QCD equation of state at nonzero baryon density in an external magnetic field

This paper is devoted to the study of quantum chromodynamics (QCD) equation of state in external magnetic field and nonzero baryon density. Our study is carried out by means of lattice simulation with $2+1$ dynamical staggered quarks at the physical masses. The simulation is conducted at imaginary baryon chemical potential what allowed us to overcome the sign problem. We expand the pressure in the baryon imaginary chemical potential and study three leading nonzero coefficients in this expansion. These coefficients were calculated for the following values of magnetic field: $eB=0.3$, 0.6, $1.2{\mathrm{GeV}}^2$ with the lattice sizes $8\times 32^3$, $10\times 40^3$, $12\times 48^3$. Using these data we take continuum limit for the coefficients. Our results indicate considerable enhancement of the expansion coefficients by the magnetic field.