A preprint posted yesterday summing up presentations from the Snowmass Conference (Snowmass is just down the road from Aspen, Colorado) that sums up the state of neutrino physics today. I'll recap some highlights in this post from this comprehensive 89 page long review article.
Our understanding of neutrinos has progressed rapidly over the last twenty years and neutrino physics remains an area of fundamental physics where there is a lot of basic information that is not known, but is knowable simply through more mid-sized budget (compared to particle accelerators) brute force experimental efforts.
The next couple of decades of neutrino physics will either reveal a fairly "boring scenario" which I predict (a "normal" neutrino mass hierarchy, with exactly three fertile Dirac neutrinos, a lightest neutrino mass of about 1 meV or less, no neutrinoless double beta decay or lepton number violations, anomalies that disappear with increased experimental and theoretical prediction precision, and significant CP violation), or more exciting "new physics."
PMNS matrix and neutrino mass state difference magnitude constants
It provides the current best global fit values for the neutrino physics constants of the PMNS matrix in equation 8 from the source (with precision on a percentage basis following the data):
* Δm221= 7.54+0.26-0.22 * 10-5 eV2 (3.2%) (this implies that the magnitude of Δm21 is about 8.68 meV).
* Δm232= 2.43+0.1-0.06 * 10-3 eV2 (3.3%) (this implies that the magnitude of Δ m32is about 49.30 meV).
* sin2ϴ12= 3.07+0.18-0.16 * 10-1 (16%)
* sin2ϴ23= 3.86+/-0.24 * 10-1 (21%)
* sin2ϴ13= 2.41+/-0.25 * 10-1 (10%)
* Dirac CP violating phase σ/π<=1.08+0.28-0.31 radians (all possible values are encompassed at 2 standard deviations of variation)
A value of zero for the CP violating phase σ would mean that there was no CP violation in neutrino oscillations (or, put differently, that the rate of which neutrino oscillations take place in different direction in time (e.g. muon neutrino to electron neutrino v. electron neutrino to muon neutrino) exactly matches. A CP violating phase of π (i.e. 180 degrees) would constitute maximal CP violation in neutrino oscillations. The best fit is for maximal or near maximal CP violation, but the measurement is very imprecise. Still, it isn't unreasonable to state that a Dirac CP violation phase of zero in neutrino oscillations is mildly disfavored by the data to date.
The CP violating phase of the CKM matrix is known to a precision of about 5%. It is 70.4+4.3-4.4 degrees (about 1.23 radians). I have explored in another post earlier this year all manner of numerological reasons to favor on Dirac CP violating phase in the PMNS matrix over another with a great many values of the constant that seem plausible present. Nothing in this latest review article sheds much more light on the matter.
We should have more precise values for all of these constants and some statistically significant estimate of the Dirac CP violating phase σ of the PMNS matrix within a decade from the half dozen major experiments in progress, and possibly within even just a few years. A definitive determination could easily take until the year 2020 or even the year 2025, however.
Absolute neutrino masses and the neutrino mass hierarchy
The absolute values of the neutrino masses are significantly bounded by experiment (with both a minimum and maximum value). The sum of the three neutrino mass states is constrained (most strongly by astronomy measurements of the cosmic background radiation methodologically very different from other sources of neutrino physics constants) to be less than 100 meV. (If a recall correctly, the best fit to the astronomy data is about 60 meV.)
Direct measurements of neutrino emissions in beta decay impose a far less strict bound due to lower experimental sensitivity with the average neutrino emitted in beta decay (predominantly electron anti-neutrinos) alone having a mass of less than 2000 meV. Later this decade, the KATRIN experiment can place an upper bound of 200meV with 90% confidence and 350meV with five sigma confidence, which is still far above the model dependent boundary indirectly determined from cosmic background radiation measurements.
If this upper bound on the sum of the three neutrino masses from astronomy data is accepted, the lightest neutrino mass state must be somewhere between 0 and 42 meV. If the neutrino hierarchy is "normal" then the lightest neutrino mass state m1 is less than 8.68 meV and the sum of the three neutrino mass states is between 58 meV and 67 meV, and is realistically at the low end of that range. Astronomy data may be able to test a boundary of about 60meV in a few years to a couple of decades.
The determination of whether the neutrino mass hierarchy is "normal" (like other Standard Model fermions) or "inverted" (with two nearly identical heavier masses and one lighter mass) is not established.
The data tends to favor a normal hierarchy which is the "default" theoretical expectation given the precedent from quarks and charged leptons that exhibit this hierarchy. One Monte Carlo analysis of reactor data puts the probability of a normal hierarchy rather than an inverted one at 98.9%, a three sigma result not rigorously integrated with other data), but this not definitive enough to declare that this has been determined at the gold standard five sigma level.
If the mass hierarchy is "normal" it is somewhat easier to resolve the Dirac CP violation phase of the PMNS matrix than it is if the mass hierarchy is "inverted."
The bottom line is that while absolute neutrino mass and the neutrino mass hierarchy have not been definitively determined, that the available data favor results that are quite specific even if they are not yet definitive to the discipline's rigorous standards. I personally strongly suspect that neutrinos have a normal mass hierarchy and that the mass of the lightest neutrino mass state is on the order of 1 meV or less.
