QCD phase transition at finite isospin density and magnetic field within the three-flavor NJL model

Abstract

Previously, the QCD phase transition at finite isospin density and magnetic field was explored within the two-flavor Nambu--Jona-Lasinio model. This work extends the study to the more realistic three-flavor case, where not only strange quark contributions but also quark mass splitting in a strong magnetic field are fully taken into account. Adopting the Ginzburg-Landau approximation and the Landau representation for fermion propagators, we re-explore the transitions from the normal chiral symmetry breaking phase to pion superfluidity or rho superconductivity. Unlike the previous study, we project the mesonic fields onto the eigenstates of a charged point particle in a magnetic field and prove that the corresponding self-energies from quark loops are gauge invariant and degenerate with respect to the extra transverse degrees of freedom. However, the numerical results are qualitatively consistent with previous findings: as the isospin chemical potential increases, pion superfluidity is favored at small magnetic fields, while rho superconductivity is favored at large magnetic fields. In the three-flavor model, since the lowest energy of the rho meson increases with stronger magnetic field, the corresponding critical isospin chemical potential also increases with the magnetic field.