Cold and dense perturbative QCD in a very strong magnetic background

We compute the pressure from first principles within perturbative QCD at finite baryon density and very high magnetic fields up to two-loops and with physical quark masses. The region of validity for our framework is given by m s ≪ μ q ≪ e B , where m s is the strange quark mass, μ q is the quark chemical potential, e is the fundamental electric charge, and B is the magnetic field strength. We include the effects of the renormalization scale in the running coupling, α s ( μ q , e B ) , and running strange quark mass. We also discuss the simplifications that come about in the chiral limit. The effectively negligible contribution of the exchange diagram allows for building a simple analytic model for the equation of state for pure quark magnetars and computing their mass and radius at very large values of B . These results provide constraints on the behavior of the maximum mass and associated radius from perturbative QCD. We also discuss the magnetic bag model for extreme magnetic fields.