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

TL;DR

This study explores how rotation and magnetic fields influence charged pion condensation within the NJL model, revealing a critical angular velocity beyond which condensation is energetically favored due to isospin enhancement.

Contribution

It provides a self-consistent analysis of charged pion condensation considering quark structures and competing effects of rotation and magnetic fields in the NJL model.

Findings

Charged pion condensation is favored at high magnetic fields and angular velocities.

Rotation induces competing effects: isospin enhancement and spin breaking.

A critical angular velocity exists where condensation becomes energetically favorable.

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. ${\bf 120}$, 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 is explored against the formation of a nonzero expectation value of the composite charged pion field $\bar{u}i\gamma_5d$. 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 ($\sqrt{eB}\sim1{\rm GeV}$) 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.