Predictions of modular symmetry fixed points on neutrino masses, mixing, and leptogenesis

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.