A bstract In this research, we investigate the vacuum structure of an extended standard model with a U(1) D global symmetry. The scalar sector consists of two SU(2) doublets as well as one complex singlet and one real singlet, resulting in a more complicated vacuum structure compared to that of the Standard Model. We analyze various theoretical constraints, including the conditions for being bounded from below, the existence of a global minimum, and perturbativity up to the Planck scale. Additionally, we consider experimental constraints from the Higgs invisible decay. Through a detailed statistical analysis using numerical methods, we show that the extended scalar potential can accommodate a stable vacuum while satisfying both theoretical and experimental constraints for a small region of the parameter space.
Nagao et al. (Thu,) studied this question.