Dibaryon Condensate in Nuclear Matter and Neutron Stars: Exact Analysis in One-dimensional Models

Phase transitions of nuclear matter to the quark-gluon plasma with subsequent restoration of chiral symmetry have been widely discussed in the literature. We investigate the possibility for occurrence of dense nuclear matter with a dibaryon Bose-Einstein condensate as an intermediate state below the quark-gluon phase transition. An exact analysis of this state of matter is presented in a one-dimensional model. The analysis is based on a reduction of the quantization rules for the N -body problem to N coupled algebraic transcendental equations. We observe that when the Fermi momentum approaches the resonance momentum, the one-particle distribution function increases near the Fermi surface. When the Fermi momentum is increased beyond the resonance momentum, the equation of state becomes softer. The observed behavior can be interpreted in terms of formation of a Bose-Einstein condensate of twofermion resonances (e.g. dibaryons). In cold nuclear matter, it should occur at 2(mN +εF ) ≥ mD where mN and mD are the nucleon and dibaryon masses and εF is the nucleon Fermi energy.