Charged and neutral vector meson under magnetic field

Abstract

The vector meson $\rho$ in the presence of external magnetic field has been investigated in the framework of the Nambu--Jona-Lasinio model, where mesons are constructed by infinite sum of quark-loop chains by using random phase approximation. The $\rho$ meson polarization function is calculated to the leading order of $1/N_c$ expansion. It is found that the constituent quark mass increases with magnetic field, the masses of the neutral vector meson ${\rho }^0$ with spin component $s_z=0,\pm 1$ and the charged vector meson ${\rho }^{\pm }$ with $s_z=0$ also increases with magnetic field. However, the mass square of the charged vector meson ${\rho }^{+}$ (${\rho }^{-}$) with $s_z=+1$ ($s_z=-1$) decreases linearly with magnetic field and drops to zero at the critical magnetic field $e{B}_c\simeq 0.2{\mathrm{GeV}}^2$, which indicates the possible condensation of charged vector meson in the vacuum. This critical magnetic field is much lower than the value $e{B}_c=0.6{\mathrm{GeV}}^2$ predicted by a point-like vector meson. We also show that if we use lowest Landau level approximation, the mass of the charged vector meson ${\rho }^{\pm }$ for $s_z=\pm 1$ cannot drop to zero at high magnetic fields.

10 pages, 8 figures

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• Heavy meson spectroscopy under strong magnetic field
• $\rho$ mesons in strong abelian magnetic field in SU(3) lattice gauge theory
• Spectral properties of $\rho$ meson in a magnetic field
• Thermodynamics of 2+1 Flavor Polyakov-Loop Quark-Meson Model under External Magnetic Field
• Modification of the masses of the lightest neutral mesons in a hadronic medium under an external magnetic field