Normal ground state of dense relativistic matter in a magnetic field

Abstract

The properties of the ground state of relativistic matter in a magnetic field are examined within the framework of a Nambu-Jona-Lasinio model. The main emphasis of this study is the normal ground state, which is realized at sufficiently high temperatures and/or sufficiently large chemical potentials. In contrast to the vacuum state, which is characterized by the magnetic catalysis of chiral symmetry breaking, the normal state is accompanied by the dynamical generation of the chiral shift parameter $\Delta$. In the chiral limit, the value of $\Delta$ determines a relative shift of the longitudinal momenta (along the direction of the magnetic field) in the dispersion relations of opposite chirality fermions. We argue that the chirality remains a good approximate quantum number even for massive fermions in the vicinity of the Fermi surface and, therefore, the chiral shift is expected to play an important role in many types of cold dense relativistic matter, relevant for applications in compact stars. The qualitative implications of the revealed structure of the normal ground state on the physics of protoneutron stars are discussed. A noticeable feature of the $\Delta$ parameter is that it is insensitive to temperature when $T \ll \mu_0$, where $\mu_0$ is the chemical potential, and {\it increases} with temperature for $T > \mu_0$. The latter implies that the chiral shift parameter is also generated in the regime relevant for heavy ion collisions.