Thermodynamic Properties of the SU ( 2 ) f Chiral Quark – Loop Soliton

We consider a chiral one-loop hedgehog soliton of the bosonized SU(2) f Nambu & Jona-Lasinio model which is embedded in a hot medium of constituent quarks. Energy and radius of the soliton are determined in self-consistent mean-field approximation. Quasi-classical corrections to the soliton energy are derived by means of the pushing and cranking approaches. The corresponding inertial parameters are evaluated. It is shown that the inertial mass is equivalent to the total internal energy of the soliton. Corrected nucleon and ∆ isobar masses are calculated in dependence on temperature and density of the medium. As a result of the self-consistently determined internal structure of the soliton the scaling between constituent quark mass, soliton mass and radius is noticeably disturbed. Chiral soliton models have proven to be a fruitful approach to the description of nucleon structure. Starting from the Nambu & Jona-Lasinio (NJL) lagrangian [1] and applying a well defined scheme of approximations one was able to obtain stationary and localized field configurations denoted as non-topological chiral one-loop NJL solitons. They can be used to model nucleons, ∆ isobars and strange baryons on the basis of interacting quarks (for review see [2, 3]). The NJL lagrangian incorporates chiral symmetry and its spontaneous breakdown [4]. It has been used to study the restoration of chiral symmetry in a hot and dense nuclear medium modeled by a gas of constituent quarks (for review see [5]). The decrease of the constituent quark mass at higher temperature and/or density of the medium describes the phase transition from the chiral condensate to the chirally symmetric phase. The calculated effects are in satisfactory agreement with the predictions of lattice calculations and of the chiral perturbation theory as well. It is an attractive idea to combine both features of the NJL lagrangian and to study the behavior of a soliton embedded in a hot gas of constituent quarks with a dynamically generated mass. Such a model incorporates the restoration of chiral symmetry and the possible dissolution of the soliton, which simulates the deconfinement transition of hadronic matter. In contrast to many other approaches studying medium modifications the non-topological soliton model equips the baryon with an internal structure which may be modified by the medium. Using this approach as a model for baryons in hot hadronic matter one should be aware of its approximative character which is even not free of inconsistencies. Below the critical values of temperature and …