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In this article, we review the status of the tension between the long-baseline accelerator neutrino experiments T2K and NO$��$A. The tension arises mostly due to the mismatch in the appearance data of the two experiments. We explain how this tension arises based on $��_��\to ��_e$ and $\bar��_��\to \bar��_e$ oscillation probabilities. We define the reference point of vacuum oscillation, maximal $��_{23}$ and $��_{CP}=0$ and compute the $��_e/\bar��_e$ appearance events for each experiment. We then study the effects of deviating the unknown parameters from the reference point and the compatibility of any given set of values of unknown parameters with the data from T2K and NO$��$A. T2K observes a large excess in the $��_e$ appearance event sample compared to the expected $��_e$ events at the reference point, whereas \nova observes a moderate excess. The large excess in T2K dictates that $��_{CP}$ be anchored at $-90^\circ$ and that $��_{23}>��/4$ with a preference for normal hierarchy. The moderate excess at NO$��$A leads to two degenerate solutions: A) NH, $0��/4$; B) IH, $-180^\circ��/4$. This is the main cause of the tension between the two experiments. We have reviewed the status of three beyond standard model (BSM) physics scenarios, (a) non-unitary mixing, (b) Lorentz invariance violation and (c) non-standard neutrino interactions, to resolve the tension., Review article, 59 pages, 17 figures, 7 tables

The latest data from the T2K and \nova experiments show a tension in their preferred values of the oscillation parameters. In this work, we try to identify the source of the tension between the data from these two experiments. An analysis of their data from various channels (individually, and combined) shows that the tension arises primarily from the $\nu_e$ appearance data, and is compounded by the $\bar{\nu}_\mu$ disappearance data. We provide an explanation for the tension based on parameter degeneracies. Apart from the analysis with the standard matter effect, we also analyse the data with the vacuum oscillation hypothesis. We find that vacuum oscillations fit the data as well as matter effects do; and also reduce the tension between the two experiments. We have also done a study of the future run of NO$\nu$A, T2K and DUNE in the context of resolving this tension., Comment: 32 pages, 13 figures, figures improved, reference updated, accepted in EPJC

In this paper, we have estimated the neutrino mass ordering and the CP violation sensitivity of the proposed Protvino to Orca (P2O) experiment after 6 years of data-taking. Both unitary and non-unitary $3\times 3$ neutrino mass mixing have been considered in the simulations. A forecast analysis deriving possible future constraints on non-unitary parameters at P2O have been performed., 26 pages, 18 figures, 2 tables

The $��_��\to ��_e$ oscillation probability over short baseline ($\lesssim 1$~km) would be negligible in case the mixing matrix for three active neutrinos is unitary. However, in case of non-unitary mixing of three neutrinos, this probability would be non-negligible due to the so-called "zero distance" effect. Hence, the near detector of the accelerator experiments such as NO$��$A can provide strong constraints on the parameters of the non-unitary mixing with very large statistics. By analyzing the NO$��$A near detector data we find that the non-unitary mixing does not improve fits to the $��_e$ or $��_��$ events over the standard unitary mixing. This leads to constraints on the non-unitary parameters: $��_{00}>0.911$, $|��_{10}|0.952$ at 90\% C.L. A combined analysis with the near and far detector data does not change these constraints significantly., 13 pages, 8 figures, data from the latest NOvA publication have been used, the systematics uncertainties have been updated, the result has changed drastically from the last version

The mixing of three active neutrino flavors is parameterized by the unitary PMNS matrix. If there are more than three neutrino flavors and if the extra generations are heavy isosinglets, the effective $3\times 3$ mixing matrix for the three active neutrinos will be non-unitary. We have analyzed the latest T2K and \nova data with the hypothesis of non-unitary mixing of the active neutrinos. We found that the 2019 NO$��$A data slightly (at $\sim 1\, ��$ C.L.) prefer the non-unitary mixing over unitary mixing. In fact, allowing the non-unitary mixing brings the \nova best-fit point in the $\sin^2��_{23}-��_{CP}$ plane closer to the T2K best-fit point. The 2019 T2K data, on the other hand, cannot rule out any of the two mixing schemes. A combined analysis of the NO$��$A and T2K 2019 data prefers the non-unitary mixing at $1\, ��$ C.L.. We derive constraints on the non-unitary mixing parameters using the best-fit to the combined NO$��$A and T2K data. These constraints are weaker than previously found. The latest 2020 data from both the experiments prefer non-unitarity over unitary mixing at $1\, ��$ C.L. The combined analysis preferes non-unitarity at $2\, ��$ C.L. The stronger tension, which exists between the latest 2020 data of the two experiments, also gets reduced with non-unitary analysis., 30 pages, 19 figures, 3 tables. Results for 2020 data from NOvA and T2K have been included, Accepted in EPJC

The $��_e$ appearance data of T2K experiment has given a glimpse of the allowed parameters in the hierarchy-$��_{CP}$ parameter space. In this paper, we explore how this data affects our expectations regarding the hierarchy sensitivity of the NO$��$A experiment. For the favourable combinations of hierarchy and $��_{CP}$, the hierarchy sensitivity of NO$��$A is unaffected by the addition of T2K data. For the unfavourable combinations, NO$��$A data gives degenerate solutions. Among these degenerate solutions, T2K data prefers IH and $��_{CP}$ in the lower half plane over NH and $��_{CP}$ in the upper half plane. Hence, addition of the T2K data to NO$��$A creates a bias towards IH and $��_{CP}$ in the lower half plane irrespective of what the true combination is., 22 pages, 14 figures