Robin Bjorkquist

Article: Improved search for a light sterile neutrino with the full configuration of the Daya Bay Experiment
Authors: Daya Bay Collaboration
Reference: arXiv:1607.01174

Today I bring you news from the Daya Bay reactor neutrino experiment, which detects neutrinos emitted by three nuclear power plants on the southern coast of China. The results in this paper are based on the first 621 days of data, through November 2013; more data remain to be analyzed, and we can expect a final result after the experiment ends in 2017.

Figure 1: Antineutrino detectors installed in the far hall of the Daya Bay experiment. Source: LBL news release.

For more on sterile neutrinos, see also this recent post by Eve.

Neutrino oscillations

Neutrinos exist in three flavors, each corresponding to one of the charged leptons: electron neutrinos ( $\nu_e$ ), muon neutrinos ( $\nu_\mu$ ) and tau neutrinos ( $\nu_\tau$ ). When a neutrino is born via the weak interaction, it is created in a particular flavor eigenstate. So, for example, a neutrino born in the sun is always an electron neutrino. However, the electron neutrino does not have a definite mass. Instead, each flavor eigenstate is a linear combination of the three mass eigenstates. This “mixing” of the flavor and mass eigenstates is described by the PMNS matrix, as shown in Figure 2.

Figure 2: Each neutrino flavor eigenstate is a linear combination of the three mass eigenstates.

The PMNS matrix can be parameterized by 4 numbers: three mixing angles (θ₁₂, θ₂₃ and θ₁₃) and a phase (δ).¹ These parameters aren’t known a priori — they must be measured by experiments.

Solar neutrinos stream outward in all directions from their birthplace in the sun. Some intercept Earth, where human-built neutrino observatories can inventory their flavors. After traveling 150 million kilometers, only ⅓ of them register as electron neutrinos — the other ⅔ have transformed along the way into muon or tau neutrinos. These neutrino flavor oscillations are the experimental signature of neutrino mixing, and the means by which we can tease out the values of the PMNS parameters. In any specific situation, the probability of measuring each type of neutrino is described by some experiment-specific parameters (the neutrino energy, distance from the source, and initial neutrino flavor) and some fundamental parameters of the theory (the PMNS mixing parameters and the neutrino mass-squared differences). By doing a variety of measurements with different neutrino sources and different source-to-detector (“baseline”) distances, we can attempt to constrain or measure the individual theory parameters. This has been a major focus of the worldwide experimental neutrino program for the past 15 years.

¹ This assumes the neutrino is a Dirac particle. If the neutrino is a Majorana particle, there are two more phases, for a total of 6 parameters in the PMNS matrix.

Sterile neutrinos

Many neutrino experiments have confirmed our model of neutrino oscillations and the existence of three neutrino flavors. However, some experiments have observed anomalous signals which could be explained by the presence of a fourth neutrino. This proposed “sterile” neutrino doesn’t have a charged lepton partner (and therefore doesn’t participate in weak interactions) but does mix with the other neutrino flavors.

The discovery of a new type of particle would be tremendously exciting, and neutrino experiments all over the world (including Daya Bay) have been checking their data for any sign of sterile neutrinos.

Neutrinos from reactors

Figure 3: Chart of the nuclides, color-coded by decay mode. Source: modified from Wikimedia Commons.

Nuclear reactors are a powerful source of electron antineutrinos. To see why, take a look at this zoomed out version of the chart of the nuclides. The chart of the nuclides is a nuclear physicist’s version of the periodic table. For a chemist, Hydrogen-1 (a single proton), Hydrogen-2 (one proton and one neutron) and Hydrogen-3 (one proton and two neutrons) are essentially the same thing, because chemical bonds are electromagnetic and every hydrogen nucleus has the same electric charge. In the realm of nuclear physics, however, the number of neutrons is just as important as the number of protons. Thus, while the periodic table has a single box for each chemical element, the chart of the nuclides has a separate entry for every combination of protons and neutrons (“nuclide”) that has ever been observed in nature or created in a laboratory.

The black squares are stable nuclei. You can see that stability only occurs when the ratio of neutrons to protons is just right. Furthermore, unstable nuclides tend to decay in such a way that the daughter nuclide is closer to the line of stability than the parent.