Dirac v. Majorana masses
It has also not be determined whether the neutrino masses are "Dirac" or "Majorana." If neutrinoless double beta decay doesn't happen, then neutrino masses must be Dirac, just like all of the other fermion masses. If neutrinoless double beta decay happens, then neutrinos could be Majorana and their absolute Majorana masses could be determined in model dependent manner from that rate. This is because if neutrinos are Majorana particles, "lepton number" (a quantum number conserved in the Standard Model) is not conserved.
Also, if neutrinos are Majorana rather than Dirac, there may be as many as three CP violating phases governing neutrino oscillations and the PMNS matrix is not necessarily unitary.
Models with lepton number violation, including supersymmetry (SUSY) and Majorana neutrino models are popular with theorists as a way to explain the matter-antimatter asymmetry in the observed universe. Neutrinoless double beta decay is the cleanest way to experimentally observe lepton number violation. But, no lepton number violation has ever been observed experimentally.
To date, the results of the only experiment claiming to detect neutrinoless double beta decay, in the Heidelberg-Moscow experiment, has been discredited by multiple other experiments that have failed to replicate the result. So, there is no credible evidence to date of neutrinoless double beta decay, although at least eight major experiments are searching for experimental evidence of it. Current and next generation experiments are sensitive to neutrinoless double beta decay at rates that would imply Majorana masses on the order of 100 meV (for a single neutrino), which is already ruled out by astronomy data. It will take experiments only in the planning stages to detect neutrinoless double beta decay at rates that would imply Majorana masses on the order of 10meV or less, although these experiments are well within the range of engineering possibility.
These planned experiments would also place serious constraints on many varieties of SUSY experiments by failing to show neutrinoless double beta decay at the rates required for the remaining portion of SUSY parameter space.
A Majorana mass of the electron neutrino of less than 20meV is inconsistent with an "inverted" mass hierarchy. For example, if other measurements found that the mass hierarchy was inverted, then a 10meV neutrino mass would imply that neutrinos had only Dirac mass.
If the Majorana masses of the neutrinos are as low as the astronomy and mass state difference magnitudes imply that they must be, if the exist at all, we shouldn't have detected neutrinoless double beta decay with current experiments in any case and may not have the experimental capacity to do so for another decade or more.
For what it is worth, my own personal expectation is that neutrinoless double beta decay and lepton violation do not occur in low energy contexts, that SUSY is false, and that neutrinos are Dirac rather than Majorana particles. But, a couple of experiments that confirm each other could easily prove me to be wrong.
Beyond The Three Neutrino Model
Three neutrinos with masses along the lines discussed above that oscillate according to the PMNS matrix with the parameters described above provide a best fit for the sum total of all available scientific data on neutrinos today.
But, cosmic background radiation data does not definitively rule out a fourth neutrino type (although it is slightly more consistent with only three neutrino types) and short-baseline neutrino oscillation experiments associated with nuclear reactors has two and three standard deviation anomalies in their data that could point to beyond the three neutrino model physics such as a fourth "sterile" neutrino species with a mass on the order of 1 eV which would be an attractive "warm dark matter" particle candidate. None of these deviations is definitive, however, and a three fertile and one sterile neutrino model poses difficulties of its own to integrate with the whole of the available scientific data.
In particular, reactor experiments are greatly limited in precision by our weak understanding of and ability to model weak force interactions of neutrinos within a nuclear environment like a fission reactor at various energy levels. This kind of neutrino behavior is called "neutrino scattering" and current calculations of these interactions have uncertainties of 10%-40%, with the data frequently differing from current crude theoretical estimates. This understanding is also necessary to better model theoretical expectations for neutrino bursts from supernovae that are observed.
We know from W and Z boson decays, for example, that there are only three kinds of neutrinos that interact via the weak nuclear force and that neutrinos come in only "left handed neutrino" and "right handed antineutrino" varieties, unlike all other fermions which have both left handed and right handed particles and antiparticles respectively - something that is no doubt related to the neutrinos' lack of electric charge, a quantum number intimately interrelated with parity as part of the CPT symmetry conserved in the Standard Model.
Searches are underway to determine in neutrinos have any measurable magnetic moment (none has been detected so far, but a large magnetic moment is possible if neutrinos are Majorana particles), and to detect any non-Standard Model forces that act on neutrinos (and possible other particles that interact with them).
Ultimately, my prediction is that the short-baseline neutrino oscillation experiment anomalies will be determined to have a cause other than a sterile or fourth generation neutrino, most likely due to miscalculated theoretical neutrino scattering expectations in current experiments. I also expect that no neutrino magnetic moment will be detected anytime soon, and that no non-Standard Model forces that act on neutrinos will be discovered.
While a warm dark matter scenario with particles with the properties of "sterile neutrinos" makes a great deal of sense and is a good fit to the data, I suspect that any such particles are not closely related to the Standard Model fermion neutrinos that we know and love. Instead, such particles may very well be creatures of the gravitational particle and force sector (as in gravi-weak unification).
Neutrino backgrounds and expectations
Over the next couple of decades we are developing increasingly refined understanding of what the background flux of neutrinos from nuclear reactions in the sun, and nuclear fission reactions inside the Earth look like, which will in turn tell us a lot about the inner workings of both the sun and the Earth. We are also struggling to understand neutrino fluxes associated with core collapse supernovae which release approximately 99% of their energy in neutrino form.
Better understandings of these backgrounds and theoretical expectations will facilitate precision measurement of neutrino fluxes that are notable because they represent signals above and beyond this background noise.