Neutrino Mass Ordering from Oscillations and Beyond: 2018 Status and Future Prospects

TL;DR

The paper analyzes how the neutrino mass ordering can be determined through multiple, complementary approaches: oscillations in matter, laboratory beta and neutrinoless double beta decays, and cosmological observations. It presents a detailed 2018 global Bayesian analysis showing a robust preference for normal ordering, driven primarily by oscillation data and strengthened by cosmological constraints when combined with external priors. It also surveys future prospects across diverse probes, highlighting upcoming facilities (DUNE, JUNO, LEGEND, DESI, 21 cm surveys, PTOLEMY) and novel ideas (21 cm cosmology, relic neutrino detection) that could cement the mass ordering within the next decade while noting model-dependence and potential complications from new physics such as sterile neutrinos. The work emphasizes the synergy between particle physics experiments and cosmology, and the importance of cross-validation among independent methods to robustly determine whether the neutrino mass spectrum follows normal or inverted ordering, with significant implications for flavor physics and beyond-Standard-Model scenarios.

Abstract

The ordering of the neutrino masses is a crucial input for a deep understanding of flavor physics, and its determination may provide the key to establish the relationship among the lepton masses and mixings and their analogous properties in the quark sector. The extraction of the neutrino mass ordering is a data-driven field expected to evolve very rapidly in the next decade. In this review, we both analyze the present status and describe the physics of subsequent prospects. Firstly, the different current available tools to measure the neutrino mass ordering are described. Namely, reactor, long-baseline (accelerator and atmospheric) neutrino beams, laboratory searches for beta and neutrinoless double beta decays and observations of the cosmic background radiation and the large scale structure of the universe are carefully reviewed. Secondly, the results from an up-to-date comprehensive global fit are reported: the Bayesian analysis to the 2018 publicly available oscillation and cosmological data sets provides \emph{strong} evidence for the normal neutrino mass ordering versus the inverted scenario, with a significance of 3.5 standard deviations. This preference for the normal neutrino mass ordering is mostly due to neutrino oscillation measurements. Finally, we shall also emphasize the future perspectives for unveiling the neutrino mass ordering. In this regard, apart from describing the expectations from the aforementioned probes, we also focus on those arising from alternative and novel methods, as 21~cm cosmology, core-collapse supernova neutrinos and the direct detection of relic neutrinos.

Figures (15)

• Figure 1: Probability of finding the $\alpha$ neutrino flavor in the $i$-th neutrino mass eigenstate as the CP-violating phase, $\delta_{\rm CP}$, is varied. Inspired by Ref. Mena:2003ug.
• Figure 2: The sum of the neutrino masses $\sum m_\nu$ as a function of the mass of the lightest neutrino, $m_1$ ($m_3$) for the normal (inverted) ordering, in red (blue) respectively. The (indistinguishable) width of the lines represents the present 3$\sigma$ uncertainties in the neutrino mass splittings from the global fit to neutrino oscillation data deSalas:2017kay. The horizontal bands illustrate two distinct $95\%$ Confidence Level (CL) limits on $\sum m_\nu$ from cosmology, see the text for details.
• Figure 3: 95.5% and 99.7% Bayesian credible intervals for the effective Majorana mass, $m_{\beta\beta}$, as a function of the lightest neutrino mass (left panel) or of the sum of the neutrino masses $\sum m_\nu$ (right panel), taking into account the current uncertainties on the neutrino mixing parameters (angles and phases), when three neutrinos are considered. The horizontal bands indicate the most conservative version (obtained by each collaboration when assuming a disfavorable value for the nuclear matrix element of the process) of some of the most competitive upper bounds, as those reported by KamLAND-Zen KamLAND-Zen:2016pfg, GERDA Phase II Agostini:2018tnm and CUORE Alduino:2017ehq. The vertical band in the right panel indicates the strongest limit reported by PlanckAghanim:2016yuo, using the Planck TT,TE,EE + SimLow + lensing data combination.
• Figure 4: Survival probability $P_{\mu \mu}$, as a function of the neutrino energy $E$ and the cosine of the zenith angle $\cos\theta_z$, for normal (inverted) ordering in the left (right) panel.
• Figure 5: Summary of neutrino oscillation parameters, 2018. Red (blue) lines correspond to normal ordering (inverted ordering). Notice that the $\Delta\chi^2$ profiles for inverted ordering are plotted with respect to the minimum for normal neutrino mass ordering.