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Register a new userNon-Zero $theta_{13}$ and $delta_{CP}$ in a Neutrino Mass Model with $A_4$ Symmetry
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In this paper, we consider a neutrino mass model based on $A_4$ symmetry. The spontaneous symmetry breaking in this model is chosen to obtain tribimaximal mixing in the neutrino sector. We introduce $Z_2 times Z_2$ invariant perturbations in this model which can give rise to acceptable values of $theta_{13}$ and $delta_{CP}$. Perturbation in the charged lepton sector alone can lead to viable values of $theta_{13}$, but cannot generate $delta_{CP}$. Perturbation in the neutrino sector alone can lead to acceptable $theta_{13}$ and maximal CP violation. By adjusting the magnitudes of perturbations in both sectors, it is possible to obtain any value of $delta_{CP}$.
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Assuming that neutrinos acquire radiative seesaw Majorana masses through their interactions with dark matter, i.e. scotogenic from the Greek scotos meaning darkness, and using the non-Abelian discrete symmetry $A_4$, we propose a model of neutrino masses and mixing with nonzero $theta_{13}$ and necessarily large leptonic CP violation, allowing both the normal and inverted hierarchies of neutrino masses, as well as quasi-degenerate solutions.
In a new simple application of the non-Abelian discrete symmetry $A_4$ to charged-lepton and neutrino mass matrices, we show that for the current experimental central value of $sin^2 2 theta_{13} simeq 0.1$, leptonic CP violation is necessarily large, i.e. $|tan delta_{CP}| > 1.3$.
Leptonic CP Violating Phase $ delta_{CP} $ in the light neutrino sector and leptogenesis via present matter antimatter asymmetry of the Universe entails each other. Probing CP violation in light neutrino oscillation is one of the challenging tasks today. The reactor mixing angle $ theta_{13} $ measured in reactor experiments, LBL, DUNE with high precision in neutrino experiments indicates towards the vast dimension of scope to detect $ delta_{CP} $. The correlation between leptonic Dirac CPV phase $ delta_{CP} $, reactor mixing angle $ theta_{13} $, lightest neutrino mass $ m_{1} $ and matter antimatter asymmetry of the Universe within the framework of $ mu-tau $ symmetry breaking assuming the type I seesaw dominance is extensively studied here. Small tiny breaking of the $ mu-tau $ symmetry allows a large Dirac CP violating phase in neutrino oscillation which in turn is characterised by awareness of measured value of $ theta_{13} $ and to provide a hint towards a better understanding of the experimentally observed near maximal value of $ u_{mu} - u_{tau} $ mixing angle $ theta_{23}simeq frac{pi}{4}$. Precise breaking of the $ mu-tau $ symmetry is achieved by adding a 120 plet Higgs to the 10 $+$ $bar{126}$ dimensional representation of Higgs. The estimated three dimensional density parameter space of lightest neutrino mass $ m_{1} $, $ delta_{CP} $, reactor mixing angle $ theta_{13} $, is constrained here for the requirement of producing the observed value of baryon asymmetry of the Universe through the mechanism of leptogenesis. Carrying out numerical analysis the allowed parameter space of $ m_{1} $, $ delta_{CP} $, $ theta_{13} $, is found out which can produce the observed baryon to photon density ratio of the Universe.
We study the possibility of generating non-zero reactor mixing angle $theta_{13}$ and baryon asymmetry of the Universe within the framework of an $A_4$ flavour symmetric model. Using the conventional type I seesaw mechanism we construct the Dirac and Majorana mass matrices which give rise to the correct light neutrino mass matrix. Keeping the right handed neutrino mass matrix structure trivial so that it gives rise to a (quasi) degenerate spectrum of heavy neutrinos suitable for resonant leptogenesis at TeV scale, we generate the non-trivial structure of Dirac neutrino mass matrix that can lead to the light neutrino mixing through type I seesaw formula. Interestingly, such a setup naturally leads to non-zero $theta_{13}$ due to the existence of anti-symmetric contraction of the product of two triplet representations of $A_4$. Such antisymmetric part of triplet products usually vanish for right handed neutrino Majorana mass terms, leading to $mu-tau$ symmetric scenarios in the most economical setups. We constrain the model parameters from the requirement of producing the correct neutrino data as well as baryon asymmetry of the Universe for right handed neutrino mass scale around TeV. The $A_4$ symmetry is augmented by additional $Z_3 times Z_2$ symmetry to make sure that the splitting between right handed neutrinos required for resonant leptogenesis is generated only by next to leading order terms, making it naturally small. We find that the inverted hierarchical light neutrino masses give more allowed parameter space consistent with neutrino and baryon asymmetry data.
Assuming that the neutrino mass matrix is diagonalized by the tribimaximal mixing matrix, we explore the textures for the charged lepton mass matrix that render an $U_{PMNS}$ lepton mixing matrix consistent with data. In particular we are interested in finding the textures with the maximum number of zeros. We explore the cases of real matrices with three and four zeros and find that only ten matrices with three zeros provide solutions in agreement with data. We present the successful Yukawa textures including the relative sizes of their non-zero entries as well as some new and interesting relations among the entries of these textures in terms of the charged lepton masses. We also show that these relations can be obtained directly from a parametrization of the charged lepton mixing matrix $U_l$.
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