Magnetic catalysis effect prevents vacuum superconductivity in strong magnetic fields

Abstract

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 π0 and ρ¯1+ (ρ+ meson with spin Sz=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, mρv<2mqv, it is found that π0 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 Sz−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, π0, η0 and η8, which is very important to suppress the mass enhancement of the effective mass eigenstates at large B.

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