Reactor experiment reveals neutrino oscillation’s third mixing angle

A major neutrino experiment set amidst six nuclear reactors on Daya Bay near Hong Kong has revealed a long-sought result. Having measured very small deficits of electron antineutrinos (ν‾_e) at various short distances from the reactors that create them, the international Daya Bay collaboration reports that θ₁₃, last of the three mixing angles that characterize neutrino oscillation, is definitely not zero. ¹ In fact, it turns out to be big enough for experimenters now to begin investigating the role of neutrinos in creating the manifest matter–antimatter asymmetry of the cosmos.

The survival of so little antimatter from the Big Bang requires that some fundamental interactions violate CP symmetry—invariance under the combined operations of mirror inversion (P) and charge conjugation (C), the replacement of particles by their antiparticles. It’s long been known that the weak interactions of quarks exhibit some CP violation. But that violation is too small to explain the cosmological asymmetry.

Hence the fervent interest in θ₁₃. If not the quarks, then perhaps neutrinos might violate CP strongly enough to do the trick. But within the purview of the standard theory of particle physics, any neutrino CP violation requires that all three mixing angles be nonzero. Earlier searches, having found no clear signal of a nonzero θ₁₃, concluded that it is at best significantly smaller than the other two mixing angles.

Mixing and oscillation

A neutrino is created or detected in one of three flavors, associated with the three charged leptons: electrons, muons, and taus. The three flavor eigenstates are different superpositions of the three neutrino-mass eigenstates. Because of quantum interference between mass states, a neutrino created with one flavor undergoes oscillatory flavor metamorphosis as it travels. Neutrino oscillation over large distances is well attested for MeV electron neutrinos created in the Sun and GeV muon neutrinos (ν_μ) created high in the atmosphere by cosmic rays. Those observations require that there must be three different neutrino masses: m₁, m₂, and m₃.

The misalignment between the flavor and mass basis states is parameterized by the three independent mixing angles θ₁₂, θ₂₃, and θ₁₃. To good approximation, neutrino oscillation in any one observational regime of distance and neutrino energy is characterized by just one θ_ij and the corresponding Δm²_ji ≡ ∣m_j² − m_i²∣. For example, the probability that a ν_μ of energy E, created in the upper atmosphere, has a different flavor after a journey of distance L is

P_atmos = sin² 2θ₂₃ sin²(L/λ₂₃),

where the energy-dependent oscillation length λ₂₃ is given by 4ℏcE/Δm²₃₂.

From the atmospheric neutrino observations, θ₂₃ is known to be close to 45° and Δm²₃₂ is 2.4 × 10⁻³ eV². The solar-neutrino data yield about 33° for θ₁₂ and 8 × 10⁻⁵ eV² for Δm²₂₁. It follows immediately that Δm²₃₁ (by definition equal to Δm²₃₂ + Δm²₂₁) is close to Δm²₃₂. So it was already clear before the Daya Bay experiment and Double Chooz, its smaller predecessor in France, that any θ₁₃ oscillation of reactor antineutrinos, with typical energies of a few MeV, would have oscillation lengths λ₁₃ of only a few kilometers.

The question facing the Daya Bay team was whether the oscillation amplitude sin² 2θ₁₃ for the disappearance of reactor antineutrinos over such distances would be big enough to detect. Recent data from Double Chooz had hinted at a nonzero θ₁₃ and set an upper limit of 0.16 on sin² 2θ₁₃, which is what such experiments measure directly. ² The Daya Bay ν‾_e detector array was designed to measure a sin² 2θ₁₃ as small as 0.01 in three years of data taking.

Happily, sin² 2θ₁₃ turns out to be an order of magnitude bigger than Daya Bay’s sensitivity limit. So with just two months of analyzed data in hand, Daya Bay spokesman Yifang Wang (Beijing Institute of High Energy Physics) was able to report in March to a worldwide webcast audience that sin² 2θ₁₃ = 0.092 ± 0.017, corresponding to a θ₁₃ of about 9°. That’s an unexpectedly prompt 5.2-standard-deviation exclusion of the possibility that there are only two nonzero neutrino mixing angles.

Daya Bay

The Daya Bay experiment, primarily a China–US collaboration, extends over a triangular area roughly 2 km on a side. Six power reactors are arrayed in two clusters near two of the triangle’s vertices. Near the third vertex is the “far” experimental hall. As shown in figure 1, it houses three of the experiment’s six detectors, separated from the reactors by distances (1.5–1.9 km) at which one would expect to find roughly maximal disappearance. The other detectors occupy two “near” halls, each monitoring its cluster of reactors at distances of about 0.5 km. The halls are deep underground to reduce penetration by cosmic-ray muons. But because neutrinos essentially ignore material barriers, every detector sees unimpeded flux from all six reactors.

