Simiplified textures of $M^{}_{\rm D}$ in the seesaw model for the trimaximal neutrino mixing

In this paper, in the basis of $M^{}_{\rm R}$ being diagonal, we survey the simplified textures of $M^{}_{\rm D}$ for realizing the trimaximal neutrino mixing and their consequences for the low-energy neutrino observables and leptogenesis. We first formulate the general texture of $M^{}_{\rm D}$ for realizing the trimaximal mixing, and then, following the Occam's razor principle, examine if its parameters can be further reduced, giving more simplified textures of it. Our analysis is restricted to the simple but instructive scenario that there is only one phase parameter $\phi$ responsible for the CP violating effects at low energies and leptogenesis. Our attention is paid to the simplified textures of $M^{}_{\rm D}$ where there are some vanishing elements (a sign of Abelian flavor symmetries) or equalities among non-vanishing elements (a sign of non-Abelian flavor symmetries). On the basis of these simplified textures, we further examine if $\phi$ can also take a particular value (a sign of CP symmetries). The consequences of the phenomenologically-viable simplified textures for the low-energy neutrino observables and leptogenesis are studied.