Abstract
We construct a model where the Yukawa couplings of the Standard Model (SM) fermions arise from the breaking of a Z2 symmetry and through mixing with a fourth family of vector-like fermions. By adding a scalar leptoquark, which is an electroweak triplet and odd under the Z2 symmetry, we obtain an explanation for {R}_{K^{left(*right)}} that is linked to the origin of the Yukawa couplings. The coupling of SM fermions to the leptoquark is mediated by the fourth family fermions, and is predicted to be related to CKM entries and mass ratios of SM fermions.
Highlights
JHEP11(2018)100 explain RK(∗), can emerge indirectly due to mixing with the fourth family [18]
We have proposed a simple extension of the Standard Model in table 1 involving a vectorlike fourth family of fermions which are distinguished from the SM fermions by a single Z2 symmetry under which the Higgs doublet is odd, preventing Yukawa couplings, together with a Z2-odd scalar leptoquark S3, and a scalar φ whose vacuum expectation value (VEV) breaks the Z2
The explicit masses of the vector-like fourth family are assumed to be of the same order as the VEV of the φ field
Summary
The model is analogous to the setup in [28], and is defined by the field content and respective symmetry assignments listed in table 1. Due to left-handed messenger dominance, y3u3,d,e dominate over the other entries (due to the contributions with M4Q,L), leading to hierarchical masses for the third family of SM fermions and allowing the use of small angle approximation in diagonalising the Yukawa. The contribution to the CKM mixing angles from the up sector is negligible, and we can take to a reasonable approximation that, in the special basis we are working so far, the up quark Yukawa couplings are already (approximately) diagonal With this reasonable assumption, we are basically considering that the family eigenstate, Q3, contains the top (the mass eigenstate, t) and the down-type counterpart decomposed with CKM elements. The model does account for the smallness of the remaining CKM angles, which are suppressed by the ratio of M4Q/M4dc
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