Rotation induced charged pion condensation in a strong magnetic field: A Nambu–Jona-Lasino model study

Abstract

We investigate the possibility of charged pion condensation in the presence of parallel rotation and magnetic field within the Nambu-Jona-Lasinio model with quarks as the fundamental degrees of freedom. Previous study based on non-interacting Klein-Gordon theory for pions showed that the charged pions will undergo Bose-Einstein condensation under this circumstance [Y. Liu and I. Zahed, Phys. Rev. Lett. 120, 032001 (2018)]. In this work, we take into account the internal quark structures of charged pions self-consistently through quark polarization loops in an interacting theory, i.e., the Nambu-Jona-Lasino model. The stability of the system against the formation of charged pion condensation, i.e., a nonzero expectation value of the composite charged pion field uiγ5d, is explored. We find that two competing effects are induced by the rotation: the isospin enhancement which favors charged pion condensation and the spin breaking which disfavors the condensation. For a strong magnetic field ( √ eB ∼ 1GeV) and system size of a few fermi, the isospin enhancement effect is stronger than the spin breaking one, and the charged pion condensation becomes energetically favored beyond a critical angular velocity of a few MeV.

Charged rho superconductor in the presence of magnetic field and rotation

“…Compared to that given in Ref. [37] but implicitly implied, the Landau levels are cut off by n max ( N f ) here, which was checked to be a good approximation for large B and = 0. For a continuous transition, the effective potential can be expressed as the form in Ginzburg-Landau (GL) theory…”

“…As mentioned in the conclusion of Ref. [37], the spins of valence quark and antiquark are along the same direction in rho vector mesons; thus, the spin-up ρ + meson is stable in the presence of either strong magnetic field B or large rotating angular velocity along z direction. Due to the mass reduction in B and effective isospin chemical potential generated by , it is quite probable that ρ ± superconductor would occur in B and keep robust to very fast rotation.…”

“…, it is controversial according to the studies in Nambu-Jona-Lasinio (NJL) model, where one is immersed in the ambiguity of the definition for Schwinger phase [37,38]. In pure magnetic field, the Schwinger phase is just the gauge dependent part of the meson propagator; but with rotation presented, we are not able to find a consistent one for all Landau levels -that causes somewhat arbitrariness.…”

“…By using the eigenfunction reconstruction method, we have given the propagator of a fermion with positive or negative charge [37]; so the u and d/s quark propagators are respectively…”

Mode decomposed chiral magnetic effect and rotating fermions

“…Now, chiral transport phenomena in general have grown up to be one major subject in not only heavyion collision but general physics [42,43]. So far, B-induced and ω-induced phenomena have been considered individually, but an interplay between B and ω would be becoming more and more attractive [44][45][46][47][48][49][50][51][52]. Among various theoretical attempts, we shall pay our special attention to Ref.…”