Constraining the 3HDM parameter space

One of the standard ways to study scenarios beyond the Standard Model involves extending the Higgs Sector. This work examines the Three Higgs Doublet Model (3HDM) in a Type-Z or democratic setup, where each Higgs doublet couples exclusively to a specific type of fermion. The particle spectrum of the 3HDM includes four charged Higgs bosons, two CP-odd scalars, and three CP-even scalars. This work investigates the allowed mass and coupling parameter space in the Type-Z 3HDM after imposing all theoretical and experimental constraints. We extract the allowed parameter space under three distinct alignment-limit conditions or mass hierarchies leveraging machine learning techniques. Specifically, we analyze scenarios where the 125 GeV Higgs is the lightest, an intermediary, or the heaviest CP-even Higgs boson. Our findings indicate that while a single lighter CP-even Higgs boson below 125 GeV still remains a possibility, the presence of two lighter Higgses is ruled out.