Chiral symmetry and pion condensation. I. Model-dependent results

Abstract

The successes of current algebra and partial conservation of axial- vector current can be interpreted as indications that the strong interactions are approximately symmetric under chiral Su(2) times SU(2) transformations. In the absence of matter, the explicit chiral-symmetry breaking defines a unique vacuum state for the theory. The smallness of the chiral-symmetry breaking, however, implies the existence of many other states, approximately degenerate in energy with, but orthogonal to, the true vacuum. In these states, in general does not equal 0; thus they contain a ''pion condensate.'' In a macroscopic system - such as a neutron star - at very high baryon density one of these pion- condensed states might become the true ground state. We study this phenomenon in the linear sigma model. We are able to calculate analytically the ''phase diagram'' describing the ground state of infinite nuclear matter as a function of baryon density. Above a critical baryon density a phase transition to a pion- condensed ground state occurs. We extend the chiral-symmetry approach to include the effects of the N* (1236) and the ill-understood $gamma$-N s waves. In addition to analyzing the ground state, we examine the spectrum of excited states. In themore » condensed phase, the meson excitation spectrum contains a ''Goldstone boson'' associated with the ground state's not being an eigenstate of the conserved operator I$sub 3$. However, when electromagnetic interactions are included, this mode disappears via the Higgs phenomenon indicating that the ground state is a superconductor. The presence of the pion condensate fosters the $beta$ decay of the fermion excitations, and the emitted neutrinos provide the cooling mechanism for neutron stars.« less