A New Phenomenological Relationship Of Neutrino Masses

A new phenomenological relationship of the neutrino mass differences is interesting, and close matches to simple formulas like this one are rare.

In the standard three-flavor paradigm, two of the three neutrino mass-squared differences are independent. The existence of an additional dependence between these oscillation parameters was recently predicted on empirical grounds, taking the form

The JUNO Collaboration has now reported the most precise measurements to date of both Δm(21)^2 and Δm(31)^2. We demonstrate that this relation is in excellent agreement with the experimental data, which yield 1.4143 +0.0036 −0.0038 corresponding to a relative precision of 0.27%. Remarkably, the central value differs by less than 0.03 standard deviations from the prediction (2‾√≈1.4142). This provides strong experimental support for the novel constraint and thereby suggests an underlying symmetry governing the neutrino mass spectrum, rather than purely independent parameters.

I. Alikhanov, "Novel dependence between neutrino mass splittings strongly supported by initial JUNO results" arXiv:2610.06738 (October 5, 2026). This updates:

I. Alikhanov, "Another relation among the neutrino mass-squared differences?", arXiv:2601.18781 (January 26, 2026).

There are more comparisons along this line from a different author, Vernon Barger, at https://arxiv.org/html/2603.00810v2.