Neutrino Phenomenology in a Model with Generalized CP symmetry within Type-I seesaw framework

We investigate the consequences of generalized CP (GCP) symmetry within the context of the two Higgs doublet model (2HDM), specifically focusing on the lepton sector. Utilizing the Type-I seesaw framework, we study an intriguing connection between the Dirac Yukawa couplings originating from both Higgs fields, leading to a reduction in the number of independent Yukawa couplings and simplifying the scalar and Yukawa sectors when compared to the general 2HDM. The CP3 constraint results in two right-handed neutrinos having equal masses and leads to a diagonal right-handed Majorana neutrino mass matrix. Notably, CP symmetry experiences a soft break due to the phase associated with the vacuum expectation value of the second Higgs doublet. The model aligns well with observed charged lepton masses and neutrino oscillation data, explaining both masses and mixing angles, and yields distinct predictions for normal and inverted neutrino mass hierarchies. It features a novel interplay between atmospheric mixing angle $\theta_{23}$ and neutrino mass hierarchy: the angle $\theta_{23}$ is below maximal for the normal hierarchy and above maximal for inverted hierarchy. Another interesting feature of the model is inherent CP violation for the inverted hierarchy.