Abstract
We point out that, in the context of the SM, $|V^2_{13}| + | V^2_{23}|$ is expected to be large, of order one. The fact that $|V^2_{13}| + |V^2_{23}| \approx 1.6 \times 10^{-3}$ motivates the introduction of a symmetry S which leads to $V_{CKM} ={1\>\!\!\!\mathrm{I}} $, with only the third generation of quarks acquiring mass. We consider two scenarios for generating the mass of the first two quark generations and full quark mixing. One consists of the introduction of a second Higgs doublet which is neutral under S. The second scenario consists of assuming New Physics at a high energy scale , contributing to the masses of light quark generations, in an effective field theory approach. This last scenario leads to couplings of the Higgs particle to $s\overline s$ and $c \overline c$ which are significantly enhanced with respect to those of the SM. In both schemes, one has scalar-mediated flavour- changing neutral currents which are naturally suppressed. Flavour violating top decays are predicted in the second scenario at the level $ \mbox{Br} (t \rightarrow h c ) \geq 5\times 10^{-5}$.
Highlights
The recent discovery of the Higgs particle at the LHC rendered it even more urgent to understand the mechanism responsible for the generation of fermion masses and mixing
We propose a possible way of avoiding this fine-tuning by introducing a symmetry S which leads to VCKM 1⁄4 1, with only the third generation of quarks acquiring mass
In the standard model (SM), without an additional symmetry, the smallness of VCKM mixings cannot be derived from the observed strong hierarchy of quark masses. (ii) We point out that the fact that jV23j2 þ jV13j2 is small may be considered as a hint of nature, suggesting the introduction of a symmetry S
Summary
The recent discovery of the Higgs particle at the LHC rendered it even more urgent to understand the mechanism responsible for the generation of fermion masses and mixing. With respect to question (ii) we consider the possibility that in leading order the SM Higgs only gives mass to the third generation. This is achieved in a natural way through the introduction of a discrete symmetry S which leads to quark mass matrices of rank 1, aligned in flavor space. We conjecture that the generation of the mass of the first two generations arises from a different source If this new source is just another Higgs doublet and if one assumes that the new doublet is neutral with respect to the symmetry S, one is led to a flavor structure analogous to what one. It turns out that the couplings to tt, bbdo not differ much from those in the SM, but the couplings to cc, ssare significantly enhanced with respect to those in the SM
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