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Register a new userScotogenic $A_4$ Neutrino Model for Nonzero $theta_{13}$ and Large $delta_{CP}$
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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.
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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. $|tan delta_{CP}| > 1.3$.
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 $delta_{CP}$.
Modular symmetries have been impeccable in neutrino and quark sectors. This motivated us, therefore, to propose a variant of scotogenic model based on modular $A_4$ symmetry to realize the neutrino mass generation at one-loop level through radiative mechanism. Alongside, the lepton flavour violating process $mu to e gamma$ and the muon $g-2$ anomaly are also addressed. The lightest Majorana fermions turn out to be potential dark matter candidates, made stable by suitable assignment of modular weights. The relic density of the same has been computed with annihilations mediated by inert scalars and new $U(1)$ gauge boson.
The Daya Bay, RENO, and Double Chooz experiments have discovered a large non-zero value for $theta_{13}$. We present a global analysis that includes these three experiments, Chooz, the Super-K atmospheric data, and the $ u_mu rightarrow u_e$ T2K and MINOS experiments that are sensitive to the hierarchy and the sign of $theta_{13}$. We report preliminary results in which we fix the mixing parameters other than $theta_{13}$ to those from a recent global analysis. Given there is no evidence for a non-zero CP violation, we assume $delta=0$. T2K and MINOS lie in a region of $L/E$ where there is a hierarchy degeneracy in the limit of $theta_{13}rightarrow 0$ and no matter interaction. For non-zero $theta_{13}$, the symmetry is partially broken, but a degeneracy under the simultaneous exchange of both hierarchy and the sign of $theta_{13}$ remains. Matter effects break this symmetry such that the positions of the peaks in the oscillation probabilities maintain the two-fold symmetry, while the magnitude of the oscillations is sensitive to the hierarchy. This renders T2K and NO$ u$A, with different baselines and different matter effects, better able in combination to distinguish the hierarchy and the sign of $theta_{13}$. The large value of $theta_{13}$ yields effects from atmospheric data that distinguish hierarchies. We find for normal hierarchy, positive $theta_{13}$, $sin^22theta_{13}=0.090pm0.020$ and is 0.2% probable it is the correct combination; for normal hierarchy, negative $theta_{13}$, $sin^22theta_{13}=0.108pm0.023$ and is 2.2% probable; for inverse hierarchy, positive $theta_{13}$, $sin^22theta_{13}=0.110pm0.022$ and is 7.1% probable; for inverse hierarchy, negative $theta_{13}$, $sin^22theta_{13}=0.113pm0.022$ and is 90.5% probable, results that are inconsistent with two similar analyses.
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.
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