^{1}

^{,*}

^{2}

^{,†}

^{2}

^{,‡}

^{3}.

We study the possibility of generating nonzero reactor mixing angle

Observations of tiny but nonzero neutrino mass and large leptonic mixing

Global fit

The standard model (SM) of particle physics, in spite of its astonishing success as a low energy theory of fundamental particles and their interactions (except gravity), cannot explain the origin of neutrino mass at renormalizable level. Because of the absence of right-handed neutrinos, there is no coupling of the Higgs field responsible for the origin of mass, with neutrinos. Even if right-handed neutrinos are introduced, one requires a Yukawa coupling with the Higgs boson of the order of

Apart from the issue of tiny neutrino mass and large leptonic mixing, another serious drawback of the SM is its inability to explain the observed baryon asymmetry of the Universe. The observed baryon asymmetry is often quoted as the baryon to photon ratio

Motivated by this, we study an

This paper is organized as follows. In Sec.

The discrete group

Fields and their transformation properties under

Choosing a more general vacuum alignment

It should be noted that we have used the

As pointed out by Fukugita and Yanagida

Decay modes of right-handed neutrino in type I seesaw.

The lepton asymmetry can be found from the following formula

As discussed before, the most general form of Dirac neutrino mass matrix (assuming a degenerate right-handed neutrino mass spectrum) can give rise to a light neutrino mass matrix from type I seesaw formula, which is consistent with

For the numerical analysis part we first fix the scale of leptogenesis by fixing the leading right-handed neutrino mass or the parameter

The leptonic mixing matrix can be written in terms of the charged lepton diagonalizing matrix

For a fixed value of right-handed neutrino mass, we can now compare the light neutrino mass matrix predicted by the model and the one calculated from the light neutrino parameters. Since there are four undetermined complex parameters of the model, we need to compare four elements. Without any loss of generality, we equate

After finding the model parameters

Following the procedures outlined in the previous section, we first randomly generate the light neutrino parameters in their

Correlation between different model parameters for normal hierarchy. The label Gen refers to the most general structure of the mass matrix discussed in the text.

Model parameters as a function of the lightest neutrino mass for normal hierarchy. The label Gen refers to the most general structure of the mass matrix discussed in the text.

Correlation between different model parameters for inverted hierarchy. The label Gen refers to the most general structure of the mass matrix discussed in the text.

Model parameters as a function of the lightest neutrino mass for inverted hierarchy. The label Gen refers to the most general structure of the mass matrix discussed in the text.

Model parameters as a function of one of the Majorana phases

We also check if there are any correlations among the known neutrino parameters in this analysis. This could arise due to the fact that there are only four parameters

Real and imaginary parts of the model parameters for normal hierarchy with the most general structure of the mass matrix discussed in the text.

Real and imaginary parts of the model parameters for inverted hierarchy with the most general structure of the mass matrix discussed in the text.

After finding the allowed neutrino as well as model parameters from the requirement of satisfying the latest neutrino oscillation data, we feed them to the calculation of the baryon asymmetry through resonant leptogenesis. The resulting values of

Baryon asymmetry as a function of model parameters for normal hierarchy. The horizontal pink line corresponds to the Planck bound

Baryon asymmetry as a function of model parameters for inverted hierarchy. The horizontal pink line corresponds to the Planck bound

Baryon asymmetry as a function of Dirac

Baryon asymmetry as a function of Majorana

Here we note that there is a difference of around 9 orders of magnitudes between the mass splitting between the right-handed neutrinos (of keV order) and their masses (of TeV order). Although in this model we have generated such tiny mass splitting naturally, by forbidding it at leading order and generating it only at higher orders (mass splitting term is suppressed by

In the most general case discussed above, the light neutrino mass matrix derived from the type I seesaw formula turns out to break

We suitably modify the field content to arrive at a more realistic

Fields and their transformation properties under

We have studied an extension of the standard model by discrete flavor symmetry

After finding the model and neutrino parameters consistent with the basic setup, we then feed the allowed parameters to the resonant leptogenesis formulas and calculate the baryon asymmetry of the Universe. We find that both the normal and inverted hierarchical scenarios can satisfy the Planck 2015 bound on baryon asymmetry