Predictions of Modular Symmetry Fixed Points on Neutrino Masses, Mixing, and Leptogenesis

Abstract

In recently proposed framework of non-holomorphic modular symmetry introduces the concept of negative and zero modular weight of Yukawa couplings. These Yukawa couplings are function of complex modulus $τ$, which is responsible for the CP asymmetry produced during leptogenesis. In this work, we restrict the $τ$ on the fixed points of modular symmetry rather than its fundamental domain in such manner Yukawa couplings are also get fixed. We have adopt this framework and propose a type III seesaw mechanism. The model is tested against neutrino oscillation data through a $χ^2$ analysis using NuFIT~6.1. To test the stability of these predictions, we also analyze regions near each fixed point by introducing a deviation $τ\rightarrow τ_{\rm fixed}(1 + εe^{iφ})$ with $ε\in (0,0.1)$ and $φ\in (-π,π)$. Our results show that certain fixed points, along with their nearby regions, are capable of producing viable neutrino phenomenology while also generating the observed baryon asymmetry of the Universe.

Figures (6)

• Figure 1: Correlation between mixing angles, real and imaginary part of $\tau$, Jarlskog invaraint , Dirac-type CP phase, CP invariants are shown. Additionally effective majorana mass with respect to lightest neutrino mass and sum of neutrino mass is also presented with minimum chi square at 0.072 for nearby fixed point $\tau = \frac{3+i}{2}$ for NH
• Figure 2: Correlation between mixing angles, real and imaginary part of $\tau$, Jarlskog invariant, Dirac-type CP phase, CP invariants are shown. Additionally effective majorana mass with respect to lightest neutrino mass and sum of neutrino mass is also presented with minimum chi square at 0.14 for nearby fixed point $\tau = 1$
• Figure 3: Correlation between mixing angles, real and imaginary part of $\tau$, Jarlskog invariant, Dirac-type CP phase, CP invariants are shown. Additionally effective majorana mass with respect to lightest neutrino mass and sum of neutrino mass is also presented with minimum chi square at 0.10 for nearby fixed point $\tau = -1$
• Figure 4: Evolution of comoving number density of $\Sigma_1$(Left) and B-L asymmetry (right) as a function of $z = M_{\Sigma_1}/T$ are shown for nearby fixed point $\tau = \frac{3+i}{2}$.
• Figure 5: Evolution of comoving number density of $\Sigma_1$(Left) and B-L asymmetry (right) as a function of $z = M_{\Sigma_1}/T$ are shown for nearby fixed point $\tau = 1$.