Flavor oscillation may be different in neutrinos and antineutrinos

In 1995 William Louis and colleagues at Los Alamos National Laboratory reported the first evidence of neutrino flavor oscillation in an accelerator experiment. The report was disquieting, and became more so over the next three years as its statistical significance was bolstered by more data from the LANL experiment.

Why the disquiet? After all, neutrino oscillation, the metamorphosis of neutrino flavors with a probability that oscillates with travel distance L like sin²(L/λ), was already well attested for neutrinos from the Sun and from cosmic-ray showers in the atmosphere. The characteristic oscillation length λ is given by 4ħE/c ³Δm ², where E is the neutrino’s energy and Δm ² is the difference between the squared masses of the two neutrino mass eigenstates involved.

The prevailing model of neutrino oscillation assumes that there are three different neutrino mass eigenstates in nature and that they are different linear superpositions of the three flavor eigenstates ν _e, ν _µ, and ν _τ, associated respectively with the three charged leptons: the electron, the muon, and the much heavier tau. The standard oscillation phenomenology presumes that, to adequate approximation, only two of the three neutrino mass states are involved in any one observational oscillation regime.

The LANL data, seeming to reveal the metamorphosis ν _µ → ν _e over distances of less than 100 meters in a low-energy accelerator beam, were well fitted by Δm ² of order 1 eV². That’s several hundred times bigger than the Δm ² measured for atmospheric neutrino oscillation and ten thousand times bigger than what’s found for solar neutrinos. But if only three mass eigenstates exist, no one Δm ² can exceed the sum of the other two.

By 1995 electron-positron collider experiments had already excluded the existence of more than three neutrino flavors participating in the weak interactions. So the LANL data seemed to require an additional “sterile” neutrino flavor, impervious to the weak interactions. That prospect was unappealing; it would have cluttered the elegant prevailing theory.

So experimenters at Fermilab responded by building the MiniBoone neutrino beam and detector, a facility explicitly designed to confirm the LANL result or lay it to rest. And indeed in 2007, with three years of data in hand, the MiniBoone collaboration announced that its results were incompatible with LANL’s claim (see Physics Today, June 2007, page 18 ). The neutrino-physics community breathed a sigh of relief.

Premature obituary

It now turns out that the sterile neutrino’s obituary was premature. In the prevailing model, flavor oscillation is the same for neutrinos ν and antineutrinos $\overline{\nu }$ . So whereas the LANL experiment had been done with a $\overline{{\nu }_{\mu }}$ beam, the MiniBoone collaboration used a ν _µ beam. They did that because, even though the fundamental physics was presumed to be the same, a ν _µ beam would permit significantly faster accumulation of data. But just to be sure, in 2006 they started taking data with a ${\overline{\nu }}_{\mu }$ beam. And lo and behold, their newly reported ${\overline{\nu }}_{\mu }$ -beam result resembles the LANL result that started all the fuss. ¹

The new result is not yet statistically robust, but it already raises the stakes. The issue is no longer just whether sterile neutrinos exist. If all three experimental results are essentially correct, we now have the first evidence of CP -symmetry violation attributable to neutrino interactions. (The symmetry operators C and P are, respectively, particle-antiparticle exchange and parity.) The only CP violation previously observed in the laboratory occurs in quark decays, and that’s too feeble an effect to explain the matter-antimatter imbalance of the cosmos. (See the article by Helen Quinn in Physics Today, February 2003, page 30 .)

The MiniBoone experiment is essentially a beam of ν _µ (or ${\overline{\nu }}_{\mu }$ ) with a broad distribution of energies around 500 MeV, passing through a 12-meter-diameter spherical detector filled with mineral oil and lined with photomultiplier tubes. The detector sits about 500 meters downstream of where the beam is formed by the decay of charged pions created by protons bombarding a metal target. The neutrino energies and travel distance are both about 15 times greater than those of the LANL experiment. But L and E enter the oscillation phenomenology only as the ratio L/E, and the MiniBoone parameters were chosen accordingly to provide maximum sensitivity to the LANL claim in an experiment with very different potential sources of error.

The bombarded target emits pions in profusion. The decay of a π⁺ or a π⁻ creates, respectively, a ν _µ or a ${\overline{\nu }}_{\mu }$ . So one can switch from a predominantly ν _µ beam to a predominantly ${\overline{\nu }}_{\mu }$ beam, albeit with lesser flux, by reversing the polarity of the magnetic “horn” that focuses pions of the desired charge onto the beam axis. Other magnets and shielding downstream of the pion-decay region clear the beam of hadrons, charged leptons, and gammas.