Nuclear power plants generate electricity by harnessing the energy released by the fission of Uranium-235. Each U-235 nucleus contains 143 neutrons and 92 protons (n/p = 1.6). When U-235 undergoes fission, the resulting fragments also have n/p ~ 1.6, because the overall number of neutrons and protons is still the same. Thus, fission products tend to lie along the white dashed line in Figure 3, which falls above the line of stability. These nuclides have too many neutrons to be stable, and therefore undergo beta decay: $n \to p + e + \bar{\nu}_e$ . A typical power reactor emits 6 × 10^20 $\bar{\nu}_e$ per second.

The Daya Bay experiment

The Daya Bay nuclear power complex is located on the southern coast of China, 55 km northeast of Hong Kong. With six reactor cores, it is one of the most powerful reactor complexes in the world — and therefore an excellent source of electron antineutrinos. The Daya Bay experiment consists of 8 identical antineutrino detectors in 3 underground halls. One experimental hall is located as close as possible to the Daya Bay nuclear power plant; the second is near the two Ling Ao power plants; the third is located 1.5 – 1.9 km away from all three pairs of reactors, a distance chosen to optimize Daya Bay’s sensitivity to the mixing angle $\theta_{13}$ .

The neutrino target at the heart of each detector is a cylindrical vessel filled with 20 tons of Gadolinium-doped liquid scintillator. The vast majority of $\bar{\nu}_e$ pass through undetected, but occasionally one will undergo inverse beta decay in the target volume, interacting with a proton to produce a positron and a neutron: $\bar{\nu}_e + p \to e^+ + n$ .

Figure 5: Design of the Daya Bay $\bar{\nu}_e$ detectors. Each detector consists of three nested cylindrical vessels. The inner acrylic vessel is about 3 meters tall and 3 meters in diameter. It contains 20 tons of Gadolinium-doped liquid scintillator; when a $\bar{\nu}_e$ interacts in this volume, the resulting signal can be picked up by the detector. The outer acrylic vessel holds an additional 22 tons of liquid scintillator; this layer exists so that $\bar{\nu}_e$ interactions near the edge of the inner volume are still surrounded by scintillator on all sides — otherwise, some of the gamma rays produced in the event might escape undetected. The stainless steel outer vessel is filled with 40 tons of mineral oil; its purpose to prevent outside radiation from reaching the scintillator. Finally, the outer vessel is lined with 192 photomultiplier tubes, which collect the scintillation light produced by particle interactions in the active scintillation volumes. The whole device is underwater for additional shielding. Source: arXiv:1508.03943.

Figure 5: Design of the Daya Bay $\bar{\nu}_e$ detectors. Each detector consists of three nested cylindrical vessels. The inner acrylic vessel is about 3 meters tall and 3 meters in diameter. It contains 20 tons of Gadolinium-doped liquid scintillator; when a $\bar{\nu}_e$ interacts in this volume, the resulting signal can be picked up by the detector. The outer acrylic vessel holds an additional 22 tons of liquid scintillator; this layer exists so that $\bar{\nu}_e$ interactions near the edge of the inner volume are still surrounded by scintillator on all sides — otherwise, some of the gamma rays produced in the event might escape undetected. The stainless steel outer vessel is filled with 40 tons of mineral oil; its purpose to prevent outside radiation from reaching the scintillator. Finally, the outer vessel is lined with 192 photomultiplier tubes, which collect the scintillation light produced by particle interactions in the active scintillation volumes. The whole device is underwater for additional shielding. Source: arXiv:1508.03943.

Figure 6: Cartoon version of the signal produced in the Daya Bay detectors by inverse beta decay. The size of the prompt pulse is related to the antineutrino energy; the delayed pulse has a characteristic energy of 8 MeV.

The positron and neutron create signals in the detector with a characteristic time relationship, as shown in Figure 6. The positron immediately deposits its energy in the scintillator and then annihilates with an electron. This all happens within a few nanoseconds and causes a prompt flash of scintillation light. The neutron, meanwhile, spends some tens of microseconds bouncing around (“thermalizing”) until it is slow enough to be captured by a Gadolinium nucleus. When this happens, the nucleus emits a cascade of gamma rays, which in turn interact with the scintillator and produce a second flash of light. This combination of prompt and delayed signals is used to identify $\bar{\nu}_e$ interaction events.

