Whither All The Missing Neutrinos?

One of six neutrino detectors at Daya Bay Reactor Neutrino Experiment in China.

How is it  that a species of neutrino can be missing en route from a source to a detector? One explanation that had arrived compliments of two Nobel -winning scientists showed that neutrinos, which are found in three “flavors,” could oscillate from one flavor to another — changing identities like a spy on the run.  These flavor states: electron, muon and tau were in fact superpositions of mass eigenstates. Hence, one explanation is that if a detector wasn't sensitive to all three flavors then the "in flight" transformation of one neutrino flavor to another could mimic a neutrino deficit. In other words, the missing neutrinos amounted to an artifact of the measurements.

Let's review again these neutrino flavors for good measure. If there are three flavors: electron, muon and tau, then there must be three different corresponding neutrino masses which we can call: m1, m2 and m3.Further, the three "flavors" are really different superpositions of the 3 basic neutrino mass states.  Moreover, and to make it more complex, we know that quantum interference between mass states means a neutrino originating in one "flavor" can transmogrify to another over its transit.

Because of the oscillations and quantum interference we need to reckon in a "misalignment" between flavor and the basic neutrino masses. This is done by reference to three independent "mixing angles": Θ_12 , Θ_23  and Θ_13. To a good approximation, oscillation in any one regime is characterized by just one Θ_ij and a corresponding mass difference, defined:

 D m _ij² = [m _j² - m _i²]

As an example, the probability that a muon neutrino of energy E acquires a different flavor after traversing distance L is:

P = sin² Θ ₂₃  sin² (l₂₃)


where l23 is the energy -dependent oscillation length, given by:

4ħ E c /  (D m ₃₂²)

How well do we know the parameters? Atmospheric neutrino observations yield:

 Θ ₂₃  ~ 45 degrees, while D m ₃₂² = 0.0024 eV². Meanwhile, solar neutrino data yield roughly 33 degrees for Θ₁₂ and  D m ₂₁² = 0.00008 eV². (Note: ħ is the Planck constant of action divided by 2 π)  If then:


D m ₃₁²  =  [D m ₂₁²    +  D m ₃₂² ] = 0.00008 eV² + 0.0024 eV²

We know, D m ₃₁²  =  0.00248

which is close to D m ₃₂²

Earlier this decade, three experiments were initiated to track the apparent "disappearance" of electron antineutrinos from nearby nuclear power plants. The experiments are the Daya Bay Reactor Neutrino Experiment in China. the Reactor Experiment for Neutrino Oscillation in South Korea, and Double Chooze in France. All three have shown that the mixing angle Θ_13 is nonzero. (Though smaller than Θ_12 and  Θ_23 )

These results, as reported in Physics Today (May, p. 16) raised hopes that the solution to the problem of matter's preponderance over antimatter in the universe could reside in neutrino physics.

It should be added here that since the nonzero finding for Θ_13 in 2012, Daya Bay has been constantly improving its measurement of Θ_13   to reach ever greater precision. The upshot has been a puzzling divergence between the measurements and models for antineutrino production in reactors. This has led to the unsavory acceptance of one of two conclusions: 1) the emergence of a new physics superseding the "Standard Model" of particle physics, or 2) there exist major deficiencies in our understanding of nuclear reactor physics.

What then are these deviations, these divergences? One is that the total flux of reactor neutrinos detected at Daya Bay has fallen short of predictions. The other is that the shape of the antineutrino spectrum doesn't match that for the theoretical models, e.g.

The lower panel shows the ratio of measured data to the theoretical prediction. The spectrum overall shows a 6 percent deficit when compared with the data. But in the 5- 7 MeV range the bump in the spectrum shows up as an excess compared with model predictions.


The new calculations took into account thousands od beta decay branches involved in reactor neutrino production. At the end of the day, so to speak Daya Bay's 6 detectors monitored electron neutrinos emitted by six reactors at distances from 300m to 2 km. Over a 217 day detection period the six detectors counted 6 % fewer electron neutrinos than the new models predict.  This deficit is in line with earlier flux measurements from the 1980 and 1990s which actually led some researchers to speculate that the discrepancy might be accounted for a 4th entity: the "sterile neutrino".

The deviation of the antineutrino spectrum also begs the question of the underlying cause. Moreover, despite the overall deficit, the Daya Bay measurements found an excess of antineutrinos between 5 MeV and 7 MeV. (1 MeV = 10 ⁶ (1.6 x 10^-19 J)  =   1.6 x 10^-13 J)

Physicist Chao Zhang at Brookhaven National Laboratory suspects the shape discrepancy in the spectrum again interjects arguments for the sterile neutrino. Quoted in Physics Today, he says:

"If the theory didn't predict the spectral shape correctly should we trust its total flux prediction?"

He has a valid point, so perhaps indeed the deficit in the flux by 6 percent, consonant with earlier flux deficits, shows there is such a thing as a sterile neutrino.

The final conclusion will likely have to await further Daya Bay measurements of the mixing angle (Θ_13  ) as well as for the antineutrino flux and spectrum.  In the meantime the "sterile neutrino" hypothesis will be kept on the backburner until new evidence either confirms it or renders it redundant.