Charged and neutral vector meson under magnetic field

Hao Liu; Lang Yu; Mei Huang

doi:10.1103/PhysRevD.91.014017

paper

Charged and neutral vector meson under magnetic field

arXiv:1408.1318 · doi:10.1103/PhysRevD.91.014017

Abstract

The vector meson $ρ$ 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 $ρ$ 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 $ρ^{0}$ with spin component $s_{z} = 0, \pm 1$ and the charged vector meson $ρ^{\pm}$ with $s_{z} = 0$ also increases with magnetic field. However, the mass square of the charged vector meson $ρ^{+}$ ( $ρ^{-}$ ) with $s_{z} = + 1$ ( $s_{z} = - 1$ ) decreases linearly with magnetic field and drops to zero at the critical magnetic field $e B_{c} ≃ 0.2 GeV^{2}$ , which indicates the possible condensation of charged vector meson in the vacuum. This critical magnetic field is much lower than the value $e B_{c} = 0.6 GeV^{2}$ 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 $ρ^{\pm}$ for $s_{z} = \pm 1$ cannot drop to zero at high magnetic fields.

arXiv comment10 pages, 8 figures

Charged and neutral vector meson under magnetic field

Abstract

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