Neutrino Physics Answers Are In the Pipeline

The two reactor based neutrino physics experiments currently under construction will be able to resolve whether the neutrino masses have a normal or inverted hierarchy once and for all. The current data favors a normal hierarchy, but not very definitively. These experiments could bring the certainty to six to nine sigma, providing a definitively scientific resolution of the issue. (Other new experiments are reviewed here).

One of the major open problems of neutrino physics is MO (mass ordering). We discuss the prospects of measuring MO with two under-construction experiments T2HK and JUNO. JUNO alone is expected to measure MO with greater than 3σ significance as long as certain experimental challenges are met. In particular, JUNO needs better than 3% energy resolution for MO measurement. On the other hand, T2HK has rather poor prospects at measuring the MO, especially for certain ranges of the CP violating parameter δCP, posing a major drawback for T2HK. In this letter we show that the synergy between JUNO and T2HK will bring two-fold advantage. Firstly, the synergy between the two experiments helps us determine the MO at a very high significance. With the baseline set-up of the two experiments, we have a greater than 9σ determination of the MO for all values of δCP. Secondly, the synergy also allows us to relax the constraints on the two experiments. We show that JUNO, could perform extremely well even for energy resolution of 5%, while for T2HK the MO problem with "bad" values of δCP goes away. The MO sensitivity for the combined analysis is expected to be greater than 6σ for all values of δCP and with just 5% energy resolution for JUNO.

Sandhya Choubey, Monojit Ghosh, Deepak Raikwal, "Neutrino Mass Ordering -- Circumventing the Challenges using Synergy between T2HK and JUNO" arXiv:2207.04784 (July 11, 2022).

Determining The Absolute Neutrino Masses

This is also be an important step towards determining the absolute neutrino masses. If the neutrino mass hierarchy is determined definitively, an accurate measurement of any one of the three neutrino masses, or of the sum of the three neutrino masses, will make it possible to determine all three of the absolute neutrino masses. 

The minimum sum of the three neutrino masses from oscillation data (assuming a zero or negligible mass for the lightest neutrino mass) in a normal hierarchy is about 0.067 eV, and is about 0.1 eV in an inverted hierarchy.

The pattern of the normal hierarchy neutrino masses would tend to favor a lightest neutrino mass of significantly less than 0.008 eV, and a sum of neutrino masses significantly less than 0.09 eV. A best guess, just looking at the established patterns in the Standard Model fermion masses, would be a lightest neutrino mass on the order of 0.001 eV and a sum of neutrino masses of about 0.07 eV. But there is really nothing solid to back up this expectation at this point.

Direct measurements cap the lightest neutrino mass at about 0.8 eV, and this could drop to something like 0.2 eV in several years (and would cap the sum of the three neutrino masses at about 0.3 eV, from about 0.9 eV now).

Cosmology based measurements cap the sum of the three neutrino masses at about 0.12-0.14 eV at about a two sigma level, with best fit values that are significantly smaller and 95% confidence interval ranges for the sum of the three neutrino masses which are consistent with zero. This is a much tighter bound by about two orders of magnitude, but is likely to improve only slightly in the near term future. If the cosmology based cap on the sum of the neutrino masses were to drop much below 0.07 eV (about 50%), we would have a contradiction and would know that the cosmology based cap has a flawed assumption of some kind. 

This cosmology bound almost rules out the inverted hierarchy of neutrino masses. But the cosmology based estimate of the neutrino masses is also much more model dependent, in a field where there are solid reasons to doubt the prevailing LambdaCDM model which is tweaked to produce the cosmology based bound on neutrino masses. One of the assumptions about neutrinos in cosmology, for example, is undermined by a recent preprint which questions the assumption that the three neutrino types are likely to be present in equal proportions in cosmological neutrinos.

Other Outstanding Questions In Neutrino Physics

The mass ordering of the neutrino masses is not the only outstanding question in neutrino physics, of course. 

But, all of the outstanding questions except a direct measurement of the absolute neutrino mass scale, and the fourth issue below are likely to be reasonably resolved, once and for all, in the time from of 2027-2037 (five to fifteen years).

* Scientists can never get too much precision in the three PMNS matrix parameters that are reasonably well known, and the two neutrino mass difference values that are reasonably well known.

* One outstanding core issue is determining the "quadrant" of the θ23 mixing angle (i.e. if it is a bit more or a bit less than 45º) for which the larger value is slightly favored, although the magnitude of the deviation form 45º is known to some precision.

* Another outstanding core issue is determining the CP violating parameter of the PMNS matrix that governs neutrino mixing, for which a near maximal amount of CP violation is weakly favored. We are very close to strongly ruling out the possibility that there is no CP violation in neutrino oscillation (e.g. ruling out the possibility that neutrinos and antineutrinos mix in exactly the same way).

* A third additional big question in Standard Model neutrino physics is whether neutrinos have Majorana or Dirac masses (or some combination of the two). If neutrinos have Majorana mass there are two more neutrino mixing parameters than the four parameters of the PMNS matrix, and neutrinoless beta decay should occur, while in a Dirac mass scenario, neutrinoless double beta decay is forbidden. The lower the absolute neutrino masses are, the less common neutrinoless double beta decay should be, and if the neutrino masses are in the ballpark of what is suggests by cosmology bounds. Current experiments are not yet capable of reliably detecting the amount of neutrinoless double beta decay predicted to occur at our cosmology informed neutrino masses, although progress is also being made on that front.