Daya Bay’s search for sterile neutrinos

Daya Bay is a neutrino disappearance experiment. The electron antineutrinos emitted by the reactors can oscillate into muon or tau antineutrinos as they travel, but the detectors are only sensitive to $\bar{\nu}_e$ , because the antineutrinos have enough energy to produce a positron but not the more massive $\mu^+$ or $\tau^+$ . Thus, Daya Bay observes neutrino oscillations by measuring fewer $\bar{\nu}_e$ than would be expected otherwise.

Based on the number of $\bar{\nu}_e$ detected at one of the Daya Bay experimental halls, the usual three-neutrino oscillation theory can predict the number that will be seen at the other two experimental halls (EH). You can see how this plays out in Figure 7. We are looking at the neutrino energy spectrum measured at EH2 and EH3, divided by the prediction computed from the EH1 data. The gray shaded regions mark the one-standard-deviation uncertainty bounds of the predictions. If the black data points deviated significantly from the shaded region, that would be a sign that the three-neutrino oscillation model is not complete, possibly due to the presence of sterile neutrinos. However, in this case, the black data points are statistically consistent with the prediction. In other words, Daya Bay sees no evidence for sterile neutrinos.

Figure 7: Some results of the Daya Bay sterile neutrino search. Source: arxiv:1607.01174.

Does that mean sterile neutrinos don’t exist? Not necessarily. For one thing, the effect of a sterile neutrino on the Daya Bay results would depend on the sterile neutrino mass and mixing parameters. The blue and red dashed lines in Figure 7 show the sterile neutrino prediction for two specific choices of $\theta_{14}$ and $\Delta m_{41}^2$ ; these two examples look quite different from the three-neutrino prediction and can be ruled out because they don’t match the data. However, there are other parameter choices for which the presence of a sterile neutrino wouldn’t have a discernable effect on the Daya Bay measurements. Thus, Daya Bay can constrain the parameter space, but can’t rule out sterile neutrinos completely. However, as more and more experiments report “no sign of sterile neutrinos here,” it appears less and less likely that they exist.

Further Reading

K. Nakamura, “Neutrino mass, mixing and oscillations,” PDG review of particle physics. (http://pdg.lbl.gov/2015/reviews/rpp2015-rev-neutrino-mixing.pdf)
C. Mariani, “Review of Reactor Neutrino Oscillation Experiments.” (arXiv:1201.6665)
Xin Qian and Wei Wang, “Reactor Neutrino Experiments: $\theta_{13}$ and Beyond.” (arXiv:1405.7217)
Antonio Palazzo, “Constraints on very light sterile neutrinos from $\theta_{13}$ -sensitive reactor experiments.” (arXiv:1308.5880)

Article: Search for the lepton flavor violating decay μ⁺ → e⁺γ with the full dataset of the MEG experiment
Authors: MEG Collaboration
Reference: arXiv:1605.05081

I work on the Muon g-2 experiment, which is housed inside a brand new building at Fermilab. Next door, another experiment hall is under construction. It will be the home of the Mu2e experiment, which is slated to use Fermilab’s muon beam as soon as Muon g-2 wraps up in a few years. Mu2e will search for evidence of an extremely rare process — namely, the conversion of a muon to an electron in the vicinity of a nucleus. You can read more about muon-to-electron conversion in a previous post by Flip.

Today, though, I bring you news of a different muon experiment, located at the Paul Scherrer Institute in Switzerland. The MEG experiment was operational from 2008-2013, and they recently released their final result.

Context of the MEG experiment

Figure 1: Almost 100% of the time, a muon will decay into an electron and two neutrinos.

MEG (short for “mu to e gamma”) and Mu2e are part of the same family of experiments. They each focus on a particular example of charged lepton flavor violation (CLFV). Normally, a muon decays into an electron and two neutrinos. The neutrinos ensure that lepton flavor is conserved; the overall amounts of “muon-ness” and “electron-ness” do not change.

Figure 2 lists some possible CLFV muon processes. In each case, the muon transforms into an electron without producing any neutrinos — so lepton flavor is not conserved! These processes are allowed by the standard model, but with such minuscule probabilities that we couldn’t possibly measure them. If that were the end of the story, no one would bother doing experiments like MEG and Mu2e — but of course that’s not the end of the story. It turns out that many new physics models predict CLFV at levels that are within range of the next generation of experiments. If an experiment finds evidence for one of these CLFV processes, it will be a clear indication of beyond-the-standard-model physics.

