Feynman rules in the type-III natural flavor-conserving two-Higgs-doublet model.

Abstract

We consider a two-Higgs-doublet model with ${\mathit{S}}_{3}$ symmetry, which implies a \ensuremath{\pi}/2 rather than 0 relative phase between the vacuum expectation values 〈${\mathrm{\ensuremath{\Phi}}}_{1}$〉 and 〈${\mathrm{\ensuremath{\Phi}}}_{2}$〉. The corresponding Feynman rules are derived accordingly and the transformation of the Higgs fields from the weak to the mass eigenstates includes not only an angle rotation but also a phase transformation. In this model, both doublets couple to the same type of fermions and the flavor-changing neutral currents are naturally suppressed. We also demonstrate that the type-III natural flavor-conserving model is valid at the tree level even when an explicit ${\mathit{S}}_{3}$ symmetry-breaking perturbation is introduced to get a reasonable CKM matrix. In the special case \ensuremath{\beta}=\ensuremath{\alpha}, as the ratio tan\ensuremath{\beta}=${\mathit{v}}_{2}$/${\mathit{v}}_{1}$ runs from 0 to \ensuremath{\infty}, the dominant Yukawa coupling will change from the first two generations to the third generation. In the Feynman rules we also find that the charged Higgs currents are explicitly left-right asymmetric. The ratios between the left- and right-handed currents for the quarks in the same generations are estimated.