Current unknowns in the three neutrino framework (1804.09678v1)

Abstract: We present an up-to-date global analysis of data coming from neutrino oscillation and non-oscillation experiments, as available in April 2018, within the standard framework including three massive and mixed neutrinos. We discuss in detail the status of the three-neutrino (3nu) mass-mixing parameters, both known and unknown. Concerning the latter, we find that: normal ordering (NO) is favored over inverted ordering (IO) at 3sigma level; the Dirac CP phase is constrained within ~15% (~9%) uncertainty in NO (IO) around nearly-maximal CP-violating values; the octant of the largest mixing angle and the absolute neutrino masses remain undetermined. We briefly comment on other unknowns related to theoretical and experimental uncertainties (within 3nu) or possible new states and interactions (beyond 3nu).

• The paper achieves precise determinations of key neutrino parameters, with squared mass differences measured to within 2.2% and 1.4% accuracy and mixing angles known within a few percent.
• The paper reveals a significant preference for normal mass ordering over inverted ordering, supported by a confidence level exceeding 3σ across diverse datasets.
• The study narrows the CP-violating phase to nearly maximal values while excluding CP conservation at high confidence, setting critical benchmarks for future experiments.

Analysis of the Three-Neutrino Framework: Current Unknowns

This paper presents a comprehensive and up-to-date global analysis of neutrino data within the context of the standard three-neutrino framework, accounting for massive and mixed neutrinos. The analysis synthesizes results from both oscillation and non-oscillation experiments available as of April 2018. Focusing on the state of the three-neutrino mass-mixing parameters, it distinguishes between known quantities and unknown features that remain to be resolved.

Key Findings and Analysis of Oscillation Data

The analysis reveals several significant findings regarding both known and unknown oscillation parameters. Initially, by focusing on known quantities, the paper provides precise measurements:

• Squared Mass Differences and Mixing Angles: The parameters $\delta m^2$ and $|\Delta m^2|$ are determined to within 2.2% and 1.4%, respectively. The mixing angles $\theta_{12}$, $\theta_{13}$, and $\theta_{23}$ are determined within a few percent accuracy, with $\sin^2\theta_{13}$ having the smallest uncertainty at about 3.8%.

Turning to the unknown parameters, the analysis highlights:

• Mass Ordering: There is a consistent preference for normal mass ordering (NO) over inverted ordering (IO) at a confidence level exceeding $3\sigma$. This preference emerges progressively with the inclusion of diverse datasets, with contributions from long-baseline accelerator data, short-baseline reactor data, and atmospheric neutrinos.
• CP-violating Phase ($\delta$): The paper identifies a range for $\delta$ centered around nearly maximal CP-violating values ($\delta \sim 3\pi/2$). The CP-conserving values $\delta = 0$ and $2\pi$ are excluded at $3\sigma$ in IO and at $>1.9\sigma$ in NO. These constraints indicate progress in measuring $\delta$ with effective $1\sigma$ accuracies of approximately 15% for NO and 9% for IO.
• Octant of $\theta_{23}$: Although the paper shows a mild preference for $\theta_{23} > \pi/4$ (especially in IO), it remains unresolved within $2\sigma$.

Implications and Prospects

The implications of these findings are twofold. In the short term, the emerging preference for NO and constraints on $\delta$ indicate a clear direction for ongoing and future experiments to validate these hints statistically and possibly achieve discovery levels. The constraints on known parameters reflect the maturity of the three-neutrino framework as a predictive model.

In the long term, the indications of NO and potential exclusion of CP conservation provide benchmarks for next-generation facilities like JUNO, T2HK, and DUNE. These experiments have the potential to resolve the mass ordering conclusively and refine the measurement of $\delta$.

Limits from Non-Oscillation Experiments

Combining oscillation data with results from neutrinoless double beta decay ($0\nu\beta\beta$) and cosmology offers additional insights, particularly regarding the constraints on absolute neutrino masses and the Majorana or Dirac nature of neutrinos:

• Cosmological Limits on $\Sigma$: Depending on the data combinations, $\Sigma$ (the sum of neutrino masses) is constrained to less than approximately 0.18 eV at $2\sigma$ under strong assumptions, which has implications for both NO and IO but more favorably excludes IO when combined with oscillation data.
• Neutrinoless Double Beta Decay ($m_{\beta\beta}$): The absence of a $0\nu\beta\beta$ signal currently places a limit on $m_{\beta\beta}$, leading to further potential insights if positive signals are observed in future experiments.

Conclusion

The global analysis in this paper advances our understanding of neutrino physics within the three-neutrino framework. Both known and unknown parameters have been scrutinized, and emerging hints provided could be pathfinders for the field. Continued and future experimental efforts across diverse platforms will be critical in transitioning from hints to confirmed discoveries, potentially revealing novel aspects beyond the current framework.