On those distance scales, the probability that flavor oscillation will render a ν‾_e invisible at a distance L from the reactor that created it is

P_react = sin² 2θ₁₃ sin² (Δm²₃₁L /4ℏcE),

where θ₁₃ was the only unknown, to be determined by shortfalls in the near and far detectors. The energy spectrum of antineutrinos emerging from the reactors peaks near 3 MeV.

At the heart of each detector is 20 tons of gadolinium-doped liquid scintillator monitored by several hundred photomultiplier tubes. Electron antineutrinos from the reactors are detected by their inverse-beta-decay reactions

ν‾_e + p → e⁺ + n

with hydrogen nuclei in the scintillator. The scintillation light generated by the emerging positron provides an approximate measure of the incident antineutrino’s energy.

Of course, radioactive and cosmic-ray interlopers produce spurious scintillation signals in spite of elaborate shielding measures. That’s why the scintillator is laced with Gd, which has an enormous capture cross section for neutrons. That capture and its subsequent nuclear-decay cascade produce a characteristic 8-MeV scintillation about 30 μs after the positron signal. So, to minimize backgrounds, the experimenters require a candidate ν‾_e event to exhibit both a prompt e⁺ signal and a delayed signal consistent with n capture by a Gd nucleus.

Disappearance and appearance

The best fit for sin² 2θ₁₃ was determined from the ν‾_e shortfalls—relative to expectations in the absence of oscillation—observed by each of the six detectors in 55 days of data taking last winter. Figure 2 summarizes those shortfalls and compares them with what the best oscillation fit predicts at their various distances from the reactors. The weighted mean distances in the plot take account of different reactor power levels and the trivial inverse-square falloff of flux with distance.

Figure 3a compares the ν‾_e energy spectrum observed in the far hall with what’s expected, assuming no oscillation, from the near-hall observations. As the theory predicts, the observed shortfall is energy dependent; it’s greatest near 3 MeV. Figure 3b shows that the observed spectral distortion is well described by the best oscillation fit.

The uncertainty on the sin² 2θ₁₃ measurement is, for now, dominated by limited statistics. “With two more detectors on the way and three more years of running, the error could come down to 4%,” says Steven Kettell (Brookhaven National Laboratory), chief scientist for the experiment’s US contingent. Knowing θ₁₃ with precision is important for fundamental particle physics as well as for cosmology.

A nonzero θ₁₃ is necessary—but not sufficient—for CP violation in neutrino interactions. Because there are three nonzero mixing angles, the unitary matrix that describes all the oscillations has an extra degree of freedom: an independent phase factor e^iδ that dictates the degree of CP violation. The situation is quite similar to quark-flavor mixing, in which three mixing angles plus one complex phase account for all the CP violation thus far observed (see PHYSICS TODAY, December 2008, page 16 ).

Standard theory can’t predict δ. It might be zero, in which case all neutrino CP-violation bets are off. But it can be measured—now that all three mixing angles are known—by accelerator experiments designed to monitor the appearance, over long distances, of other flavors in GeV ν_μ beams from accelerators that create their parent pions in sufficient profusion. Such a one is the proposed Long-Baseline Neutrino Experiment (LBNE). The plan is to direct an intense ν_μ beam from Fermilab at a detector inside the DUSEL underground laboratory in South Dakota. But LBNE has funding problems, and its future is in question (see page 30 of this issue).

The path from establishing neutrino CP violation to explaining the cosmic antimatter shortage is not straightforward. Cosmologists generally favor the idea that the CP-violating neutrinos actually responsible for the disappearance of antimatter after the Big Bang were not the light ones we know—all of them lighter than 1 eV. (For comparison the electron’s mass is 0.5 MeV.) Rather, they were short-lived, ultramassive neutrinos, impervious to the standard weak interactions, proposed by a number of theorists around 1980 to explain why neutrinos are so much lighter than the charged leptons and quarks.

The putative heavy neutrinos in that widely credited “seesaw model” have masses something like 10¹⁰ GeV, so that the quark and charged-lepton masses would approximate the geometric mean of the light and heavy neutrinos. The lighter the one, the heavier the other; hence the seesaw metaphor. The immediate relevance of the Daya Bay result for cosmology, then, is that the degree of CP violation by the heavy seesaw neutrinos should be comparable to that of the neutrinos we know.

As we go to press, the South Korean RENO collaboration reports that its reactor experiment has confirmed Daya Bay’s sin² 2θ₁₃ measurement. ³