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With the recent measurement of reactor mixing angleθ13the knowledge of neutrino oscillation parameters has improved significantly except the CP violating phaseδCP, mass hierarchy, and the octant of the atmospheric mixing angleθ23. 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 NOνA and T2K experiments as well as the forthcoming T2HK experiment in addressing these questions. In particular, we evaluate the sensitivity of NOνA to determine neutrino mass hierarchy, octant degeneracy, andδCPafter running for its scheduled period of 3 years in neutrino mode and 3 years in antineutrino mode. We then extend the analysis to understand the discovery potential if the experiments will run for (5ν+5ν¯) years and (7ν+3ν¯) years. We also show how the sensitivity improves when we combine the data from NOνA, T2K, and T2HK experiments with different combinations of run period. The CP violation sensitivity is marginal for T2K and NOνA experiments even for ten-year data taking of NOνA. T2HK has a significance above5σfor a fraction of two-fifths values of theδCPspace. We also find thatδCPcan be determined to be better than 35°, 21°, and 9° for all values ofδCPfor T2K, NOνA, and T2HK respectively.

Recently, the reactor mixing angle 13 θ 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 13 θ . Using the fact that the neutrino mixing matrix can be represented as V U U P l PMNS † = ν ν , where U l and U ν result from the diagonalization of the charged lepton and neutrino mass matrices and P ν 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 the 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 13 θ , and one can also obtain limits on the charge-conjugation parity-violating Dirac phase CP δ and Jarlskog invariant J CP for most of the cases. We then explore whether our findings can be tested in the currently running NuMI Off-axis v e Appearance experiment with three years of data taking in neutrino mode followed by three years with the anti-neutrino mode. PMNS PMNS 12 13 12 13 13 i 12 23 12 13 23 i 12 23 12 13 23 i 13 23 12 23 12 13 23 i 12 23 12 13 23 i 13 23 CP CP CP CP CP

Neutrinos are the fundamental particles, blind to all kind of interactions except the weak and gravitational. Hence, they can propagate very long distances without any deviation. This characteristic property can thus provide an ideal platform to investigate Planck suppressed physics through their long distance propagation. In this work, we intend to investigate CPT violation through Lorentz invariance violation (LIV) in the long-baseline accelerator based neutrino experiments. Considering the simplest four-dimensional Lorentz violating parameters, for the first time, we obtain the sensitivity limits on the LIV parameters from the currently running long-baseline experiments T2K and $$\hbox {NO}\nu \hbox {A}$$NOνA. In addition to this, we show their effects on mass hierarchy and CP violation sensitivities by considering $$\hbox {NO}\nu \hbox {A}$$NOνA as a case study. We find that the sensitivity limits on LIV parameters obtained from T2K are much weaker than that of $$\hbox {NO}\nu \hbox {A}$$NOνA and the synergy of T2K and $$\hbox {NO}\nu \hbox {A}$$NOνA can improve these sensitivities. All these limits are slightly weaker ($$2 \sigma $$2σ level) compared to the values extracted from Super-Kamiokande experiment with atmospheric neutrinos. Moreover, we observe that the mass hierarchy and CPV sensitivities are either enhanced or deteriorated significantly in the presence of LIV as these sensitivities crucially depend on the new CP-violating phases. We also present the correlation between $$\sin ^2 \theta _{23}$$sin2θ23 and the LIV parameter $$|a_{\alpha \beta }|$$|aαβ|, as well as $$\delta _{CP}$$δCP and $$|a_{\alpha \beta }|$$|aαβ|.