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Register a new userA compact analytical approximation for a light sterile neutrino oscillation in matter
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The existence of light sterile neutrinos is a long standing question for particle physics. Several experimental ``anomalies could be explained by introducing ~eV mass scaled light sterile neutrinos. Many experiments are actively hunting for such light sterile neutrinos through neutrino oscillation. For long baseline experiments, matter effect needs to be treated carefully for precise neutrino oscillation probability calculation. However, it is usually time-consuming or analytical complexity. In this manuscript we adopt the Jacobi-like method to diagonalize the Hermitian Hamiltonian matrix and derive analytically simplified neutrino oscillation probabilities for 3 (active) + 1 (sterile)-neutrino mixing for a constant matter density. These approximations can reach quite high numerical accuracy while keeping its analytical simplicity and fast computing speed. It would be useful for the current and future long baseline neutrino oscillation experiments.
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We investigate the performance of T2HK in the presence of a light eV scale sterile neutrino. We study in detail its influence in resolving fundamental issues like mass hierarchy, CP-violation (CPV) induced by the standard CP-phase $delta_{13}$ and new CP-phase $delta_{14}$, and the octant ambiguity of $theta_{23}$. We show for the first time in detail that due to the impressive energy reconstruction capabilities of T2HK, the available spectral information plays an important role to enhance the mass hierarchy discovery reach of this experiment in 3$ u$ framework and also to keep it almost intact even in $4 u$ scheme. This feature is also of the utmost importance in establishing the CPV due to $delta_{14}$. As far as the sensitivity to CPV due to $delta_{13}$ is concerned, it does not change much going from $3 u$ to 4$ u$ case. We also examine the reconstruction capability of the two phases $delta_{13}$ and $delta_{14}$, and find that the typical 1$sigma$ uncertainty on $delta_{13}$ ($delta_{14}$) in T2HK is $sim15^0$ ($30^0$). While determining the octant of $theta_{23}$, we face a complete loss of sensitivity for unfavorable combinations of unknown $delta_{13}$ and $delta_{14}$.
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.
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.
A considerable experimental effort is currently under way to test the persistent hints for oscillations due to an eV-scale sterile neutrino in the data of various reactor neutrino experiments. The assessment of the statistical significance of these hints is usually based on Wilks theorem, whereby the assumption is made that the log-likelihood is $chi^2$-distributed. However, it is well known that the preconditions for the validity of Wilks theorem are not fulfilled for neutrino oscillation experiments. In this work we derive a simple asymptotic form of the actual distribution of the log-likelihood based on reinterpreting the problem as fitting white Gaussian noise. From this formalism we show that, even in the absence of a sterile neutrino, the expectation value for the maximum likelihood estimate of the mixing angle remains non-zero with attendant large values of the log-likelihood. Our analytical results are then confirmed by numerical simulations of a toy reactor experiment. Finally, we apply this framework to the data of the Neutrino-4 experiment and show that the null hypothesis of no-oscillation is rejected at the 2.6,$sigma$ level, compared to 3.2,$sigma$ obtained under the assumption that Wilks theorem applies.
We investigate the potential for the Deep Underground Neutrino Experiment (DUNE) to probe the existence and effects of a fourth neutrino mass-eigenstate. We study the mixing of the fourth mass-eigenstate with the three active neutrinos of the Standard Model, including the effects of new sources of CP-invariance violation, for a wide range of new mass-squared differences, from lower than 10^-5 eV^2 to higher than 1 eV^2. DUNE is sensitive to previously unexplored regions of the mixing angle - mass-squared difference parameter space. If there is a fourth neutrino, in some regions of the parameter space, DUNE is able to measure the new oscillation parameters (some very precisely) and clearly identify two independent sources of CP-invariance violation. Finally, we use the hypothesis that there are four neutrino mass-eigenstates in order to ascertain how well DUNE can test the limits of the three-massive-neutrinos paradigm. In this way, we briefly explore whether light sterile neutrinos can serve as proxies for other, in principle unknown, phenomena that might manifest themselves in long-baseline neutrino oscillation experiments.
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