Abstract
In the context of two Higgs doublet models, we study the conditions required in order to have stable quasi-alignment in flavour space. We show that stability under the renormalisation group equations imposes strong constraints on the flavour structure of the Yukawa couplings associated to each one of the Higgs doublets. In particular, we find a novel solution, where all Yukawa couplings are proportional to the so-called democratic matrix. This solution is rather unique, since it is the only stable solution which is a good starting point for reproducing the observed pattern of quark masses and mixing. We also show that this stable solution can be obtained by imposing on the Lagrangian a \(Z_3 \times Z^\prime _3\) flavour symmetry. Quark masses of the lighter quark generations are generated through the breaking of this discrete symmetry, and, at this stage, scalar-mediated flavour-changing neutral-currents arise, but they are naturally suppressed by the smallness of the light quark masses. In this way, we relate Higgs alignment to the hierarchy of the quark masses through a discrete family symmetry.
Highlights
(i) Glashow and Weinberg [4] have pointed out that one can avoid flavour-changing neutral-currents (FCNCs) at tree level by introducing a Z2 symmetry under which the two Higgs doublets transform differently
(iii) Another possibility has been proposed some time ago [12] by Branco, Grimus and Lavoura (BGL) who have pointed out that there is a symmetry which, when imposed on the Lagrangian, constrains the Yukawa couplings in such a way that FCNCs do arise at tree level, but are entirely determined by the VCKM matrix, with no other free parameters
Assuming that the Yukawa couplings of the two Higgs doublets are aligned, i.e., proportional to each other, we study under what conditions the alignment is maintained by the renormalisation group
Summary
(i) Glashow and Weinberg [4] have pointed out that one can avoid FCNCs at tree level by introducing a Z2 symmetry under which the two Higgs doublets transform differently. BGL models have been extended to the leptonic sector [13], their relation to minimal flavour violation models has been studied [14] and their phenomenological implications have been recently analysed [15,16,17] This is not a complete list of possible schemes to avoid large FCNC in 2HDM, some other plausible solutions consist in postulating concrete Yukawa structures, such as the renowned Cheng and Sher [18] ansatz, or in decoupling the heavy Higgs states. One obtains in this framework, a quasi-alignment of the Yukawa couplings, as a result of the Z3 × Z3 symmetry, together with the strong hierarchy of quark masses. We do not introduce neutrino masses since these are not relevant for our analysis
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