* A fourth outstanding issue in neutrino physics is tt even if neutrinos have Dirac mass, there is still the open question of whether this arises from the Higgs mechanism, as the masses of the quarks, the charged leptons, the W boson, the Z boson and the Higgs boson do, or whether neutrino masses have another source. There are really no experiments in the foreseeable future that seem likely to resolve that question.

Resolved Questions In Neutrino Physics

Other issues that are still the subject of new papers (especially speculative theoretical papers), are in my opinion basically resolved.

* While not all experts in the field are currently convinced, I am comfortable that there are no sterile neutrinos that oscillate with the three active neutrinos of the Standard Model since anomalies that tended to support that hypothesis have been adequately explained. Direct searches for heavy neutral leptons, the strongest of which now come from the Large Hadron Collider (LHC) are also quite strong. And, there are quite strong limitations from astronomy on keV mass sterile neutrino dark matter.

The BEST experiment is claiming 4 sigma evidence of a sterile neutrino state in what it calls a "Gallium anomaly", but as I explore in a post at the Physics Forums, the claim is patently absurd. The abstract of the new BEST paper, "Search for electron-neutrino transitions to sterile states in the BEST experiment" (pre-print at https://arxiv.org/abs/2201.07364; popular mechanics description: https://www.popularmechanics.com/science/a40396201/sterile-neutrino/) is as follows:

No other experimental hints of an oscillation to a sterile neutrino this massive, and with such a large mixing angle have been noticed before in other experiments, which seems unthinkable if the sterile neutrino hypothesis were correct.

The sterile neutrino implied by the Reactor Anti-Neutrino Anomaly data, which has now been explained by flaws in the nuclear model used, had best fit parameters for this sterile state to absorb the anomaly was found around 1 eV^2 for the oscillation frequency (∆m^2) (i.e. less than a third what the BEST result estimates) and 0.14 for the amplitude sin^2(2θ) (about a third of the mixing angle).

Also note that the upward uncertainty in ∆m^2 in their sterile neutrino model is a flabbergasting + ∞.

Taken literally, this means that the BEST experiment believes that there is a 68% chance that their sterile neutrino has a mass eigenstate somewhere between 1.0 eV^2 and the mass of the Milky Way galaxy in excess of the most massive of the three active neutrino mass eigenstates (which is experimentally constrained to be between 0.06 eV to 0.90 eV). 

What heck does that mean?

I would argue strenuously that you can not simultaneously claim a 4 sigma significance signal and have an infinity sign in one the key error bars expressing your conclusion.

Also, while Gallium and Germanium are hardly "exotic", we have far less operational experience with these elements than with Uranium and Plutonium, which have had full time engineers and scientists at nuclear power plants and in weapons programs all over the world for the last eighty years devoted to understanding their nuclear decay properties and generating massive amounts of data and expertise in the process to model it. So, it would hardly be surprising if the nuclear model for Gallium and Germanium were not quite as accurate as it is for Uranium and Plutonium.

* Also, I am comfortable that there is no evidence to suggest that there are any "non-standard neutrino interactions" (NSI) based upon a litany of null result experimental tests of that hypothesis.

* There is likewise no evidence that neutrinos have a magnetic moment significantly different from the negligible Standard Model value. The LZ dark matter detector, as an unintended bonus, has tightened by a factor of five the upper experimental bound on the neutrino magnetic moment:

the new LUX-ZEPLIN data allows us to set the most stringent limit on the neutrino magnetic moment when compared to the other laboratory bounds, namely  

μeffν<6.3×10−12μB at 90% C.L.

This limit supersedes the previous best one set by the Borexino Collaboration by almost a factor of 5 and it rejects by more than 5σ the hint of a possible neutrino magnetic moment found by the XENON1T Collaboration.

(Once again, positive signals from XENON1T have proven misleading due to uncontrolled large possible backgrounds, although its exclusions remain sound.)

The main difficulty in determining the Standard Model expectation here is to figure out what the Standard Model expectation even is, because while we know that neutrinos are massive, there is dispute about where that mass comes from:

In the SM, neutrinos are considered massless, and therefore neutrino MMs [magnetic moments] are vanishing. Nevertheless, from the fact that neutrino oscillates, we know that the SM must be extended in order to give masses to the neutrinos. 

In the minimal extension of the SM in which neutrinos acquire Dirac masses through the introduction of right-handed neutrinos, the neutrino MM is given by: 

µ(ν)=((3eG(F))/(8 √ 2π^2))*m(ν)  

∼ 3.2 × 10^−19(m(ν)/eV)*µ(B) (5) 

where µ(B) is the Bohr magneton, m(ν) is the neutrino mass and e is the electric charge. Taking into account the current upper limit on the neutrino mass, this value is less than µ(ν) ∼ 10^−18µ(B), which is too small to be observed experimentally. Nevertheless, given that in some BSM scenarios the neutrino MM is predicted to be larger, a positive observation would represent a clear signal of physics beyond the minimally extended SM. For this reason, neutrino MM is the most investigated neutrino electromagnetic property, both theoretically and experimentally.