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Register a new userParameter degeneracy and hierarchy sensitivity of NO$ u$A in presence of sterile neutrino
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The first hint of neutrino mass hierarchy is expected to come from the NO$ u$A experiment in Fermilab as the present best-fit parameter space i.e., normal hierarchy and $delta_{CP}=-90^circ$ is the favourable parameter space for NO$ u$A where there is no degeneracy. But this situation may change if the standard three flavour framework is not complete and there is existence of new physics. In this work we consider the presence of an extra light sterile neutrino at the eV scale and study the new degeneracies which are absent in the standard three flavour framework. We also study the effect of these new degeneracies on the hierarchy measurement of NO$ u$A.
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We study in detail the impact of a light sterile neutrino in the interpretation of the latest data of the long baseline experiments NO$ u$A and T2K, assessing the robustness/fragility of the estimates of the standard 3-flavor parameters with respect to the perturbations induced in the 3+1 scheme. We find that all the basic features of the 3-flavor analysis, including the weak indication ($sim$1.4$sigma$) in favor of the inverted neutrino mass ordering, the preference for values of the CP-phase $delta_{13} sim 1.2pi$, and the substantial degeneracy of the two octants of $theta_{23}$, all remain basically unaltered in the 4-flavor scheme. Our analysis also demonstrates that it is possible to attain some constraints on the new CP-phase $delta_{14}$. Finally, we point out that, differently from non-standard neutrino interactions, light sterile neutrinos are not capable to alleviate the tension recently emerged between NO$ u$A and T2K in the appearance channel.
The $ u_e$ appearance data of T2K experiment has given a glimpse of the allowed parameters in the hierarchy-$delta_{CP}$ parameter space. In this paper, we explore how this data affects our expectations regarding the hierarchy sensitivity of the NO$ u$A experiment. For the favourable combinations of hierarchy and $delta_{CP}$, the hierarchy sensitivity of NO$ u$A is unaffected by the addition of T2K data. For the unfavourable combinations, NO$ u$A data gives degenerate solutions. Among these degenerate solutions, T2K data prefers IH and $delta_{CP}$ in the lower half plane over NH and $delta_{CP}$ in the upper half plane. Hence, addition of the T2K data to NO$ u$A creates a bias towards IH and $delta_{CP}$ in the lower half plane irrespective of what the true combination is.
ESS$ u$SB is a proposed neutrino super-beam project at the ESS facility. We study the performance of this setup in the presence of a light eV-scale sterile neutrino, considering 540 km baseline with 2 years (8 years) of $ u$ ($bar u$) run-plan. This baseline offers the possibility to work around the second oscillation maximum, providing high sensitivity towards CP-violation (CPV). We explore in detail its capability in resolving CPV generated by the standard CP phase $delta_{13}$, the new CP phase $delta_{14}$, and the octant of $theta_{23}$. We find that the sensitivity to CPV induced by $delta_{13}$ deteriorates noticeably when going from $3 u$ to 4$ u$ case. The two phases $delta_{13}$ and $delta_{14}$ can be reconstructed with a 1$sigma$ uncertainty of $sim15^0$ and $ sim35^0$ respectively. Concerning the octant of $theta_{23}$, we find poor sensitivity in both $3 u$ and $4 u$ schemes. Our results show that a setup like ESS$ u$SB working around the second oscillation maximum with a baseline of 540 km, performs quite well to explore CPV in 3$ u$ scheme, but it is not optimal for studying CP properties in 3+1 scheme.
The main aim of the ESS$ u$SB proposal is the discovery of the leptonic CP phase $delta_{CP}$ with a high significance ($5sigma$ for 50% values of $delta_{CP}$) by utilizing the physics at the second oscillation maxima of the $P_{mu e}$ channel. It can achieve $3sigma$ sensitivity to hierarchy for all values of $delta_{CP}$. In this work, we concentrate on the hierarchy and octant sensitivity of the ESS$ u$SB experiment. We show that combining the ESS$ u$SB experiment with the atmospheric neutrino data from the proposed India-based Neutrino Observatory(INO) experiment can result in an increased sensitivity to mass hierarchy. In addition, we also combine the results from the ongoing experiments T2K and NO$ u$A assuming their full runtime and present the combined sensitivity of ESS$ u$SB + ICAL@INO + T2K + NO$ u$A. We show that while by itself ESS$ u$SB can have up to $3sigma$ hierarchy sensitivity, the combination of all the experiments can give up to $5sigma$ sensitivity depending on the true hierarchy-octant combination. The octant sensitivity of ESS$ u$SB is low by itself. However the combined sensitivity of all the above experiments can give up to $3sigma$ sensitivity depending on the choice of true hierarchy and octant. We discuss the various degeneracies and the synergies that lead to the enhanced sensitivity when combining different experimental data.
We discuss the analytical expression of the oscillation probabilities at low energy long baseline experiments, such as T2HK and T2HKK in the presence of nonstandard interactions (NSIs). We show that these experiments are advantageous to explore the NSI parameters ($epsilon_D$, $epsilon_N$), which were suggested to be nonvanishing to account for the discrepancy between the solar neutrino and KamLAND data. We also show that, when the NSI parameters are small, parameter degeneracy in the CP phase $delta$, $epsilon_D$ and $epsilon_N$ can be resolved by combining data of the T2HK and T2HKK experiments.
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