Abstract
We propose a model of fermion masses and mixings based on SU(5) grand unified theory (GUT) and a D4 flavor symmetry. This is a highly predictive 4D SU(5) GUT with a flavor symmetry that does not contain a triplet irreducible representation. The Yukawa matrices of quarks and charged leptons are obtained after integrating out heavy messenger fields from renormalizable superpotentials while neutrino masses are originated from the type I seesaw mechanism. The group theoretical factors from 24- and 45-dimensional Higgs fields lead to ratios between the Yukawa couplings in agreement with data, while the dangerous proton decay operators are highly suppressed. By performing a numerical fit, we find that the model captures accurately the mixing angles, the Yukawa couplings and the CP phase of the quark sector at the GUT scale. The neutrino masses are generated at the leading order with the prediction of trimaximal mixing while an additional effective operator is required to account for the baryon asymmetry of the universe (BAU). The model is remarkably predictive because only the normal neutrino mass ordering and the lower octant of the atmospheric angle are allowed while the CP conserving values of the Dirac neutrino phase δCP are excluded. Moreover, the predicted values of the effective Majorana mass mββ can be tested at future neutrinoless double beta decay experiments. An analytical and a numerical study of the BAU via the leptogenesis mechanism is performed. We focused on the regions of parameter space where leptogenesis from the lightest right-handed neutrino is successfully realized. Strong correlations between the parameters of the neutrino sector and the observed BAU are obtained.
Highlights
We propose a model of fermion masses and mixings based on SU(5) grand unified theory (GUT) and a D4 flavor symmetry
The neutrino masses are generated at the leading order with the prediction of trimaximal mixing while an additional effective operator is required to account for the baryon asymmetry of the universe (BAU)
We find that for the third family Yukawa coupling we have the well-known b − τ unification; yτ = yb which is still compatible with experimental constraints [33], while for the first two families — instead of the Georgi Jarlskog (GJ) relation — we find alternative GUT predictions with modified CG factors given as ye yd
Summary
We describe the different sectors of our SU(5) × D4 × U(1) GUT proposal and fix some notations. The 45-dimensional Higgs is usually used to produce the GJ relations differentiating between the (2-2) entry of the down quark and charged lepton mass matrices; it has been shown in [33, 34] that there are many other options which are preferred compared to GJ relations. In the down quark and charged lepton sector, four flavon fields denoted as φ, φ, Ω and Φ are needed for D4 × U(1) invariance When these flavons acquire their VEVs, they break the D4 group and lead to appropriate mass matrices of down quarks and charged leptons. The quantum numbers under D4 × U(1) of these five flavons is as depicted in table 3
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