Fermion-field nontopological solitons. II. Models for hadrons

Abstract

We examine the possibility, and its consequences, that in a relativistic local field theory, consisting of color quarks $q$, scalar gluon $\ensuremath{\sigma}$, color gauge field ${V}_{\ensuremath{\mu}}$, and color Higgs field $\ensuremath{\varphi}$, the mass of the soliton solution may be much lower than any mass of the plane-wave solutions; i.e., the quark mass ${m}_{q}$, the gluon mass ${m}_{\ensuremath{\sigma}}$, etc. There appears a rather clean separation between the physics of these low-mass solitons and that of the high-energy excitations, in the range of ${m}_{q}$ and ${m}_{\ensuremath{\sigma}}$, provided that the parameters $\ensuremath{\xi}\ensuremath{\equiv}{(\frac{\ensuremath{\mu}}{{m}_{q}})}^{2}$ and $\ensuremath{\eta}\ensuremath{\equiv}\frac{\ensuremath{\mu}}{{m}_{\ensuremath{\sigma}}}$ are both \ensuremath{\ll}1, where $\ensuremath{\mu}$ is an overall low-energy scale appropriate for the solitions [but the ratio $\frac{\ensuremath{\eta}}{\ensuremath{\xi}}$ is assumed to be $O(1)$, though otherwise arbitrary]. Under very general assumptions, we show that, independently of the number of parameters in the original Lagrangian, the mathematical problem of finding the quasiclassical soliton solutions reduces, through scaling, to that of a simple set of two coupled first-order differential equations, neither of which contains any explicit free parameters. The general properties and the numerical solutions of this reduced set of differential equations are given. The resulting solitons exhibit physical characteristics very similar to those of a "gas bubble" immersed in a "medium": there is a constant surface tension and a constant pressure exerted by the medium on the gas; in addition, there are the "thermodynamical" energy of the gas and the related gas pressure, which are determined by the solutions of the reduced equations. Both a SLAC-type bag and the Creutz-Soh version of the MIT bag may appear, but only as special limiting cases. These soliton solutions are applied to the physical hadrons; their static properties are calculated and, within a 10-15% accuracy, agree with observations.