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

We have studied how the equation of state of thermal QCD with two light flavors is modified in a strong magnetic field. We calculate the thermodynamic observables of hot QCD matter up to one-loop, where the magnetic field affects mainly the quark contribution and the gluon part is largely unaffected except for the softening of the screening mass. We have first calculated the pressure of a thermal QCD medium in a strong magnetic field, 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 understood from the dominant scale of thermal medium in the strong magnetic field, being the magnetic field, in the same way that the temperature dominates in a thermal medium in the absence of magnetic field. Thus although the presence of a strong magnetic field makes the pressure of hot QCD medium larger, the dependence of pressure on the temperature becomes less steep. Consistent with the above observations, the entropy density is found to decrease with the temperature in the presence of a strong magnetic field which is again consistent with the fact that the strong magnetic field restricts the dynamics of quarks to two dimensions, hence the phase space becomes squeezed resulting in the reduction of number of microstates. Moreover the energy density is seen to decrease and the speed of sound of thermal QCD medium increases in the presence of a strong magnetic field. These findings could have phenomenological implications in heavy ion collisions because the expansion dynamics of the medium produced in non-central ultra-relativistic heavy ion collisions is effectively controlled by both the energy density and the speed of sound.