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/Nc 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 sz = 0, ±1 and the charged vector meson ρ ± with sz = 0 also increases with magnetic field. However, the mass square of the charged vector meson ρ + (ρ − ) with sz = +1 (sz = −1) decreases linearly with magnetic field and drops to zero at the critical magnetic field eBc ≃ 0.2GeV 2 , which indicates the possible condensation of charged vector meson in the vacuum. This critical magnetic field is much lower than the value eBc = 0.6GeV 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 ± for sz = ±1 cannot drop to zero at high magnetic fields.
We investigate both (pseudo)scalar mesons and diquarks in the presence of external magnetic field in the framework of the two-flavored Nambu-Jona-Lasinio (NJL) model, where mesons and diquarks are constructed by infinite sum of quark-loop chains by using random phase approximation. The polarization function of the quark-loop is calculated to the leading order of 1/Nc expansion by taking the quark propagator in the Landau level representation. We systematically investigate the masses behaviors of scalar σ meson, neutral and charged pions as well as the scalar diquarks, with respect to the magnetic field strength at finite temperature and chemical potential. It is shown that the numerical results of both neutral and charged pions are consistent with the lattice QCD simulations. The mass of the charge neutral pion keeps almost a constant under the magnetic field, which is preserved by the remnant symmetry of QCD×QED in the vacuum. The mass of the charge neutral scalar σ is around two times quark mass and increases with the magnetic field due to the magnetic catalysis effect, which is an typical example showing that the polarized internal quark structure cannot be neglected when we consider the meson properties under magnetic field. For the charged particles, the one quark-antiquark loop contribution to the charged π ± increases essentially with the increase of magnetic fields due to the magnetic catalysis of the polarized quarks. However, the one quark-quark loop contribution to the scalar diquark mass is negative comparing with the point-particle result and the loop effect is small.
In the chiral symmetric phase, the polarized instanton-anti-instanton molecule pairing induces a nontrivial repulsive interaction in the iso-scalar axial-vector channel. As a consequence, one unusual property is observed that in the chiral restoration phase, there is a first order phase transition for the spontaneous generation of local CP violation and chirality imbalance. Furthermore, it is found that external magnetic fields will lower the critical temperature for the local CP-odd phase transition and catalyze the chirality imbalance, which destroys the chiral condensate with pairing quarks between different chiralities. A reasonable strength of the repulsive interaction in the iso-scalar axial-vector channel can naturally explain the inverse magnetic catalysis around the critical temperature under external magnetic fields.
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