The signal that indicates the sought-after metamorphosis ${\overline{\nu }}_{\mu }$ → ${\overline{\nu }}_{\text{e}}$ would be the appearance in the detector of more ${\overline{\nu }}_{\text{e}}$ interactions than could be attributed to impostors or beam contaminants. A neutrino rarely interacts with a nucleon it’s traversing. But when it does and turns into a charged lepton, it reveals its flavor by the kind of lepton it becomes. The phototube array distinguishes between muons and positrons or electrons by the Cherenkov light they generate in the oil: The heavier muons have straighter tracks in the oil and therefore project cleaner circles of Cherenkov light onto the detector’s wall.

The best-fit oscillation parameters from the LANL experiment predict that in the MiniBoone antineutrino beam, only one ${\overline{\nu }}_{\mu }$ in about 400 will have turned into a ${\overline{\nu }}_{\text{e}}$ by the time it enters the detector. The positrons created by those few changelings would be greatly outnumbered by impostors and positrons from various sources of background. So one wants to run the experiment long enough to reduce statistical uncertainties to the point where excesses over estimated background signals could be convincing.

The new result

The new MiniBoone result is based on three years of running in the antineutrino mode. But it is still statistically weaker than the earlier neutrino-mode null result. Figure 1(a) shows the number of positron-like interactions recorded by the detector as a function of the incident neutrino’s energy E. That energy is calculated from the phototube array’s measurement of the emerging charged lepton’s energy and direction, on the assumption that the reaction was

$${\overline{\nu }}_{\text{e}}+\text{p}\to {\text{e}}^{+}+\text{n}\text{.}$$

Figure 1(a) also shows the estimated contributions from various backgrounds such as the creation of gammas by interactions in the detector and the contamination of the beam with electron neutrinos from the decays of kaons and muons. Because the backgrounds are worst for E less than 475 MeV, the collaboration ignored events below that cutoff in determining the best oscillation fit to the data. It’s the same cutoff that the group had “blindly” chosen—from calibration data only—to avoid event-selection bias in its 2007 analysis of the neutrino-mode data.

In figure 1(b), the observed energy distribution and the fit are shown with the estimated background subtracted off. Above 475 MeV, the observed excess is only about 25 events. But fitting the data with a background-only hypothesis is excluded at the 99.5% confidence level. That by itself signifies a neutrino-oscillation signal only 2.7 standard deviations (σ) above background. But as shown in figure 1(b), the distribution of excess events is reasonably well described by an appropriately scaled fit to the LANL data, for which a more robust 3.8-σ oscillation signal had been claimed.

Any particular neutrino-oscillation fit is characterized by two parameters: Δm ², which determines the oscillation length λ, and A, the amplitude of the probability oscillation. The latter, which can range from 0 to 1, is a measure of the misalignment in Hilbert space between the flavor and mass basis states.

Figure 2 shows the regions of the parameter space favored by the LANL and MiniBoone antineutrino data. The two experiments are clearly in substantial agreement. The single best fit to the MiniBoone data has A nearly maximal. But the likelihood distribution is fairly flat over a large parameter range, and A bigger than 10% seems to be excluded by limits from experiments at reactors.

Violating CP symmetry

Taken seriously and together, the MiniBoone antineutrino result and its LANL antecedent appear to reveal a new Δm ² much larger than the sum of those that fit the solar and atmospheric oscillation data. That inequality would require a fourth neutrino mass eigenstate, predominantly sterile in flavor, and presumably much heavier than the other three.

But given the absence of any oscillation signal in the earlier neutrino-mode MiniBoone data, a single sterile neutrino state probably won’t do. Incorporating that kind of CP violation into the standard model of particle theory requires interference between the couplings of two different sterile mass eigenstates to the known neutrinos.

Therefore MiniBoone team member Georgia Karagiorgi (MIT) and coworkers have tried to fit all three accelerator results plus limits from other relevant experiments with a very general model with two sterile mass states. ² “We did succeed in fitting the neutrino and antineutrino data separately,” says Karagiorgi. “But the two fits weren’t mutually compatible.”

“The failure to get a global fit with so general a model is instructive,” says Fermilab theorist Boris Kayser. “It suggests that if the data faithfully reflect nature, they may be hinting at new interactions beyond the standard model.” And indeed, theorists Evgeny Akhmedov and Thomas Schwetz at the Max Planck Institute for Nuclear Physics in Heidelberg have now reported a global fit with just one sterile neutrino state plus non-standard-model interactions. ³ The MiniBoone team is continuing to run in antineutrino mode, hoping at least to double its event tally before Fermilab’s accelerator complex is scheduled to shut down in March 2012 for major reconfiguration.