Phenomenology of an extended $$1+2$$ Higgs doublet model with $$S_3$$ family symmetry

Abstract In order to explain the mass hierarchy and mixing pattern in the leptonic sector, we explore an extension of the Standard Model whose scalar sector includes one active and two inert doublets as well as some scalar singlets. The model includes a $$S_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> family symmetry supplemented by extra cyclic symmetries. As a consequence of our construction, a Dark Matter (DM) candidate is predicted and its properties are consistent with the observed cosmic abundances and the constraints imposed by direct and indirect detection experiments. The model allows Charged Lepton Flavor Violation (CLFV) processes like $$\mu \rightarrow e\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>→</mml:mo> <mml:mi>e</mml:mi> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> and $$\mu \rightarrow 3e$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>→</mml:mo> <mml:mn>3</mml:mn> <mml:mi>e</mml:mi> </mml:mrow> </mml:math> , but the predicted branching ratios align with experimental limits. Additionally, our analysis elucidates the generation of the active neutrino masses through a one-loop radiative seesaw mechanism matching the observed neutrino oscillation data. The model agrees with experimental data on Higgs Diphoton decay rates and on oblique parameters.