Sterile Neutrinos Largely Ruled Out Up To 3eV

A reactor neutrino study has largely ruled out sterile neutrinos up to 3 eV, and possibly up to 4.5 eV. This rules out the Gallium anomaly (explained here), which already has many explanations that do not require new physics.

The preprint and its abstract are as follows:

The PROSPECT experiment is designed to perform precise searches for antineutrino disappearance at short distances (7-9 ~m) from compact nuclear reactor cores. This Letter reports results from a new neutrino oscillation analysis performed using the complete data sample from the PROSPECT-I detector operated at the High Flux Isotope Reactor in 2018. 

The analysis uses a multi-period selection of inverse beta decay neutrino interactions with reduced backgrounds and enhanced statistical power to set limits on electron-flavor disappearance caused by mixing with sterile neutrinos with 0.2-20 eV^2 mass splittings. 

Inverse beta decay positron energy spectra from six different reactor-detector distance ranges are found to be statistically consistent with one another, as would be expected in the absence of sterile neutrino oscillations. The data excludes at 95% confidence level the existence of sterile neutrinos in regions above 3~eV^2 previously unexplored by terrestrial experiments, including all space below 10~eV^2 suggested by the recently strengthened Gallium Anomaly. The best-fit point of the Neutrino-4 reactor experiment's claimed observation of short-baseline oscillation is ruled out at more than five standard deviations.

M. Andriamirado, et al., "Final Search for Short-Baseline Neutrino Oscillations with the PROSPECT-I Detector at HFIR" arXiv:2406.10408 (June 14, 2024).

Neutrino-less double beta decay has also been further constrained: 

We present a search for neutrinoless double-beta (0νββ) decay of 136Xe using the full KamLAND-Zen 800 dataset with 745 kg of enriched xenon, corresponding to an exposure of 2.097 ton yr of 136Xe. This updated search benefits from a more than twofold increase in exposure, recovery of photo-sensor gain, and reduced background from muon-induced spallation of xenon. 

Combining with the search in the previous KamLAND-Zen phase, we obtain a lower limit for the 0νββ decay half-life of T(0ν1/2) > 3.8×10^26 yr at 90% C.L., a factor of 1.7 improvement over the previous limit. The corresponding upper limits on the effective Majorana neutrino mass are in the range 28-122 meV using phenomenological nuclear matrix element calculations.

S. Abe, et al., "Search for Majorana Neutrinos with the Complete KamLAND-Zen Dataset" arXiv:2406.11438 (June 17, 2024).

Analysis 

This is still a long way from ruling out neutrinos with purely Majorana mass in either the inverted hierarchy (which requires a half-life about 1000 times as long), or the normal hierarchy. (which requires a half-life 100,000 to 1,000,000 times as long).

This upper bound on Majorana mass implies a maximum sum of the three neutrino masses, if neutrinos have purely Majorana mass and an inverted hierarchy, of about 0.5 eV.

The upper bound on the sum of the three neutrino masses due to direct measurements of the lightest neutrino mass at Katrin of 0.8 eV is currently about 2.51 eV. When Katrin runs its course, this should fall to a lightest neutrino mass of less than 0.2 eV  and a sum of the three neutrino masses of less than 0.71 eV.

The lower bound on the sum of the neutrino masses based upon neutrino oscillation data is about 0.059 eV in the normal hierarchy and 0.109 eV in the inverted hierarchy.

Cosmology bounds on the sum of the three neutrino masses are much tighter, but with the DESI data set, the bounds on the sum of the three neutrino masses from all sources are on the verge of being over constrained (i.e. the cosmology bounds favor a sum of the three neutrino masses under 0.059 eV), which suggests that the cosmology model used to set these bound may be flawed.