Do JUNO Results Support a Novel Dependence Between Neutrino Mass Splittings?

A √2 ratio replaces two independent splittings

In the standard three-flavor picture, three neutrino mass-squared differences exist — Δm²₂₁, Δm²₃₁ and Δm²₃₂ — but only two are independent, tied by the consistency condition Δm²₃₁ − Δm²₂₁ = Δm²₃₂. The paper tests a stronger, recently proposed constraint that goes beyond this bookkeeping: (√Δm²₃₁ + √Δm²₂₁) / (√Δm²₃₁ − √Δm²₂₁) = √2.

If that relation holds, the number of independent neutrino mass splittings drops from two to one. The paper stresses that this is not part of the standard paradigm, which treats two of the three splittings as free parameters; accepting the ratio would imply an underlying mechanism or symmetry governing the neutrino mass spectrum. The ratio is the quantity being tested, not the individual splittings themselves.

JUNO's two splittings feed a single ratio

The test uses the JUNO Collaboration's most precise measurements to date of both splittings, based on 207.2 live days of data and assuming normal mass ordering. The solar splitting Δm²₂₁ has a central value of 7.388 × 10⁻⁵ eV² with a 1σ range of 7.310 to 7.466; the atmospheric splitting Δm²₃₁ has a central value of 2.509 × 10⁻³ eV² with a 1σ range of 2.484 to 2.536.

Substituting these central values into the left-hand side of the relation and applying standard first-order error propagation for independent variables yields 1.4143 (+0.0036/−0.0038). The paper justifies treating the two splittings as independent because their spectral modulations in the JUNO reactor antineutrino spectrum are physically distinct, so the correlation between them is expected to be negligibly small. That assumption is what makes the simple error propagation appropriate here.

The measured ratio sits 0.03σ from √2

The extracted ratio of 1.4143 differs from the prediction √2 ≈ 1.4142 by less than 0.03 standard deviations, and the match is achieved at a sub-percent relative experimental precision of 0.27%. The paper describes this as excellent agreement and as strong experimental support for the novel constraint.

Two numbers should not be conflated. The 0.27% figure is the relative precision of the ratio itself; the roughly 1% figure is the world-leading precision JUNO has reached on the individual mass splittings. The ratio's tightness comes from combining both splittings, not from either measurement alone. The paper also flags that this level of agreement is preliminary, since JUNO is still accumulating statistics and refining its results.

The constraint turns parameter space into a line

Solving the relation for Δm²₂₁ gives Δm²₂₁ = (√9 − √8)² Δm²₃₁, a strict linear relation between the solar and atmospheric splittings. Under the hypothesis, the allowed (Δm²₂₁, Δm²₃₁) parameter space becomes effectively one-dimensional, shrinking from a two-dimensional region to a single trajectory.

This yields a distinct, testable signature: experimental points must fall on that line. The paper plots the initial JUNO result against the trajectory and reports that the point corresponding to the experimental central values coincides almost perfectly with it. Within the proposed framework, any future shift of that point is strictly restricted to the linear trajectory — which is what makes continued JUNO exposure a meaningful check rather than a repetition.

Inverted ordering fits the ratio less well

The main analysis assumes normal mass ordering, where m₁ < m₂ < m₃. As a check, the paper substitutes the absolute value of JUNO's corresponding atmospheric splitting under the inverted ordering hypothesis, where m₃ < m₁ < m₂, and obtains 1.4170 ± 0.0037.

That value still agrees with √2 within the 1σ interval, but its central value sits visibly farther away, a 0.75σ deviation. The paper reads this as the relation preliminarily favoring normal ordering, while noting that whether this prospective sensitivity to the mass ordering scenarios persists must be verified with upcoming data. The comparison is a preference, not a determination of the ordering.

A phenomenological hint awaiting a quantum derivation

The paper argues it is intuitively difficult to dismiss the match as purely accidental, pointing to the symmetry of the relation — numerator and denominator share the same mathematical structure — and to the appearance of a specific irrational number. It suggests a plausible origin in a cancellation of underlying quantum mechanical quantities, producing an overall normalization factor or an effect stemming from the mixing angles, and notes that particle physics often produces ratios yielding simple square roots such as √2, √3 or √6.

This explanatory part is the author's interpretation, not a derived result. The paper is explicit that the relation was predicted on phenomenological grounds and that deriving it within a quantum-field-theoretical framework would provide a rigorous foundation. Until such a derivation exists, the constraint remains an empirical pattern that the data currently support.

Early data support the ratio, not a settled symmetry

The strongest claim the evidence carries is conditional and time-stamped: on 207.2 live days of JUNO data, assuming normal ordering, the two splittings reproduce the predicted ratio to 0.03σ at 0.27% relative precision, and the central-value point lies almost perfectly on the predicted line. The paper's own framing keeps this preliminary because JUNO continues to accumulate statistics and refine its results.

The most decision-relevant feature for readers is therefore the linear trajectory itself. It converts a vague question about whether the splittings are related into a concrete test: future JUNO points must stay on that line, and the inverted-ordering variant, at 1.4170 ± 0.0037 and 0.75σ away, is the comparison that currently separates the two orderings. Watching whether refined data hold the line — and whether the ordering preference survives — is the paper-specific priority, not the single 0.03σ number on its own.

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