Reactor experiment reveals neutrino oscillation’s third mixing angle
May 2012, page 13
A nonzero value for this elusive parameter offers a possible explanation for the cosmic shortage of antimatter.
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.
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 (νμ) 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 θij and the corresponding Δm2ji ≡ ∣mj2 − mi2∣. For example, the probability that a νμ of energy E, created in the upper atmosphere, has a different flavor after a journey of distance L is
Patmos = 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.
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
Preact = 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.
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 eiδ 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 νμ 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 νμ 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
- F. P. An et al. (Daya Bay collaboration), Phys. Rev. Lett. (in press), available at http://arxiv.org/abs/1203.1669.
- Y. Abe et al. (Double Chooz collaboration), Phys. Rev. Lett. 108, 131801 (2012).
- J. K. Ahn et al. (RENO collaboration), http://arxiv.org/abs/1204.0626.