A new phenomenological relationship of the neutrino mass differences is interesting.
(I'm using an image rather than text because the equations are hard to reproduce in Blogger.)
The rotation curves of the 175 disk galaxies in the SPARC database are confronted, one by one and under identical conditions, with the two mass models that have dominated the missing-mass debate for four decades: a cold dark-matter halo of Navarro-Frenk-White (NFW) form, and Milgromian dynamics (MOND) with the acceleration constant held at a0=1.2×10^−10 m s^−2. Stellar mass-to-light ratios, distances and inclinations are treated as nuisance parameters with priors set by the 3.6 μm photometry and by the SPARC error budget, and every galaxy is sampled with a Markov-chain Monte Carlo.
Three findings emerge.
(i) Judged by the Bayesian information criterion, the free NFW halo is preferred in 96 galaxies and MOND in 79; once the halo is required to obey the ΛCDM concentration-mass relation the score becomes 86 to 89, i.e. a draw. The two theories fail in different places: MOND loses in massive, high-surface-brightness, bulge-dominated systems, NFW loses in slowly rising dwarf rotation curves.
(ii) The NFW concentrations demanded by the data sit a median 0.24 dex below the ΛCDM expectation, and 53% of the sample lies more than 2σ below it, independent of halo mass; this is the core-cusp problem expressed as a scaling-relation offset rather than as a handful of anecdotes.
(iii) The radial acceleration relation built from the full sample has a0= (1.13 ±0 .02) × 10^−10 m s^−2 and an observed scatter of 0.14 dex, yet the value of a0 preferred by individual galaxies spans more than a decade and correlates with surface brightness. The two statements are not in contradiction: the population-level relation is tight because it averages over exactly the degeneracies with mass-to-light ratio and distance that make a0 ill-determined galaxy by galaxy. The full table of fits is provided.
The gallium anomaly as a 20% deviation from the expected number of neutrino interactions with a gallium atom, which was pointed at as evidence of sterile neutrinos. Only, it turns out that what was wrong was a 20% error in the calculation of the theoretically expected value by ignoring parts of the calculation that were too important to ignore. When calculated correctly, theory and experiment were consistent (in what has become, by now, a familiar pattern).
For more than 30 years, scientists have found that roughly 20% fewer electron neutrinos are captured by gallium nuclei than expected. Dubbed the gallium anomaly, this discrepancy has raised the possibility that something fundamental might be missing from our understanding of neutrinos or atomic nuclei. Now Matteo Cadeddu at the National Institute for Nuclear Physics (INFN) and the University of Cagliari, both in Italy, and his colleagues have shown that this mismatch may instead originate from the way the electron-neutrino capture rate is calculated [1]. . . .
When an electron neutrino is captured by a gallium nucleus, an electron is created and a neutron turns into a proton, transforming gallium into germanium. In the standard capture-rate calculation, the behavior of the nucleus is treated separately from that of the neutrino and electron. This approximation simplifies the calculation but may overlook key aspects of the capture process. Cadeddu and his colleagues instead developed a more rigorous approach that fully accounts for the interplay between the nucleus, neutrino, and electron. Using this technique, the researchers predicted a capture rate about 20% lower than previous estimates, closely matching the experimental results. This finding offers a solution to the gallium anomaly without requiring new physics. It disfavors one of the previously leading explanations: the existence of so-called sterile neutrinos. . . .
[1] M. Cadeddu, et al., "Possible solution to the gallium anomaly moving beyond the leptonic wave-function factoriziation," 137 Phys. Rev. Lett. 131805 (September 24, 2026).
From here.