Baryons in the Nambu–Jona-Lasinio models

The octet and decuplet <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:msub> <a:mrow> <a:mo>(</a:mo> <a:mn>3</a:mn> <a:mo>)</a:mo> </a:mrow> <a:mi>f</a:mi> </a:msub> </a:mrow> </a:math> baryons are studied with the Polyakov, Nambu, and Jona-Lasinio model, in a diquark-quark approach, via the resolution of the Bethe-Salpeter equation. This work includes estimations of their masses according to the temperature and the baryonic density, with or without the isospin symmetry. Several improvements of this modeling are proposed and tested: the treatment of the baryons' unstable regime, the inclusion of the diquark momentum dependence, the possibility to model baryons without the static approximation, the description of the octet baryons via scalar and axial flavor components, and the use of a Nambu and Jona-Lasinio diquark propagator instead of a structureless one. The effects of the color superconductivity on the nucleon mass are also investigated. Certain of the mentioned improvements can be applied simultaneously. The advantages and limitations of each of them are highlighted.