Hadronic matter in a nontopological soliton model.

Abstract

We have calculated ground-state properties of hadronic matter in a mean-field approximation to a nontopological soliton model in one spatial dimension. The high-density phase of the model is a free Fermi gas of massless fermions. The low-density phase, on the other hand, is a soliton crystal characterized by spatial density oscillations. For certain values of the parameters there is an additional uniform phase in which the underlying chiral symmetry of the Lagrangian is broken and the fermion mass is dynamically generated. A stability analysis of this uniform phase via linear response theory revealed ground-state instabilities at low density and for strong coupling. These findings were consistent with the predictions obtained by solving the mean-field equations by direct matrix diagonalization. In the weak-coupling limit the soliton crystal is characterized by fermion clustering around regions of strongest attraction (shallow bags). The strong-coupling limit, on the other hand, is reminiscent of the soliton kink solution where fermions are excluded from sectors of strongest attraction and are, instead, concentrated in regions where they are effectively massless.