamic evolution, we have revisited the Bjorken boost-invariant picture with our paramagnetic EOS as an input in the equation of motion for the energy-momentum conservation. We have noticed that the energy density evolves faster than in the absence of strong magnetic field, i.e. cooling becomes faster, which could have implications on the heavy-ion phenomenology. As mentioned earlier, this observation can be understood by the enhancement of the speed of sound.