Abstract
We propose a simple U(2) model of flavor compatible with an SU(5) GUT structure. All hierarchies in fermion masses and mixings arise from powers of two small parameters that control the U(2) breaking. In contrast to previous U(2) models this setup can be realized without supersymmetry and provides an excellent fit to all SM flavor observables including neutrinos. We also consider a variant of this model based on a D6 × U(1)F flavor symmetry, which closely resembles the U(2) structure, but allows for Majorana neutrino masses from the Weinberg operator. Remarkably, in this case one naturally obtains large mixing angles in the lepton sector from small mixing angles in the quark sector. The model also offers a natural option for addressing the Strong CP Problem and Dark Matter by identifying the Goldstone boson of the U(1)F factor as the QCD axion.
Highlights
Yukawas arise from powers of these small order parameters
In contrast to previous U(2) models this setup can be realized without supersymmetry and provides an excellent fit to all SM flavor observables including neutrinos
A more recent study has been performed in ref. [6], which has shown that the problematic relation can be fixed by taking flavor quantum numbers compatible only with an SU(5) GUT structure
Summary
We consider an extension of the SM with a global flavor symmetry group U(2)F. Locally this group is isomorphic to SU(2)F × U(1)F , under which SM fermions are charged. One can perturbatively diagonalize the Yukawa matrices, and obtain the following estimates for singular values and CKM matrix elements (neglecting O(1) coefficients): yu ∼ ε4χ/ε2φ , yc ∼ ε2φ , yt ∼ 1 , yd ∼ ye ∼ ε4χ/ε2φ , ys ∼ yμ ∼ ε2φεχ/ ε2φ + ε2χ , yb ∼ yτ ∼ ε2φ + ε2χ , Vub ∼ ε2χ/εφ , Vcb ∼ εφ , Vus ∼ ε2χ/ε2φ These expressions can be compared to the (1σ) ranges for fermion mass ratios and CKM elements, taken for definiteness at 10 TeV mu ≈ λ(7.1÷7.7) , mt mc ≈ λ3.5 , mt md ≈ λ(4.2÷4.4) , mb ms ≈ λ(2.4÷2.5) , mb me ≈ λ5.1 , mτ mμ ≈ λ1.8 , mτ. This is the reason why here this angle is taken to be large, sR23d ∼ cR23d ∼ 1/ 2, which allows to obtain an excellent fit to CKM angles as we demonstrate (see refs. [4, 6, 7])
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