Survival of charged ρ condensation at high temperature and density

Abstract：

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/N_c expansion. The charged ρ meson mass decreases with the magnetic field and drops to zero at a critical magnetic field eB_c, 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.