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Register a new userOctant of $theta_{23}$ in danger with a light sterile neutrino
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Present global fits of world neutrino data hint towards non-maximal $theta_{23}$ with two nearly degenerate solutions, one in the lower octant ($theta_{23} <pi/4$), and the other in the higher octant ($theta_{23} >pi/4$). This octant ambiguity of $theta_{23}$ is one of the fundamental issues in the neutrino sector, and its resolution is a crucial goal of next-generation long-baseline (LBL) experiments. In this letter, we address for the first time, the impact of a light eV-scale sterile neutrino towards such a measurement, taking the Deep Underground Neutrino Experiment (DUNE) as a case study. In the so-called 3+1 scheme involving three active and one sterile neutrino, the $ u_mu to u_e$ transition probability probed in the LBL experiments acquires a new interference term via active-sterile oscillations. We find that this novel interference term can mimic a swap of the $theta_{23}$ octant, even if one uses the information from both neutrino and antineutrino channels. As a consequence, the sensitivity to the octant of $theta_{23}$ can be completely lost and this may have serious implications in our understanding of neutrinos from both the experimental and theoretical perspectives.
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Current 3$ u$ global fits predict two degenerate solutions for $theta_{23}$: one lies in lower octant ($theta_{23} <pi/4$), and the other belongs to higher octant ($theta_{23} >pi/4$). Here, we study how the measurement of $theta_{23}$ octant would be affected in the upcoming Deep Underground Neutrino Experiment (DUNE) if there exist a light eV-scale sterile neutrino. We show that in 3+1 scheme, a new interference term in $ u_mu to u_e$ oscillation probability can spoil the chances of measuring $theta_{23}$ octant completely.
We investigate the implications of one light eV scale sterile neutrino on the physics potential of the proposed long-baseline experiment DUNE. If the future short-baseline experiments confirm the existence of sterile neutrinos, then it can affect the mass hierarchy (MH) and CP-violation (CPV) searches at DUNE. The MH sensitivity still remains above 5$sigma$ if the three new mixing angles ($theta_{14}, theta_{24}, theta_{34}$) are all close to $theta_{13}$. In contrast, it can decrease to 4$sigma$ if the least constrained mixing angle $theta_{34}$ is close to its upper limit $sim 30^0$. We also assess the sensitivity to the CPV induced both by the standard CP-phase $delta_{13} equiv delta$, and the new CP-phases $delta_{14}$ and $delta_{34}$. In the 3+1 scheme, the discovery potential of CPV induced by $delta_{13}$ gets deteriorated compared to the 3$ u$ case. In particular, the maximal sensitivity (reached around $delta_{13}$ $sim$ $pm$ $90^0$) decreases from $5sigma$ to $4sigma$ if all the three new mixing angles are close to $theta_{13}$. It can further diminish to almost $3sigma$ if $theta_{34}$ is large ($sim 30^0$). The sensitivity to the CPV due to $delta_{14}$ can reach 3$sigma$ for an appreciable fraction of its true values. Interestingly, $theta_{34}$ and its associated phase $delta_{34}$ can influence both the $ u_e$ appearance and $ u_mu$ disappearance channels via matter effects, which in DUNE are pronounced. Hence, DUNE can also probe CPV induced by $delta_{34}$ provided $theta_{34}$ is large. We also reconstruct the two phases $delta_{13}$ and $delta_{14}$. The typical 1$sigma$ uncertainty on $delta_{13}$ ($delta_{14}$) is $sim20^0$ ($30^0$) if $theta_{34} =0$. The reconstruction of $delta_{14}$ (but not that of $delta_{13}$) degrades if $theta_{34}$ is large.
We study the possibility of determining the octant of the neutrino mixing angle $theta_{23}$, that is, whether $theta_{23}> 45^circ$ or $theta_{23}<45^circ$, in long baseline neutrino experiments. Here we numerically derived the sensitivity limits within which these experiments can determine, by measuring the probability of the $ u_{mu}to u_{e}$ transitions, the octant of $theta_{23}$ with a $5sigma$ certainty. The interference of the CP violation angle $delta$ with these limits, as well as the effects of the baseline length and the run-time ratio of neutrino and antineutrino modes of the beam have been analyzed.
We point out that leptonic weak-basis invariants are an important tool for the study of the properties of lepton flavour models. In particular, we show that appropriately chosen invariants can give a clear indication of whether a particular lepton flavour model favours normal or inverted hierarchy for neutrino masses and what is the octant of $theta_{23}$. These invariants can be evaluated in any conveniently chosen weak-basis and can also be expressed in terms of neutrino masses, charged lepton masses, mixing angles and CP violation phases.
We study the impact of one light sterile neutrino on the prospective data expected to come from the two presently running long-baseline experiments T2K and NOvA when they will accumulate their full planned exposure. Introducing for the first time, the bi-probability representation in the 4-flavor framework, commonly used in the 3-flavor scenario, we present a detailed discussion of the behavior of the numu to nue and numubar to nuebar transition probabilities in the 3+1 scheme. We also perform a detailed sensitivity study of these two experiments (both in the stand-alone and combined modes) to assess their discovery reach in the presence of a light sterile neutrino. For realistic benchmark values of the mass-mixing parameters (as inferred from the existing global short-baseline fits), we find that the performance of both these experiments in claiming the discovery of the CP-violation induced by the standard CP-phase delta13 equivalent to delta, and the neutrino mass hierarchy get substantially deteriorated. The exact loss of sensitivity depends on the value of the unknown CP-phase delta14. Finally, we estimate the discovery potential of total CP-violation (i.e., induced simultaneously by the two CP-phases delta13 and delta14), and the capability of the two experiments of reconstructing the true values of such CP-phases. The typical (1 sigma level) uncertainties on the reconstructed phases are approximately 40 degree for delta13 and 50 degree for delta14.
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