Electrical neutrality and β\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 $\beta$-equilibrium. It has been shown recently that chiral imbalance can generate charged pion condensation in dense quark matter, so it was interesting to verify that this phenomenon takes place in realistic physical scenarios such as electrically neutral matter in $\beta$-equilibrium, because a window of pion condensation 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 pion condensation is generated by chiral imbalance in the dense electric neutral quark/baryonic matter in $\beta$-equilibrium, i. e. matter in neutron stars. It has been also demonstrated that pion condensation is inevitable phenomenon in dense quark matter with chiral imbalance if there is non-zero chiral imbalance in two forms, chiral and chiral isospin one. It seems that in this case pion condensation phase can be hardly avoided by any physical constraint on isopin 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 piont (physical pion mass) has been considered and it was shown that the appearance of pion condensation is not much affected by the consideration of non-zero current quark mass.Comment: 16 pages, 14 figure

Magnetic field instability in a neutron star driven by the electroweak electron-nucleon interaction versus the chiral magnetic effect

We show that the Standard Model electroweak interaction of ultrarelativistic electrons with nucleons ($eN$ interaction) in a neutron star (NS) permeated by a seed large-scale helical magnetic field provides its growth up to $\gtrsim 10^{15}\thinspace\text{G}$ during a time comparable with the ages of young magnetars $\sim 10^4\thinspace\text{yr}$. The magnetic field instability originates from the parity violation in the $eN$ interaction entering the generalized Dirac equation for right and left massless electrons in an external uniform magnetic field. We calculate the averaged electric current given by the solution of the modified Dirac equation containing an extra current for right and left electrons (positrons), which turns out to be directed along the magnetic field. Such current includes both a changing chiral imbalance of electrons and the $eN$ potential given by a constant neutron density in NS. Then we derive the system of the kinetic equations for the chiral imbalance and the magnetic helicity which accounts for the $eN$ interaction. By solving this system, we show that a sizable chiral imbalance arising in a neutron protostar due to the Urca-process $e^-_\mathrm{L} + p\to N + \nu_\mathrm{eL}$ diminishes very rapidly because of a huge chirality flip rate. Thus the $eN$ term prevails the chiral effect providing a huge growth of the magnetic helicity and the helical magnetic field.Comment: 6 pages in Revtex4.1, two columns, 2 eps figures; text was slightly extended, multiple misprints were corrected, some references were added; version published in Phys.Rev.D as a Rapid Communicatio

Dynamical evolution of the chiral magnetic effect: Applications to the quark-gluon plasma

We study the dynamical evolution of the so-called chiral magnetic effect in an electromagnetic conductor. To this end, we consider the coupled set of corresponding Maxwell and chiral anomaly equations, and we prove that these can be derived from chiral kinetic theory. After integrating the chiral anomaly equation over space in a closed volume, it leads to a quantum conservation law of the total helicity of the system. A change in the magnetic helicity density comes together with a modification of the chiral fermion density. We study in Fourier space the coupled set of anomalous equations and we obtain the dynamical evolution of the magnetic fields, magnetic helicity density, and chiral fermion imbalance. Depending on the initial conditions we observe how the helicity might be transferred from the fermions to the magnetic fields, or vice versa, and find that the rate of this transfer also depends on the scale of wavelengths of the gauge fields in consideration. We then focus our attention on the quark-gluon plasma phase, and analyze the dynamical evolution of the chiral magnetic effect in a very simple toy model. We conclude that an existing chiral fermion imbalance in peripheral heavy ion collisions would affect the magnetic field dynamics, and consequently, the charge dependent correlations measured in these experiments.Comment: 41 pages, 14 figures, 3 appendices. Version 2: new global structure (appendix added), more explanations and additional references. Version accepted for publication in Physical Review D journa