Speaker
Summary
In the chiral effective Nambu--Jona-Lasinio (NJL) model with two- and three-flavor quarks, we demonstrate that the naively expected neutral pion ($\pi^0$) superfluidity (NPSF) and vacuum superconductivity (VSC) in constant magnetic field ${\bf B}=B\hat z$ are both disfavored, due to the well-known magnetic catalysis effect (MCE) to chiral symmetry breaking. 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 $B$ and thus of NPSF and VSC tendencies. 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 $775~{\rm MeV}$. 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 $B$.
