Sabine Hoffenfelder's latest blog post talks about the sterile neutrino anomaly seen at the Liquid Scintillator Neutrino Detector, LSND for short, which ran from 1993 to 98 and again at the Mini Booster Neutrino Experiment experiment at Fermilab since 2003 seeming to show a six sigma anomaly by 2018. She wonders why it isn't a big deal now.
While it is common to talk about a five sigma threshold for discovery of new physics, there are really two more parts of that test: the result needs to be replicated rather than being contradicted by other experiments, and there has to be a plausible physics based theory to explain the result.
Usually, Sabine is a voice of reason and spot on (I bought her book "Lost in Math" and agree with almost everything that she says in it). But on this score, I don't agree with her. She states that:
15 years ago, I worked on neutrino mixing for a while, and in my impression back then most physicists thought the LSND data was just wrong and it’d not be reproduced.
But, most physicists still think that the LSND/MiniBooNE data is wrong, and it wasn't reproduced by other experiments. Instead, multiple experiments and astronomy observations using different methods that make their results robust contradict the LSND/MiniBooNE result.
Equally important, several independent important sources of systemic error were identified with the LSND data and its successor MiniBooNE experiment's data. Basically, these experiments failed to consider the mix of fuels in the nuclear reactors they were modeling, used a wrong oscillation parameter, and failed to correlate their near and far detector results in ways that overestimated the number of neutrinos that should appear which made it look like there were more neutrinos disappearing than there actually were.
Thus, there is very strong evidence that the LSND/MiniBooNE apparent detection of a sterile neutrino was wrong.
Instead, there is strong evidence that there are no sterile neutrinos that oscillate with ordinary neutrinos that have masses of under 10 eV.
For what it is worth, searches for non-standard neutrino interactions (other than CP violation) have also come up empty so far and severely constrained that possibility. See, e.g., a paper from IceCube, a paper from ANTARES, an analysis of data from Daya Bay, and a summary of results from six other experiments.
Furthermore, there are no beyond the Standard Model active neutrinos with masses of under 10 TeV. This is also an important part of the argument that there are also no fourth generation quarks or charged leptons, because, for reasons of theoretical consistency, each generation of Standard Model fundamental fermions must be complete.
Other Experiments Contradict LSND/MiniBooNE And There Are Plausible Sources Of Systemic Error
The big problem with the reactor anomaly is that these two sets of results rather than being replicated, were repeatedly contradicted, and instead a plausible physics based explanation for why it was wrong was established.
Three different recent experiments (STEREO, PROSPECT and DANSS) have contradicted the LSND/MiniBooNE result. And, the anomalies seen at LSND/MiniBooNE were determined to most likely be due to a failure to model the mix of reactor fuels between Uranium-235 and Plutonium-239 properly, resulting in an error in the predicted number of neutrino events that the actual detections were compared to in determining that there was a deficit of neutrinos that could be explained by an oscillation to one or more sterile neutrino flavors. See Matthieu Licciardi "Results of STEREO and PROSPECT, and status of sterile neutrino searches" arxiv.org (May 28, 2021) (Contribution to the 2021 EW session of the 55th Rencontres de Moriond). See also additional analysis of the fuel mix issue, additional results from Moriond 2021 (including IceCube), and the results from the MINOS, MINOS+, Daya Bay, and Bugey-3 Experiments (these may be the same experiments mentioned above with different names) which found in a preprint that was subsequently published in a peer reviewed journal:
Searches for electron antineutrino, muon neutrino, and muon antineutrino disappearance driven by sterile neutrino mixing have been carried out by the Daya Bay and MINOS+ collaborations. This Letter presents the combined results of these searches, along with exclusion results from the Bugey-3 reactor experiment, framed in a minimally extended four-neutrino scenario. Significantly improved constraints on the θμe mixing angle are derived that constitute the most stringent limits to date over five orders of magnitude in the sterile mass-squared splitting Δm241, excluding the 90% C.L. sterile-neutrino parameter space allowed by the LSND and MiniBooNE observations at 90% CLs for Δm241<5eV^2. Furthermore, the LSND and MiniBooNE 99% C.L. allowed regions are excluded at 99% CLs for Δm241 < 1.2 eV^2.
