Simiplified textures of the seesaw model for the trimaximal neutrino mixings

In the seesaw framework, in the basis of $M^{}_{\rm R}$ being diagonal, we explore the simplified textures of $M^{}_{\rm D}$ that can naturally yield the trimaximal neutrino mixings and their consequences for the neutrino parameters and leptogenesis. We first formulate the generic textures of $M^{}_{\rm D}$ that can naturally yield the trimaximal mixings and then examine if their parameters can be further reduced. Our analysis is restricted to the simple but instructive scenario that there is only one phase parameter $\phi$ responsible for both the CP violating effects at low energies and leptogenesis. Our attention is paid to the textures of $M^{}_{\rm D}$ that possess some vanishing or equal elements. On the basis of these results, we further examine if $\phi$ can also take a particular value. The consequences of the phenomenologically-viable simplified textures for the neutrino parameters and leptogenesis are studied. A concrete flavor-symmetry model that can realize one representation of them is given.