One-loop QCD thermodynamics in a strong homogeneous and static magnetic field

Abstract

We have studied how the equation of state of thermal QCD with two light flavours is modified in strong magnetic field by calculating the thermodynamic observables of hot QCD matter up to one-loop, where the magnetic field affects mainly the quark contribution and the gluonic part is largely unaffected except for the softening of the screening mass due to the strong magnetic field. To begin with the effect of magnetic field on the thermodynamics, we have first calculated the pressure of a thermal QCD medium in strong magnetic field limit (SML), where the pressure at fixed temperature increases with the magnetic field faster than the increase with the temperature at constant magnetic field. This can be envisaged from the dominant scale of thermal medium in SML, which is the magnetic field, like the temperature in thermal medium in absence of strong magnetic field. Thus although the presence of strong magnetic field makes the pressure of hot QCD medium harder but the increase of pressure with respect to the temperature becomes less steeper. Corroborated to the above observations, the entropy density is found to decrease with the temperature in the ambience of strong magnetic field which resonates with the fact that the strong magnetic field restricts the dynamics of quarks in two dimensions, hence the phase space gets squeezed resulting the reduction of number of microstates. Moreover the energy density is seen to decrease and the speed of sound of thermal QCD medium is increased in the presence of strong magnetic field. These crucial findings in strong magnetic field could have phenomenological implications in heavy ion collisions because the expansion dynamics of the medium produced in noncentral ultrarelativistic heavy ion collisions is effectively controlled by both the energy density and the speed of sound.