The data pointing to the neutrino mass ordering, its CP violating parameter, and tensions between two different ways of measuring one of the neutrino oscillation parameters has gotten weaker.
To recap, the big open questions in neutrino physics are:
1. Is there a normal ordering or inverted ordering of neutrino masses?
The downgraded 2.7 sigma preference implies that there is a 98% chance that the mass ordering is normal rather than inverted.
2. What is the lightest neutrino rest mass eigenstate?
There is good reason to believe that it is significantly less than the difference between the lightest and second lightest neutrino rest mass eigenstate (which in a normal ordering is about 8.66 milli-electron volts, a.k.a. meV) and is greater than zero.
3. Is PMNS matrix parameter θ23 a little more than 45º or a little less (with the same magnitude of difference from 45º in either case)?
There is roughly an 85% chance that it is more, and a roughly 15% chance that it is less, given the 1.6 sigma preference for the higher value.
4. What is the CP violating phase of the PMNS matrix?
The available observations suggest that the CP violation due to the CP violating phase of the PMNS matrix is more likely to happen than it is to not happen, and could be maximal, but the measurement uncertainty is too great to be very specific. There are myriad theoretical predictions of this phase which take on almost every conceivable value of the parameter.
5. Are there non-sphaleron processes like neutrinoless double beta decay involving neutrinos that do not conserve lepton number?
The Standard Model answer to this question is "no", but the existing experimental tests aren't powerful enough to resolve the question because the expected number of neutrinoless double beta decay events is expected to be very small for neutrino masses of the magnitude that the combined available evidence especially from cosmology favors. In most of the beyond the Standard Model theories that are discussed in published scientific journal articles, the answer is "yes".
6. By what means do neutrinos acquire their rest mass?
There is not a Standard Model answer to the question. The other fundamental particles of the Standard Model acquire their mass via interactions with the Higgs field, but due to the absence of a right handed neutrino and left handed anti-neutrino in the Standard Model, an extension of this mechanism to the neutrinos is not obvious or straightforward. Until neutrino oscillation and neutrino mass were confirmed, the Standard Model assumed taht neutrinos were massless. There is still some semantic dispute over whether neutrino mass and neutrino oscillation are actually truly part of the Standard Model of Particle Physics in the narrow sense of that term.
7. Do sterile neutrinos that oscillate with ordinary neutrinos exist?
The Standard Model answer to the question is "no", and quite a bit of evidence from multiple sources (both cosmology and terrestrial experiment data) supports this answer. But there is some experimental evidence from neutrino oscillation data using neutrinos emitted by nuclear reactors (with the data from different experiments being somewhat inconsistent) that supports the existence of at least one sterile neutrino that oscillates with ordinary active neutrinos and such a neutrino is a dark matter particle candidate.
8. What is the ratio of neutrinos to antineutrinos in the Universe?
We don't have a reliable measurement of any great precision. The electron neutrino asymmetry could be on the order of 3% and the muon and tau neutrino asymmetry could be on the order of 50%.
9. Is some other aspect of the Standard Model description of neutrinos incorrect?
The Standard Model answer is obviously "no" and there is no strong evidence to suggest otherwise. The most plausible deviations from the Standard Model are discussed in the question above. Experimental searches for "non-standard interactions" (NSI) of neutrinos have not differed in a statistically significant manner from the null hypothesis.
10. Finally, it is always desirable to measure each of the seven experimentally measured neutrino property parameters of the Standard Model more precisely.
The measurement of the CP violating phase of the PMNS matrix is the least precisely measured experimentally determined constant in the entire Standard Model (or for that matter, in general relativity either, the other part of "Core Theory").
11. Bonus: Why do the seven experimentally measured neutrino property parameters take the values that they do?
There is not a Standard Model answer to the question and it does not aspire to provide one. The Standard Model does not aspire to explain why any of its experimentally measured fundamental constants take on the values that they do, except to demonstrate that a few of them (like the electromagnetic coupling constant, weak force coupling constant, W boson mass, Z boson mass, and Higgs vev) are functionally related to each other.
The preprint and its abstract are as follows:
To recap, the big open questions in neutrino physics are:
1. Is there a normal ordering or inverted ordering of neutrino masses?
The downgraded 2.7 sigma preference implies that there is a 98% chance that the mass ordering is normal rather than inverted.
2. What is the lightest neutrino rest mass eigenstate?
There is good reason to believe that it is significantly less than the difference between the lightest and second lightest neutrino rest mass eigenstate (which in a normal ordering is about 8.66 milli-electron volts, a.k.a. meV) and is greater than zero.
3. Is PMNS matrix parameter θ23 a little more than 45º or a little less (with the same magnitude of difference from 45º in either case)?
There is roughly an 85% chance that it is more, and a roughly 15% chance that it is less, given the 1.6 sigma preference for the higher value.
4. What is the CP violating phase of the PMNS matrix?
The available observations suggest that the CP violation due to the CP violating phase of the PMNS matrix is more likely to happen than it is to not happen, and could be maximal, but the measurement uncertainty is too great to be very specific. There are myriad theoretical predictions of this phase which take on almost every conceivable value of the parameter.
