Deviation from tri-bimaximal mixings in two types of inverted hierarchical neutrino mass models

An attempt is made to explore the possibility for deviations of solar mixing angle ($\theta_{12}$) from tri-bimaximal mixings, without sacrificing the predictions of maximal atmospheric mixing angle ($\theta_{23}=\pi/4$) and zero reactor angle ($\theta_{13}=0$). We find that the above conjecture can be automatically realised in the inverted hierarchical neutrino mass model having 2-3 symmetry, in the basis where charged lepton mass matrix is diagonal. For the observed ranges of $\bigtriangleup m^2_{21}$ and $\bigtriangleup m^2_{23]$, we calculate the predictions on $\tan^2\theta_{12}=0.5, 0.45, 0.35$ for different input values of the parameters in the neutrino mass matrix. We also observe a possible crossing over from one type of inverted hierarchical model having same CP parity (Type-IHA) to other type having opposite CP parity (Type-IHB). Such neutrino mass matrices can be obtained from the canonical seesaw formula using diagonal form of Dirac neutrino mass matrix and non-diagonal texture of right-handed Majorana mass matrix, and may have important implications in model building using discrete as well as non-abelian symmetry groups.