Mass OrderingEdit
Mass ordering
Mass ordering refers to the arrangement of the three known neutrino mass eigenstates in increasing or decreasing mass. In the standard three-neutrino framework, the flavor states that participate in weak interactions are quantum superpositions of mass eigenstates m1, m2, and m3. Oscillation experiments measure two independent mass-squared differences, but they do not yet determine the sign of one of them, leaving two distinct possibilities for the spectrum. This ambiguity is commonly described as either a normal ordering, where m1 < m2 < m3, or an inverted ordering, where m3 is the lightest. The question of which ordering nature chooses has implications for experimental design, model building, and our understanding of the absolute neutrino mass scale and the nature of neutrinos themselves.
In the three-neutrino paradigm, the mixing between flavor and mass eigenstates is encoded in the Pontecorvo–Maki–Nakagawa–Sakata matrix, or PMNS matrix, expressed in terms of three mixing angles θ12, θ23, θ13, and a CP-violating phase δCP, along with potential Majorana phases if neutrinos are their own antiparticles. The probabilities for neutrino flavor conversion depend on the mass-squared differences Δm21^2 and Δm31^2 (or Δm32^2), as well as on the path length and energy of the neutrinos. The sign of Δm31^2 is the key discriminator between the two mass-ordering scenarios: it is positive in the normal ordering and negative in the inverted ordering. The ordering is intimately connected to the absolute mass scale, since oscillation experiments are sensitive to mass differences but not to the overall mass of the lightest state.
Formalism and terminology
- Neutrino flavors and mass states: The electron, muon, and tau neutrinos are denoted as νe, νμ, and ντ, and are related to the mass eigenstates through the PMNS matrix Pontecorvo–Maki–Nakagawa–Sakata matrix.
- Mass-squared differences: The solar mass splitting Δm21^2 ≈ 7×10^-5 eV^2 and the atmospheric splitting |Δm31^2| ≈ 2.5×10^-3 eV^2 set the scale for oscillations. The sign of Δm31^2 distinguishes the two orderings.
- Normal ordering vs inverted ordering: In normal ordering, m1 < m2 < m3, with Δm31^2 > 0; in inverted ordering, m3 is lightest, with Δm31^2 < 0. See neutrino mass ordering and neutrino mass ordering for formal labeling and context.
- Absolute mass scale and related observables: Oscillations do not fix the overall mass scale. Experiments probing the absolute mass, such as beta-decay kinematics in KATRIN or cosmological observations in cosmology, constrain Σ mν, the sum of the neutrino masses; neutrinoless double beta decay searches probe the Majorana nature of neutrinos via the effective mass mββ.
Experimental status
- Global perspective: The body of data from solar, atmospheric, reactor, and accelerator experiments constrains the mass-squared differences and mixing angles with increasing precision. Across these measurements, a mild but persistent preference for the normal ordering has emerged, though the statistical significance is not yet decisive. This remains an active area of experimental and phenomenological work.
- Long-baseline and atmospheric probes: Experiments such as NOvA and T2K analyze neutrino and antineutrino oscillations over hundreds of kilometers, where matter effects in the Earth and the CP-violating phase δCP can influence apparent mass ordering signals. These efforts are complemented by broader global fits that combine multiple datasets.
- Reactor-based determinations: Facilities like JUNO are designed to determine the ordering by accurately measuring the interference pattern of oscillations driven by the solar and atmospheric scales in reactor νe disappearance. JUNO aims to achieve a high-sensitivity determination of the hierarchy by exploiting precise energy resolution and statistics.
- Prospects from upcoming facilities: Next-generation projects such as DUNE and Hyper-Kamiokande will test the ordering with high precision by exploiting long baselines, detailed event reconstruction, and large event samples. These experiments also address CP violation and the θ23 octant, tying the mass ordering to broader questions about lepton flavor.
- Complementary constraints: The sum of neutrino masses Σ mν inferred from cosmology (including data from the Planck mission and large-scale structure surveys) places upper bounds that intersect with the allowed ranges for the mass orderings. Direct kinematic limits from KATRIN contribute to the overall picture of the absolute mass scale, though they are not ordering determinations by themselves.
Implications and connections
- Neutrinoless double beta decay: If neutrinos are Majorana particles, the rate of neutrinoless double beta decay depends on the effective mass mββ, which is a function of the masses, mixing angles, and phases. The ordering affects the possible range of mββ, with inverted ordering generally predicting a more accessible region for next-generation experiments. See neutrinoless double beta decay.
- Cosmological sensitivity: The sum of neutrino masses influences the evolution of cosmic structure and the cosmic microwave background. Current and future cosmological measurements place progressively tighter constraints on Σ mν, narrowing the viable parameter space for each ordering. See cosmology.
- Theoretical implications: The pattern of masses and ordering feeds into models of neutrino mass generation, such as the seesaw mechanism and related flavor theories. The ordering can serve as guidance for constructing and testing ultraviolet completions of the Standard Model that include neutrino masses.
- Experimental strategy: A confirmed ordering helps optimize the design and analysis of future experiments, including detector technologies, baselines, and energy ranges, to maximize sensitivity to related questions like CP violation and the absolute mass scale.
Controversies and debates
- Significance of current hints: While there is a tendency in global analyses toward normal ordering, the evidence is not yet conclusive. Critics emphasize the role of statistical fluctuations and systematic uncertainties across diverse experiments, arguing that scheduling a firm claim is premature until next-generation data are in.
- Interplay with new physics: Some proposals invoke sterile neutrinos, non-standard interactions, or other beyond-Standard-Model effects as alternative explanations for observed oscillation patterns. Proponents argue that careful, model-independent analyses are essential to separate true mass ordering from potential new physics signatures.
- Prioritization of measurements: Debates occasionally center on resource allocation and which experimental avenues offer the most robust route to a definitive ordering. Proponents of a multi-pronged approach contend that cross-checks among reactor, accelerator, and cosmological probes are the most reliable path to resolution.