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Three Higgs Doublet Model and an A_4 Symmetry

Three Higgs Doublet Model and an A_4 Symmetry. V. Pleitez , J. C. Montero and A. C. B. Machado IFT-Unesp. Outlook. 1. Motivation 2. Proposal 3. Results 4. Final Remarks. Motivation. THE FLAVOUR PROBLEM:.  Why do weak isospin partners have different masses?.

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Three Higgs Doublet Model and an A_4 Symmetry

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  1. Three Higgs Doublet Model and an A_4 Symmetry V. Pleitez, J. C. Montero and A. C. B. Machado IFT-Unesp

  2. Outlook 1. Motivation 2. Proposal 3. Results 4. Final Remarks

  3. Motivation THE FLAVOUR PROBLEM:  Why do weak isospin partners have different masses?  Why are quark and lepton masses split?  Why is there a mass hierarchy between generations? • Whyisthere a hierarchy in the quark mixingbutnot in • thelepton sector? In the SM with only 1 Higgs scalar doublet the fermion mass and mixing matrices remain arbitrary.

  4. Motivation Multi-Higgs models are more predictive scenarios. [Porto and Zee ``private Higgs Bosons´´ PLB666, 491 (2008) Machado & Pleitez PLB674, 223 (2009)]. However, when building a multi-Higgs model, the scalar potential has to be specified and analyzed. Any model with two Higgs doublets has 14 free parameters, which make the minimization hard to be worked out in detail. The number of free parameters in the potential grows fast as the number of Higgs multiplets increases.

  5. Motivation With additional symmetries introduced in the model, it is possible to reduce the number of free parameters, what makes the potential a little simpler. The symmetries could be discrete or continous, Abelian or non- Abelian. The full list of symmetries that can be imposed on the scalar potential of multi-Higgs are unknow. Multi Higgs extension of the SM: we turn the problem upside down the fermion mass matrices become of the form M=_i (_i)<_i> M=f<>+... Machado & Pleitez, PLB674, 223 (2009)

  6. Proposal We consider here the mass spectrum of a scalar potential with three Higgs doublets and a discrete symmetry, the A_4 symmetry. The extra symmetry are the same that are useful for Expleiningt the fermion masses and mixing. We present the scalar sector in three different situations. In one of them there are no light scalars, but in the others, if the A4 symmetry is softly broken, one light scalar field survives.

  7. The scalar potential The scalar potential invariant under A_4 and the SM symmetries:

  8. The scalar potential Explicitly:

  9. Results From the constraint eqs. which minimize the scalar potential:

  10. Results

  11. Results

  12. Final Remarks Under some conditions, in a model with three scalar doublets and with A_4 symmetry, the scalar mass spectrum may have no light scalar even if some of the VEVs are smaller than the electroweak energy scale. In cases where light scalars are unavoidable at tree level, these fields may be safe, from the phenomenological point of view, since they couple mainly to neutrinos and/or they become heavier due to quantum corrections. Also, the imaginary partners are heavier and cannot be produced at LEP energies. For more details see Machado et al arXiv:1011.5855

  13. In the context of the model of PLB674, 223 (2009), 3 doublet is realistic in the charged lepton sector, however, for the quark sector the case of 6 doublet and a singlet is more reallistic.

  14. GRACIAS!

  15. 22 doublets 1 complex singlet, 3 triplets: 57 parameters!

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