"Splitting" 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 $\mathbf{B}=B\hat{z}$ 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 ${\pi }^0$ and ${\bar{\rho }}_1^{+}$ (${\rho }^{+}$ 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 to ${\bar{\rho }}_1^{+}$ meson with physical vacuum mass $775\mathrm{MeV}$. Then, restricted to $\rho$ meson mass below two-quark threshold in vacuum, that is $m_{\rho }^v<2m_q^v$, it is found that ${\pi }^0$ mass decreases and then increases with $B$ slowly, and ${\bar{\rho }}_1^{+}$ 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, ${\bar{\rho }}_1^{+}$ meson mass is found to be consistent with the LQCD results semi-quantitatively in smaller $B$ region but increase in 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: ${\pi }^0,{\eta }_0$ and ${\eta }_8$, which is very important to suppress the mass enhancement of the effective mass eigenstates at large $B$.

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• Chiral properties of (2+1)-flavor QCD in strong magnetic fields at zero temperature
• Recent progresses on QCD phases in a strong magnetic field -- views from Nambu--Jona-Lasinio model
• Rotation induced charged pion condensation in a strong magnetic field: A Nambu--Jona-Lasino model study
• Extracting the magnitude of magnetic field at freeze-out in heavy-ion collisions
• Neutral pseudoscalar and vector meson masses under strong magnetic fields in an extended NJL model: mixing effects
• Charged pseudoscalar and vector meson masses under strong magnetic fields in an extended NJL model
• Charged rho superconductor in the presence of magnetic field and rotation
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• Gauge independence of pion masses in a magnetic field within the Nambu--Jona-Lasinio model
• ${\pi }^0\to 2\gamma$ decay under strong magnetic fields in the NJL model