Connecting Majorana phases to the Geometric Parameters of Majorana Unitarity Triangle in a model of Neutrino Mass Matrix

Abstract

We have investigated a possible connection between the Majorana phases and geometric parameters of leptonic unitarity triangle(LUT) in two-texture zero neutrino mass matrix. Such analytical relations can, also, be obtained for other theoretical models viz. hybrid textures, neutrino mass matrix with vanishing minors and have profound implications for geometric description of $CP$ violation. As an example, we have considered two-texture zero neutrino mass model to obtain relation between Majorana phases and LUT parameters. In particular, we find that Majorana phases depend on only one of the three interior angles of LUT in each class of two-texture zero neutrino mass matrix. We have, also, constructed LUT for class $A$, $B$ and $C$ neutrino mass matrices. Non-vanishing areas and nontrivial orientations of these Majorana unitarity triangles indicate non-zero $CP$ violation as a generic feature of this class of mass models.