Proca-Higgs balls and stars in a UV completion for Proca self-interactions

We consider a Proca-Higgs model wherein a complex vector field gains mass via spontaneous symmetry breaking, by coupling to a real scalar field with a Higgs-type potential. This vector version of the scalar Friedberg-Lee-Sirlin model, can be considered as a UV completion of a complex Proca model with self-interactions. We study the flat spacetime and self-gravitating solitons of the model, that we dub Proca-Higgs \textit{balls} and \textit{stars} respectively, exploring the domain of solutions and describing some of their mathematical and physical properties. The stars reduce to the well-known (mini-)Proca stars in some limits. The full model evades the hyperbolicity problems of the self-interacting Proca models, offering novel possibilities for dynamical studies beyond mini-Proca stars.