Magnetic catalysis effect prevents vacuum superconductivity in strong magnetic fields

摘要

By comparing the two- and three-flavor Nambu–Jona-Lasinio (NJL) models, we demonstrate that the naively expected vacuum superconductivity (VSC) in constant magnetic field B = Bz is disfavored due to the splitting magnetic catalysis effect (MCE) to chiral condensates with different quark flavors. Based on the simple two-flavor NJL model, we illuminate, in the lowest Landau-level approximation, the similar origins of π~0 and ρ_1~+ (ρ~+ meson with spin S_z = 1) mass reductions with smaller B and their different features at larger B.With the full Landau levels, the two-flavor NJL model is found to be invalid to study the magnetic field effect on the ρ_1~+ meson with physical vacuum mass 775 MeV. Then, restricted to the ρ meson mass below the two-quark threshold in vacuum, that is, m_ρ~v< 2m_q~v, it is found that π~0 mass decreases and then increases with B slowly, and the ρ_1~+ mass vanishing point is delayed to larger B compared to the point particle result. In the more realistic three-flavor NJL model, all the quark masses split in strong magnetic field as a combinatorial result of their different current masses and electric charges. By choosing a vacuum mass closer to the physical one, the ρ_1~+ meson mass is found to be consistent with the lattice QCD results semiquantitatively in the smaller B region but increase in the larger B region. These features are mainly outcomes of the interplay between the S_z ? B coupling effect and splitting MCE to the composite u and d quarks, which definitely disfavors VSC when the latter dominates. Furthermore, mesonic flavor mixing is modified by B among the neutral pseudoscalars, π~0, η_0 and η_8, which is very important to suppress the mass enhancement of the effective mass eigenstates at large B.