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 $m_s\ll {\mu }_q\ll \sqrt{eB}$, where $m_s$ is the strange quark mass, ${\mu }_q$ 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, ${\alpha }_s({\mu }_q,\sqrt{eB})$, 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.

• Received 3 January 2024
• Accepted 2 March 2024

DOI:https://doi.org/10.1103/PhysRevD.109.054033

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Published by the American Physical Society