Charged rho superconductor in the presence of magnetic field and rotation

Abstract

In this work, we mainly explore the possibility of charged rho ($$\rho ^\pm $$ ρ ± ) superconductor in the presence of parallel magnetic field and rotation within three-flavor Nambu–Jona-Lasino model. By following similar schemes as in the previous studies of charged pion ($$\pi ^\pm $$ π ± ) superfluid, the $$\rho ^\pm $$ ρ ± superconductor is found to be favored for both choices of Schwinger phase in Minkowski and curved spaces. Due to the stability of the internal spin structure, charged rho begins to condensate at a smaller threshold of angular velocity than charged pion for the given large magnetic fields. Even the axial vector meson condensation is checked – the conclusion is that $$\rho ^\pm $$ ρ ± superconductor is the robust ground state at strong magnetic field and fast rotation, which actually sustains to very large angular velocity.

Recent progresses on QCD phases in a strong magnetic field -- views from Nambu--Jona-Lasinio model

“…with S being the area of the xy-plane. Even though N is not necessary when boundary condition is taken into account [48], it still serves a good approximation in present simplified discussions [110]. As the action of the ladder operators on the pre-matrix of the eigenfunction gives…”

“…In 2019, the contradiction between the conclusions of two-flavor NJL model and LQCD was well discussed by extending the study to three-flavor NJL model [47], and the underlying reason was attributed to mass splitting between u and d quarks in external magnetic field. At this point, it is worth mentioning that the possibility of ρ ± superconductivity can be greatly enhanced to be real by introducing a large rotation parallel to B [48].…”

“…For that sake, we consider a cylinder system with radius R and the rotation effect is transmitted from the boundary to the bulk if possible. It is clear that the boundary would induce gaps to the particle energies for different l 3 and S 3 , which then avoid the disaster of meson condensations of all kinds in rotational system [48,110]. Here, we neglect the boundary effect on quarks for simplicity, but one should keep in mind that there can be no particles in the system when the container is rotating.…”

“…But with the chemical potential like effect induced by rotation, the Vafa-Witten theorem is not valid anymore, so the ρ ± condensation is not forbidden in principle, similar to the π ± condensation at finite µ I . In parallel magnetic field and rotation, the lowest dispersion of ρ ± is modified to [48]…”

Macroscopic transports in a rotational system with an electromagnetic field

“…The divergence of J µ 5 at I 1 = 0 seems weird. Actually, the point is that we didn't take into account the boundary effect [39][40][41], which is necessary for a rotational system to satisfy causality. A finite boundary will induce a mass gap δm to the fermions in the bulk [39][40][41]; then take chiral density for example, the final expression alters to Thus, the divergence is safely avoided but the chiral current J µ 5 indeed can be greatly enhanced by reducing I 1 .…”