Magnetic catalysis effect prevents vacuum superconductivity in strong magnetic fields

Abstract

In the chiral effective Nambu-Jona-Lasinio (NJL) model with two-and three-flavor quarks, we demonstrate that the naively expected neutral pion (π 0 ) superfluidity (NPSF) and vacuum superconductivity (VSC) in constant magnetic field B = Bẑ 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 π 0 andρ + 1 (ρ + meson with spin Sz = 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 toρ + 1 meson with physical vacuum mass 775 MeV. Then, restricted to ρ meson mass below two-quark threshold in vacuum, that is m v ρ < 2m v q , it is found that π 0 mass decreases and then increases with B slowly, andρ + 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,ρ + 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 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: π 0 , η0 and η8, which is very important to suppress the mass enhancement of the effective mass eigenstates at large B.

Charged rho superconductor in the presence of magnetic field and rotation

“…by further adopting the four fermion vector interaction channels with coupling constant G V . Compared to the two-flavor NJL model, the advantage of three-flavor NJL model is that: there the vacuum superconductivity or ρ ± superconductor cannot happen due to the mass splitting of quarks in pure magnetic field [35], which is consistent with lattice QCD simulations [33,34,36].…”

“…, the effective mass of ρ + ↑ or ρ − ↓ decreases as m 2 ρ + |eB|(2λ 0 l − 1) on one hand [24], the effective isospin chemical potential increases as (l + 1) on the other hand. Then, it seems that ρ + ↑ condensation would overwhelm the π + condensation to be the true ground state when is large enough that As the VW theorem might forbid the decreasing of composite ρ + ↑ mass to zero in pure magnetic field [33][34][35][36], the estimation of the ρ + ↑ mass is not correct at all for large B in the point particle picture. However, as mentioned in the introduction, invalids the proof of the theorem thus the isospin chemical potential effect of (l + 1) can still be qualitatively correct in the point particle picture.…”

“…. , 8) are defined in three-flavor space, so the extra diagonal terms (ψλ 3 ψ) 2 and (ψλ 8 ψ) 2 allow mass splitting among all the flavors in contrary to the two-flavor case [35]. The U A (1) symmetry violating term L 6 [49] only involves scalar-pseudoscalar channels with the determinant defined in flavor space, ± = 1 ± γ 5 and K the coupling constant.…”

“…In some sense, the extreme conditions a e-mail: caogaoqing@mail.sysu.edu.cn (corresponding author) open a wide realm for the searching of new phases, such as ρ ± superconductor in pure magnetic field [24,25], neutral pseudoscalar superfluid in parallel EM field [26][27][28][29] and π ± superfluid in parallel magnetic field and rotation (B ) [30]. Among others, the possibility of ρ ± superconductor was under fierce debate since its proposal [24,25,[31][32][33][34][35][36], mainly concerning the internal quark-antiquark effect on rho mesons.…”

“…In Sect. 3, we present the formalism for SU (3) NJL model in rotating frame with a parallel magnetic field, where the simplest forms of vector interactions are introduced to explore rho meson physics [35]. Then, the quadratic coefficient in Ginzburg-Landau expansion will be evaluated analytically in Sect.…”