Electrical neutrality and $$\beta $$-equilibrium conditions in dense quark matter: generation of charged pion condensation by chiral imbalance

The phase diagram of dense quark matter with chiral imbalance is considered with the conditions of electric neutrality and $$\beta $$ β -equilibrium. It has been shown recently that chiral imbalance can generate charged pion condensation (PC) in dense quark matter. It was, therefore, interesting to verify that this phenomenon takes place in realistic physical scenarios such as electrically neutral quark matter in $$\beta $$ β -equilibrium, because a window of charged PC at dense quark matter phase diagram (without chiral imbalance) predicted earlier was closed by the consideration of these conditions at the physical current quark mass. In this paper it has been shown that the charged PC phenomenon is generated by chiral imbalance in the dense electric neutral quark/baryonic matter in $$\beta $$ β -equilibrium, i.e. matter in neutron stars. It has also been demonstrated that charged PC is an inevitable phenomenon in dense quark matter with chiral imbalance if there is nonzero chiral imbalance in two forms, chiral and chiral isospin one. It seems that in this case charged PC phase can be hardly avoided by any physical constraint on isospin imbalance and that this conclusion can be probably generalized from neutron star matter to the matter produced in heavy ion collisions or in neutron star mergers. The chiral limit and the physical point (physical pion mass) have both been considered and it was shown that the appearance of charged PC is not much affected by the consideration of nonzero current quark mass.