The general two higgs doublet model can neither give masses to neutrinos without considering a see-saw mechanism nor it can unify gravity with other three forces. To explain dark matter also we have to introduce extra symmetry to the theory. Then why do we need this theory?

  • $\begingroup$ What do you mean by "need"? If you mean how it is motivated, one motivation is that supersymmetric versions of the standard model come with at least two doublets. E.g. when you remove all superpartners from the MSSM you have a 2-Higgs doublet model. $\endgroup$ – user178876 Apr 18 at 4:40
  • $\begingroup$ Thank you.. My question is what we can do using this model? $\endgroup$ – Manas Saikia Apr 18 at 5:32

The main motivations are (see e.g., 1106.0034):

  • Two Higgs doublets are required in supersymmetric models as the superpotential must be holomorphic and to avoid triangle anomalies (see e.g., 9709356).
  • Two Higgs doublets could introduce extra sources of CP-violation, an ingredient for baryogenesis (see Sahkarov's conditions). The CP-violation could be explicit or in fact spontaneous in some more exotic models.
  • Two Higgs doublets could have a richer vacuum structure, with more chances for a strongly first-order phase transition. Such a transition could provide a departure from equilibrium, another ingredient for baryogenesis.
  • It is a simple extension of the SM that doesn't shift the the $\rho$-parameter.

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