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

TL;DR

This paper explores the relationship between Majorana phases and the geometric parameters of leptonic unitarity triangles within two-texture zero neutrino mass models, revealing that Majorana phases depend on specific triangle angles and indicating inherent CP violation.

Contribution

It establishes analytical relations connecting Majorana phases to geometric parameters of leptonic unitarity triangles in two-texture zero neutrino mass models, highlighting their dependence on specific interior angles.

Findings

Majorana phases depend on one specific angle of the LUT in each model class.

Non-zero areas of LUT indicate the presence of CP violation.

Constructed LUTs for classes A, B, and C demonstrate geometric features related to CP violation.

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.