Trilinear self-couplings in an S(3) flavored Higgs model

In this paper, we analyze the Higgs sector of the minimal S(3)-invariant extension of the Standard Model. This extension includes three Higgs SU(2) doublets fields and CP invariant. We compute the Higgs boson physical masses in terms of the potential parameters and the scalar Higgs matrix rotation angles theta(S) and omega(3) (tan theta(P) = tan theta(C) = cot omega(3)). The angles theta(S), theta(P) and theta(C) are related to the scalar, pseudoscalar and charged Higgs matrix rotation respectively. Furthermore, within this model we can also write down in an explicit form the trilinear self-couplings lambda(ijk) in terms of the Higgs masses and two free parameters, theta(S) and omega(3). Moreover, we show that the Higgs masses and trilinear Higgs boson self-couplings are closely linked to the Higgs potential structure given by the discrete symmetry S(3), which can be helpful in distinguishing this model from other extensions. In our analysis the lightest Higgs boson mass is taken to be fixed to 125 GeV. In concordance with the results reported in the literature for other Standard Model extensions, one finds that the numerical values lambda(ijk) of the minimal S(3)-invariant extension of the Standard Model are significantly different from the trilinear Higgs self-coupling of the Standard Model.