Figure 2: Some examples of muon processes that do not conserve lepton flavor. Also listed are the current/upcoming experiments that aim to measure the probabilities of these never-before-observed processes.

Results from MEG

The goal of the MEG experiment was to do one of two things:

Measure the branching ratio of the μ⁺ → e⁺γ decay, or
Establish a new upper limit

Outcome #1 is only possible if the branching ratio is high enough to produce a clear signal. Otherwise, all the experimenters can do is say “the branching ratio must be smaller than such-and-such, because otherwise we would have seen a signal” (i.e., outcome #2).

MEG saw no evidence of μ⁺ → e⁺γ decays. Instead, they determined that the branching ratio is less than 4.2 × 10^-13 (90% confidence level). Roughly speaking, that means if you had a pair of magic goggles that let you peer directly into the subatomic world, you could stand around and watch 2 × 10^12 muons decay without seeing anything unusual. Because real experiments are messier and less direct than magic goggles, the MEG result is actually based on data from 7.5 × 10^14 muons.

Before MEG, the previous experiment to search for μ⁺ → e⁺γ was the MEGA experiment at Los Alamos; they collected data from 1993-1995, and published their final result in 1999. They found an upper limit for the branching ratio of 1.2 × 10^-11. Thus, MEG achieved a factor of 30 improvement in sensitivity over the previous result.

How the experiment works

Figure 3: The MEG signal consists of a back-to-back positron and gamma, each carrying half the rest energy of the parent muon.

A continuous beam of positive muons enters a large magnet and hits a thin plastic target. By interacting with the material, about 80% of the muons lose their kinetic energy and come to rest inside the target. Because the muons decay from rest, the MEG signal is simple. Energy and momentum must be conserved, so the positron and gamma emerge from the target in opposite directions, each with an energy of 52.83 MeV (half the rest energy of the muon).¹ The experiment is specifically designed to catch and measure these events. It consists of three detectors: a drift chamber to measure the positron trajectory and momentum, a timing counter to measure the positron time, and a liquid xenon detector to measure the photon time, position, and energy. Data from all three detectors must be combined to get a complete picture of each muon decay, and determine whether it fits the profile of a MEG signal event.

Figure 4: Layout of the MEG experiment. Source: arXiv:1605.05081.

In principle, it sounds pretty simple….to search for MEG events, you look at each chunk of data and go through a checklist:

Is there a photon with the correct energy?
Is there a positron at the same time?
Did the photon and positron emerge from the target in opposite directions?
Does the positron have the correct energy?

Four yeses and you might be looking at a rare CLFV muon decay! However, the key word here is might. Unfortunately, it is possible for a normal muon decay to masquerade as a CLFV decay. For MEG, one source of background is “radiative muon decay,” in which a muon decays into a positron, two neutrinos and a photon; if the neutrinos happen to have very low energy, this will look exactly like a MEG event. In order to get a meaningful result, MEG scientists first had to account for all possible sources of background and figure out the expected number of background events for their data sample. In general, experimental particle physicists spend a great deal of time reducing and understanding backgrounds!

What’s next for MEG?

The MEG collaboration is planning an upgrade to their detector which will produce an order of magnitude improvement in sensitivity. MEG-II is expected to begin three years of data-taking late in 2017. Perhaps at the new level of sensitivity, a μ⁺ → e⁺γ signal will emerge from the background!

¹ Because photons are massless and positrons are not, their energies are not quite identical, but it turns out that they both round to 52.83 MeV. You can work it out yourself if you’re skeptical (that’s what I did).

Further Reading

Robert H. Bernstein and Peter S. Cooper, “Charged Lepton Flavor Violation: An Experimenter’s Guide.” (arXiv:1307.5787)
S. Mihara, J.P. Miller, P. Paradisi and G. Piredda, “Charged Lepton Flavor–Violation Experiments.” (DOI: 10.1146/annurev-nucl-102912-144530)
André de Gouvêa and Petr Vogel, “Lepton Flavor and Number Conservation, and Physics Beyond the Standard Model.” (arXiv:1303.4097)

Author: Robin Bjorkquist

Daya Bay and the search for sterile neutrinos

Probing the Standard Model with muons: new results from MEG