Survival of charged rho condensation at high temperature and density

TL;DR

This paper investigates how charged rho mesons behave under strong magnetic fields at high temperature and density, revealing conditions where electromagnetic superconductivity could occur in extreme astrophysical and collider environments.

Contribution

It demonstrates that charged rho meson condensation can persist at high temperature and density, extending the understanding of electromagnetic superconductivity in extreme conditions.

Findings

Charged rho meson mass decreases with magnetic field and drops to zero at a critical value.

Charged rho condensation can survive at high temperature and density.

Potential for electromagnetic superconductivity inside compact stars and at LHC energies.

Abstract

The charged vector $\rho$ mesons in the presence of external magnetic fields at finite temperature $T$ and chemical potential $\mu$ have been investigated in the framework of the Nambu--Jona-Lasinio model. We compute the masses of charged $\rho$ mesons numerically as a function of the magnetic field for different values of temperature and chemical potential. The self-energy of the $\rho$ meson contains the quark-loop contribution, i.e. the leading order contribution in $1/N_c$ expansion. The charged $\rho$ meson mass decreases with the magnetic field and drops to zero at a critical magnetic field $eB_c$, which means 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 $\rho$ 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 the charged $\rho$ condensation might occur inside compact stars. At zero density, in the temperature range $0.2-0.5~ {\rm GeV}$, the critical magnetic field for charged $\rho$ condensation is in the range of $0.2-0.6~ {\rm GeV}^2$, which indicates that the high temperature electromagnetic superconductor could be created at LHC.