Fermion masses and mixings in aμ-τsymmetricSO(10)

Abstract

Thesymmetry imposed on the neutrino mass matrix in the flavor basis is known to be quite predictive. We integrate this very specific neutrino symmetry into a more general framework based on the supersymmetric SOð10Þ grand unified theory. As in several other models, the fermion mass spectrum is determined by Hermitian mass matrices resulting from the renormalizable Yukawa couplings of the 16plet of fermions with the Higgs fields transforming as 10, 126, and 120 representations of the SOð10Þ group. Thesymmetry is spontaneously broken through the 120-plet. Consequences of this scheme are considered for fermion masses using both a type-I and a type-II seesaw mechanism. This scenario is shown to lead to a generalized CP invariance of the mass matrices and vanishing CP violating phases if the Yukawa couplings are invariant under thesymmetry. Small explicit breaking of thesymmetry is then shown to provide a very good understanding of all of the fermion masses and mixing. Detailed fits to the fermion spectrum are presented in several scenarios. One obtains a very good fit to all observables in the context of the type-I seesaw mechanism, but the type-II seesaw model also provides a good description except for the overall scale of the neutrino masses. Three major predictions on the leptonic mixing parameters in the type-I seesaw case are (i) the atmospheric mixing angle l 23 close to maximal, (ii) l 13 close to the present upper bound, and (iii) a negative but very small Dirac CP violating phase in the neutrino oscillations.

An SO(10) model with adjoint fermions for double seesaw neutrino masses

“…In addition we had imposed a generalized parity symmetry [27] which makes the complex matrices M 0 and M 2 real thereby reducing the number of free parameters. Thus the model that we consider is SO(10)⊗Z 2 µ−τ ⊗Z P 2 [14]. However it is to be mentioned that if we assume exact µ − τ (anti)symmetry in (M 2 ) M 0 then a generalized CP-invariance holds [14] and the CKM matrix comes out as real.…”

“…Thus the model that we consider is SO(10)⊗Z 2 µ−τ ⊗Z P 2 [14]. However it is to be mentioned that if we assume exact µ − τ (anti)symmetry in (M 2 ) M 0 then a generalized CP-invariance holds [14] and the CKM matrix comes out as real. This can be rectified either by assuming some of the vevs to be complex or by allowing a small explicit breaking of µ − τ symmetry in M 0 .…”

“…The 126 H relates the Majorana mass of the neutrinos to the Dirac mass as well as other charged fermion masses making the model predictive. It is also possible and in some cases advantageous to include all the three Higgs representations [13,14]. The model with 10 H + 120 H [15,16], on the other hand, does not have the requisite scalars to lead to neutrino masses through the seesaw mechanism.…”

“…Small deviation from these exact values may be generated by breaking the µ − τ symmetry by a small amount. Combining µ − τ flavour symmetry with GUTs has been considered in the case of SU (5) in [26] and also for SO(10) [14]. Here we impose µ − τ symmetry on the Yukawa matrix for the 10 H and 16 H whereas the one for 120 H is taken to be antisymmetric.…”

“…We also impose a parity symmetry leading to Hermitian Yukawa matrices. Thus we consider the model SO(10) ⊗ Z (µ−τ ) 2 ⊗ Z P 2 [14]. Imposition of these two symmetries help in reducing the number of unknown parameters in the Yukawa sector.…”