Precision measurement of the neutrino mixing parameters and the determination of mass hierarchy are the primary goals of the present and upcoming neutrino experiments. In this work, we study the sensitivity of T2K,NO$ u$A and LBNE experiments to disc
over leptonic CP violation and the determination of neutrino mass hierarchy. We obtain the correlation between the CP violating phase $delta_{CP}$ and the mixing angles $theta_{13}$, $theta_{23}$ and the sensitivity to determine the octant of atmospheric mixing angle $theta_{23}$. The entire analysis is done for a total 10 years (5$ u$+ 5$bar u$) of running of T2K, NO$ u$A and LBNE experiments. Furthermore, we also consider the impact of cross section uncertainties on the CP violation sensitivity of LBNE experiment.
With the recent measurement of reactor mixing angle $theta_{13}$ the knowledge of neutrino oscillation parameters that describe PMNS matrix has improved significantly except the CP violating phase $delta_{CP}$. The other unknown parameters in neutrin
o oscillation studies are mass hierarchy and the octant of the atmospheric mixing angle $theta_{23}$. Many dedicated experiments are proposed to determine these parameters which may take at least 10 years from now to become operational. It is therefore very crucial to use the results from the existing experiments to see whether we can get even partial answers to these questions. In this paper we study the discovery potential of the ongoing NO$ u$A and T2K experiments as well as the forthcoming T2HK experiment in addressing these questions. In particular, we evaluate the sensitivity of NO$ u$A to determine neutrino mass hierarchy, octant degeneracy and to obtain CP violation phase after running for its scheduled period of 3 years in neutrino mode and 3 years in anti-neutrino mode. We then extend the analysis to understand the discovery potential if the experiments will run for (5$ u$+5$bar{ u}$) years and (7$ u$+3$bar{ u}$) years. We also show how the sensitivity improves when we combine the data from (3$ u$+3$bar{ u}$) years of NO$ u$A run with (3$ u$+2$bar{ u}$) years of T2K and (3$ u$+7$bar{ u}$) years of T2HK experiments. The CP violation sensitivity is marginal for T2K and NO$ u$A experiments even for ten years data taking of NO$ u$A. T2HK has a significance above 5$sigma$ for a fraction of two-fifth values of the $delta_{CP}$ space. We also find that $delta_{CP}$ can be determined to be better than $35^circ $, $21^circ $ and $9^circ $ for all values of $delta_{CP}$ for T2K, NO$ u$A and T2HK respectively.
Recently, the reactor mixing angle $theta_{13}$ has been measured precisely by Daya Bay, RENO and T2K experiments with a moderately large value. However, the standard form of neutrino mixing patterns such as bimaximal, tri-bimaximal, golden ratio of
types A and B, hexagonal etc., which are based on certain flavor symmetries, predict vanishing $theta_{13}$. Using the fact that the neutrino mixing matrix can be represented as $V_{rm PMNS}=U_l^{dagger} U_ u P_ u$, where $U_l$ and $U_ u$ result from the diagonalization of the charged lepton and neutrino mass matrices and $P_ u$ is a diagonal matrix containing Majorana phases, we explore the possibility of accounting for the large reactor mixing angle by considering deviations both in the charged lepton and neutrino sector. In the charged lepton sector we consider the deviation as an additional rotation in the (12) and (13) planes, whereas in neutrino sector we consider deviations to various neutrino mixing patterns through (13) and (23) rotations. We find that with the inclusion of these deviations it is possible to accommodate the observed large reactor mixing angle $theta_{13}$, and one can also obtain limits on the CP violating Dirac phase $delta_{CP}$ and Jarlskog invariant $J_{CP}$ for most of the cases. We then explore whether our findings can be tested in the currently running NO$ u$A experiment with 3 years of data taking in neutrino mode followed by 3 years with anti-neutrino mode.
The recent T2K, MINOS and Double Chooz oscillation data hint a relatively large $theta_{13}$, which can be accommodated by some general modification of the Tribimaximal/Bimaximal/Democratic mixing matrices. Using such matrices we analyze several Majo
rana mass matrices with texture one-zero and show whether they satisfy normal or inverted mass hierarchy and phenomenologically viable or not.
