A theoretical scan of neutrino mixing leaves two modified forms within the paper’s quoted comparison ranges, while all three unmodified forms are rejected. The surviving forms are labelled Vb′ and Vc′, and the reported comparison covers normal ordering.
The paper asks whether a perturbatively modified democratic mixing matrix can produce solar, reactor and atmospheric mixing angles compatible with NuFIT 6.1 and recent JUNO findings. All of the reported comparisons use normal ordering, the mass arrangement examined in this analysis.
A small change to the starting pattern
The construction begins with the matrix the authors call democratic. It adds a real perturbation parameter, epsilon, to conserve unitarity, the mathematical consistency condition imposed on the mixing matrix, and then applies rotations in the 1-2, 1-3 or 2-3 sectors.
The numerical analysis scans the free parameters epsilon, alpha and theta to accommodate mixing angles within the NuFIT 6.1 constraint. The reported outputs are therefore ranges generated by combinations of model parameters, rather than measurements from a new experimental sample.
One choice is built into the calculation: when solving the modified-matrix constraints, the authors set x4 and x7 to zero and express the remaining xi in terms of epsilon.
Two mathematical forms remain
Before the perturbation is introduced, the three options Va, Vb and Vc are all marked as excluded under the paper’s stated compatibility criteria. They correspond to the unperturbed democratic construction combined with the three sector rotations considered in the analysis.
After modification, only Vb′ and Vc′ are reported as viable. Va′ is rejected, with the paper reporting Ue3 = 0 for that form.
The solar-angle result is the clearest overlap with JUNO. For both Vb′ and Vc′, the scan is reported to reproduce the allowed NuFIT global data while placing a narrow band inside the quoted JUNO 3-sigma interval, sin² θ12 from 0.3005 to 0.3179.
For Vb′, the reported range is 0.2893 to 0.3294 for the solar angle, 0.02070 to 0.02420 for the reactor angle and 0.5642 to 0.5869 for the atmospheric angle. Its JCP range is -0.0124 to -0.00006, while δCP runs from 339.18° to 359.88°.
For Vc′, the solar-angle range is 0.2894 to 0.3294 and the reactor-angle range is 0.02070 to 0.02420. The atmospheric angle spans 0.4373 to 0.5864, JCP spans -0.0181 to -0.0003, and δCP spans 328.24° to 359.48°.
The difference between the two surviving forms is most visible in the atmospheric angle and δCP. Vc′ has the broader reported ranges in both quantities, and the authors describe it as the more flexible and predictable texture.
What the match does, and does not, establish
The paper also compares the CP-related quantity JCP with a stated experimental interval from -0.04 to 0.04. The predicted interval is -0.0124 to -0.00006 for Vb′ and -0.0181 to -0.0003 for Vc′, so both reported ranges lie within that window.
The word “compatible” here refers to a range comparison. The Vb′ and Vc′ results are parameter-scan ranges, not reported confidence intervals, and the paper gives no statistical probability for the JUNO overlap or the JCP result.
The scope is also limited to normal ordering. The paper says that a similar exercise for inverted ordering remains to be done, so these results do not establish compatibility for that alternative.
The supplied document is an arXiv version-one preprint dated 26 August 2026. Its conclusion is that the democratic ansatz is phenomenologically viable under real perturbations with rotations in the 1-3 and 2-3 sectors, with Vc′ described as more flexible and predictable than Vb′.
Paper data and sources
Original title: A Rotational Perturbative Correction to Democratic Neutrino Mixing and JUNO Compatibility
Authors: Maibam Ricky Devi, Swaraj Kumar Nanda, Sudhanwa Patra
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text