Revisiting the fermion-field nontopological solitons

Nontopological fermionic solitons exist across a diverse range of particle physics models and have rich cosmological implications. This study establishes a general framework for calculating fermionic soliton profiles under arbitrary scalar potentials, utilizing relativistic mean field theory to accurately depict the interaction between the fermion condensate and the background scalar field. Within this framework, the conventional "fermion bound states" are revealed as a subset of fermionic solitons. In addition, we demonstrate how the analytical formulae in previous studies are derived as special cases of our algorithm, discussing the validity of such approximations. Furthermore, we explore the phenomenology of fermionic solitons, highlighting new formation mechanisms and evolution paths, and reconsidering the possibility of collapse into primordial black holes.