Survival of charged ρ condensation at high temperature and density

The charged vector ρ mesons in the presence of external magnetic fields at finite temperature T and chemical potential μ have been investigated in the framework of the Nambu–Jona-Lasinio model. We compute the masses of charged ρ mesons numerically as a function of the magnetic field for different values of temperature and chemical potential. The self-energy of the ρ meson contains the quark-loop contribution, i.e. the leading order contribution in 1/Nc expansion. The charged ρ meson mass decreases with the magnetic field and drops to zero at a critical magnetic field eBc, which indicates that the charged vector meson condensation, i.e. the electromagnetic superconductor can be induced above the critical magnetic field. Surprisingly, it is found that the charged ρ condensation can even survive at high temperature and density. At zero temperature, the critical magnetic field just increases slightly with the chemical potential, which indicates that charged ρ condensation might occur inside compact stars. At zero density, in the temperature range 0.2–0.5 GeV, the critical magnetic field for charged ρ condensation is in the range of 0.2–0.6 GeV2, which indicates that a high temperature electromagnetic superconductor might be created at LHC.