Predictive $S_4$ flavon model with ${\text{TM}}_1$ mixing and baryogenesis through leptogenesis

Abstract

We use $S_4$ discrete group to construct a neutrino flavour model which leads to $T{M}_1$ mixing and is consistent with the neutrino oscillation data. Using the model's constrained parameter space, we predict the values of Dirac $CP$ phase and the light neutrino mass as $-1<\sin \delta <-0.9$ and $1.7<m_1(\text{meV})<5.5$ respectively. We thoroughly examine the usefulness of this model in explaining the observed baryon asymmetry of the Universe. Near-maximal breaking of CP symmetry (arising due to the ${\text{TM}}_1$ constraint) helps us in generating adequate baryon asymmetry through leptogenesis. We study the evolution of the asymmetry (generated due to the decay of the heavy Majorana neutrinos) starting from the primordial Universe in two different ways (i)explicitly solving network of Boltzmann equations, (ii) using approximate analytic solution and we have shown the extent of their equivalence. Nearly accurate analytical fits are used thereafter to evaluate baryon asymmetry for the whole parameter space allowed by $3\sigma$ global fit of oscillation data and to impose a constraint on the yet unbounded mass scale parameter of Dirac neutrino mass matrix. Furthermore, significant contribution of $N_2$ decay in the context of flavoured leptogenesis is also estimated.

arXiv comment49 pages, 12 figures, two more subsections (Construction of the flavon potentials and CP asymmetry parameters in terms of Casas Ibarra parametrization) have been added in the appendix, version published in JHEP

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• Baryon asymmetry and lower bound on right handed neutrino mass in fast expanding Universe: an analytical approach
• Simiplified textures of the seesaw model for the trimaximal neutrino mixings
• Symmetries of stationary points of the $G$-invariant potential and the framework of the auxiliary group
• ${\text{TM}}_1$ neutrino mixing with $\sin {\theta }_{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}$