5. Are there non-sphaleron processes like neutrinoless double beta decay involving neutrinos that do not conserve lepton number?
The Standard Model answer to this question is "no", but the existing experimental tests aren't powerful enough to resolve the question because the expected number of neutrinoless double beta decay events is expected to be very small for neutrino masses of the magnitude that the combined available evidence especially from cosmology favors. In most of the beyond the Standard Model theories that are discussed in published scientific journal articles, the answer is "yes".
6. By what means do neutrinos acquire their rest mass?
There is not a Standard Model answer to the question. The other fundamental particles of the Standard Model acquire their mass via interactions with the Higgs field, but due to the absence of a right handed neutrino and left handed anti-neutrino in the Standard Model, an extension of this mechanism to the neutrinos is not obvious or straightforward. Until neutrino oscillation and neutrino mass were confirmed, the Standard Model assumed taht neutrinos were massless. There is still some semantic dispute over whether neutrino mass and neutrino oscillation are actually truly part of the Standard Model of Particle Physics in the narrow sense of that term.
7. Do sterile neutrinos that oscillate with ordinary neutrinos exist?
The Standard Model answer to the question is "no", and quite a bit of evidence from multiple sources (both cosmology and terrestrial experiment data) supports this answer. But there is some experimental evidence from neutrino oscillation data using neutrinos emitted by nuclear reactors (with the data from different experiments being somewhat inconsistent) that supports the existence of at least one sterile neutrino that oscillates with ordinary active neutrinos and such a neutrino is a dark matter particle candidate.
8. What is the ratio of neutrinos to antineutrinos in the Universe?
We don't have a reliable measurement of any great precision. The electron neutrino asymmetry could be on the order of 3% and the muon and tau neutrino asymmetry could be on the order of 50%.
9. Is some other aspect of the Standard Model description of neutrinos incorrect?
The Standard Model answer is obviously "no" and there is no strong evidence to suggest otherwise. The most plausible deviations from the Standard Model are discussed in the question above. Experimental searches for "non-standard interactions" (NSI) of neutrinos have not differed in a statistically significant manner from the null hypothesis.
10. Finally, it is always desirable to measure each of the seven experimentally measured neutrino property parameters of the Standard Model more precisely.
The measurement of the CP violating phase of the PMNS matrix is the least precisely measured experimentally determined constant in the entire Standard Model (or for that matter, in general relativity either, the other part of "Core Theory").
11. Bonus: Why do the seven experimentally measured neutrino property parameters take the values that they do?
There is not a Standard Model answer to the question and it does not aspire to provide one. The Standard Model does not aspire to explain why any of its experimentally measured fundamental constants take on the values that they do, except to demonstrate that a few of them (like the electromagnetic coupling constant, weak force coupling constant, W boson mass, Z boson mass, and Higgs vev) are functionally related to each other.
The preprint and its abstract are as follows:
Our herein described combined analysis of the latest neutrino oscillation data presented at the Neutrino2020 conference shows that previous hints for the neutrino mass ordering have significantly decreased, and normal ordering (NO) is favored only at the 1.6σ level. Combined with the χ2 map provided by Super-Kamiokande for their atmospheric neutrino data analysis the hint for NO is at 2.7σ.
The CP conserving value δCP=180∘ is within 0.6σ of the global best fit point. Only if we restrict to inverted mass ordering, CP violation is favored at the ∼3σ level.
We discuss the origin of these results - which are driven by the new data from the T2K and NOvA long-baseline experiments -, and the relevance of the LBL-reactor oscillation frequency complementarity.
The previous 2.2σ tension in Δm^2(21) preferred by KamLAND and solar experiments is also reduced to the 1.1σ level after the inclusion of the latest Super-Kamiokande solar neutrino results.
Finally we present updated allowed ranges for the oscillation parameters and for the leptonic Jarlskog determinant from the global analysis.
Ivan Esteban, M.C. Gonzalez-Garcia, Michele Maltoni, Thomas Schwetz, Albert Zhou "The fate of hints: updated global analysis of three-flavor neutrino oscillations" arXiv (July 27, 2020). This is largely in accord with another recent review of the same matters by different authors.
Other conclusions from the body text:
Despite slightly different tendencies in some parameter regions, T2K, NOvA and reactor experiments are statistically in very good agreement with each other. We have performed tests of various experiment and analysis combinations, which all show consistency at a CL below 2σ.
We obtain a very mild preference for the second octant of θ23, with the best fit point located at sin^2(θ23) = 0.57 (slightly more non-maximal than the best fit of 0.56 in NuFIT 4.1), but with the local minimum in the first octant at sin^2(θ23) = 0.455 at a ∆χ 2 = 0.53 (2.2) without (with) SK-atm. Maximal mixing (sin^2(θ23) = 0.5) is disfavored with ∆χ 2 = 2.4 (3.9) without (with) SK-atm.
The best fit for the complex phase is at δCP = 195◦ . Compared to previous results (e.g., NuFIT 4.1), the allowed range is pushed towards the CP conserving value of 180◦ , which is now allowed at 0.6σ with or without SK-atm. If we restrict to IO, the best fit of δCP remains close to maximal CP violation, with CP conservation being disfavored at around 3σ.
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