Daya Bay, MINOS+ Collaborations, "Improved Constraints on Sterile Neutrino Mixing from Disappearance Searches in the MINOS, MINOS+, Daya Bay, and Bugey-3 Experiments" arXiv 2002.00301 (February 2, 2020).
A similar conclusion was reached using overlapping data but also data from the Planck cosmic microwave background observations here.
The KATRIN experiment also contradicts the sterile neutrino anomaly up to 1000 eV sterile neutrino candidates.
In addition to these issues, an analysis back in 2014 already noticed data contradicting the sterile neutrino hypothesis at the ICARUS and OPERA, and observed that some of the parameters used to make the estimates were off and that using the right ones greatly reduced the statistical significance of the anomaly. See Boris Kayser "Are There Sterile Neutrinos" (February 13, 2014). MINOS and Daya Bay had already contradicted the reactor anomaly back in 2014 as well. More recent analysis has likewise downgraded the statistical significance of the anomalies previously reported, although it has not entirely eliminated it.
Cosmology Data Strongly Disfavors Sterile Neutrinos
Cosmology data strongly supports the hypothesis that there are exactly three generations of neutrinos when combined with this result; if sterile neutrinos have a mass of 10,000,000,000 meV/c^2 or less (see also here).
Cosmology measures also place a cap on neutrino mass including the sum of the neutrino masses of about 0.087 eV or less, in a manner indifferent between sterile neutrinos of less than about 10 eV, and active neutrinos, which doesn't leave room for a reactor anomaly sterile neutrino. See Eleonora Di Valentino, Stefano Gariazzo, Olga Mena "On the most constraining cosmological neutrino mass bounds" arXiv:2106.16267 (June 29, 2021).
A far heavier sterile neutrino would not be discernible as a neutrino from cosmology data and instead would look like a type of dark matter particle. But, the LSND/MiniBooNE result was pointing to a sterile neutrino with a mass of under 5 eV, so it would be subject to the cosmology bounds.
Also, there are strict direct detection exclusions on heavier dark matter particles as well, although none of those would bar a truly sterile neutrino with no interactions with ordinary matter other than oscillations with active neutrinos.
The main criticism of reliance on cosmology data is that it is highly model dependent, even though this particular conclusion is quite robust to different cosmology models.
Limits On Active Neutrinos
We can also be comfortable that there are no active neutrinos (e.g. a fourth generation neutrino otherwise identical to the three Standard Model neutrinos) with masses of less than about 10 TeV, when direct measurements paired with oscillation data limit the most massive of the three Standard Model neutrino masses to not more than 0.9 eV, and cosmology data limits the most massive of the three Standard Model neutrino masses to not more than 0.09 eV.
Data from W and Z boson decays likewise tightly constrain the number of active neutrinos with masses of less than 45,000,000,000,000 meV/c^2 to exactly three.
Dark dark matter detection experiments have ruled out particles that make up most of hypothetical dark matter particles having weak force interaction coupling constants equal to Standard Model neutrinos at masses of up to about 10 TeV (i.e. 10,000 GeV). In the chart below, that cross section is the blue dotted line marked "Z portal C(x)=1" by a factor of 1,000,000. So, even if the flux of 45 GeV+ Standard Model neutrinos were a million times smaller than the hypothetical flux of dark matter particles through Earth, they would be ruled out by the direct detection experiments up to about 10 TeV.
Direct measurement of the lightest neutrino mass from the Katrin experiment of about 0.8 eV, which means that all of the active neutrino masses have to be less than about 0.9 eV based upon the oscillation data. This means that the sterile neutrino mass predicted by the LSND/MiniBooNE result relative to the active neutrino masses still couldn't have been so massive that it would have evaded cosmology bounds.
Neutrinoless double beta decay results rule out Majorana mass neutrinos above about 180 meV (according to the body text of the linked paper). The same experiments will soon be able to confirm or rule out the scenario of sterile neutrinos heavier than 10 eV that cosmology tools cannot constrain.