Neutrinos have mass — but only a little, and nobody knows exactly how much. Of the three flavors of neutrino (electron neutrino, muon neutrino, tau neutrino), the heaviest has at least one 10‑millionth the electron's mass and could have more than 10 times that much. But which flavor is the heaviest? That too is uncertain.

Neutrinos come in three flavors, but detectors see mixtures of the flavors' characteristic masses. Scientists have measured differences among the three mixed states, but the masses themselves are unknown. Also unknown is whether the biggest difference marks the heaviest mixed state (the so-called normal hierarchy) or the lightest one (an inverted hierarchy).

"Determining neutrino mass will have profound implications for astrophysics and cosmology," says Kam-Biu Luk of the Physics Division, a leader in neutrino studies who is also a professor of physics at UC Berkeley. "We hope to learn how leptons" — electrons and their relatives — "came into existence in the moments after the Big Bang, a process that could account for why there is more matter than antimatter in the universe."

Answering such fundamental questions will only be possible if the value of a term referred to as "neutrino mixing angle theta one three," written θ₁₃, turns out to be more than zero.

To pin down the value of θ₁₃ with high precision, Luk and colleagues in China, the U.S., and other countries are planning to make use of the powerful nuclear reactors at China's Daya Bay. The project will require three kilometers (almost two miles) of tunnels drilled under granite mountains hundreds of meters high; in chambers shielded from cosmic rays by the overlying rock the researchers will install eight identical antineutrino detectors, each weighing 100 metric tons, which can be rolled from location to location inside the tunnel system.

Berkeley Lab leads the U.S. participation in Daya Bay, with the Lab's associate director for general sciences, James Siegrist, representing Berkeley Lab in international talks. The Daya Bay experiment's scientific spokespersons are Berkeley Lab's Luk and Yi-Fang Wang of the Institute of High Energy Physics in Beijing. Bill Edwards of Berkeley Lab's Engineering Division is the U.S. Project Manager overseeing construction of the experiment; Karsten Heeger of Physics is a member of the Daya Bay scientific team, and Joe Wang and Pat Dobson of Earth Sciences aided the geological survey.

Scores of U.S. and Chinese personnel have joined with colleagues in Russia, Taiwan, and the Czech Republic in the Daya Bay experiment — more than 20 institutions in all. The Chinese Academy of Sciences has led the way in committing funds to the project, with other Chinese funding agencies and regional governments following suit.

As for the U.S., "the Department of Energy wants to make Daya Bay happen," says Siegrist. DOE is sponsoring U.S. research and development, with a review scheduled for November, 2006 to establish the basis for further support, which will eventually total $20 to $30 million.

The hunt for neutrino mass

"Neutrinos interact with other particles only through the weak force and gravity, which means hardly at all," Siegrist says. "Billions pass right through your body every second. To stop all of them would require lead shielding several light‑years thick." 

	Beginning in the 1960s Ray Davis (inset left) built an experiment to detect solar neutrinos deep in the Homestake Mine in South Dakota, but he found only about a third the number of neutrinos predicted by theorist John Bahcall (right).

With particles so wispy and standoffish, why is knowing their mass important? For one thing, mass allows neutrinos to change flavors, or oscillate. Between 1998 and 2002, the confirmation that neutrinos really do oscillate solved a longstanding mystery. Beginning in the mid-1960s, experiments designed to count solar neutrinos had found only a third of the number expected to be detectable as products of nuclear fusion in the sun. The answer to this conundrum: it seems that on their way to Earth, electron neutrinos change flavors, many arriving as elusive muon or tau neutrinos.

Neutrinos oscillate at a steady rate because the characteristic masses of each type — their mass "eigenstates" — don't sync up with their characteristic flavors. Every neutrino detected is a mixture of three characteristic masses that continually interfere with one another like different radio frequencies, rhythmically changing their proportions. The probability of finding a given type of neutrino at a certain distance from where it was created depends on values called mixing angles, which express the proportion of mass eigenstates 1, 2, and 3 in each kind of neutrino detected.

Two of the three mixing angles, θ₁₂ and θ₂₃, have been measured with some precision, at least enough to estimate the differences among neutrino masses: there's a modest difference between neutrino 1 (presumably mostly electron flavor) and the slightly heavier neutrino 2 (with a larger proportion of muon flavor), and a much greater difference between these and neutrino 3 (probably mostly tau flavor). But the masses themselves are unknown; even their hierarchy is unknown. Neutrino 3 is very different from the others in mass, but is it the heaviest of them all or the lightest? 

The mixing angle θ₁₃ will reveal how much electron flavor is in neutrino 3. (The actual measurement isn't θ₁₃ directly, rather it is sin² 2θ₁₃, the sine squared of twice θ₁₃.) Eventually this will help determine whether tau is the heaviest flavor or the lightest, and what the actual masses of the other neutrinos are as well.

Knowing θ₁₃ will also shed light upon (if not wholly solve) several outstanding puzzles, including that of CP violation, characteristic of particles that interact purely by the weak interaction. In some way not yet wholly understood, CP violation is responsible for why there is so much matter in the universe and so little antimatter — or, to put it another way, why there is anything at all in the universe, for if matter and antimatter had been created equally, they would have annihilated each other. 

C stands for charge conjugation symmetry and P stands for parity symmetry ("left-right" symmetry). Neutrinos have no electrical charge, of course, but C more generally means changing particles into antiparticles, or vice versa. A C‑invariant process works the same way in both directions, when particles and antiparticles are transformed into each other. Not so for neutrinos, which "maximally violate" C. Instead of an equal number of left- and right-handed neutrinos and antineutrinos, all neutrinos are left-handed; all antineutrinos are right-handed.

Considered alone, both C and P are maximally violated by neutrinos, but taken together, as in the "CP mirror" at right, CP invariance can explain the existence of only left-handed neutrinos and only right-handed antineutrinos. Yet are neutrinos really CP invariant? Many fundamental processes depend on the answer.

Parity invariance means that physical processes should work equally well "in the mirror," that is, when the only difference between two particles is their orientation and direction. Since all physical processes produce only left-handed neutrinos or right-handed antineutrinos, neutrinos violate P as well.

When C and P are taken together, however, everything seems to come out all right. CP turns a left-handed neutrino into a right-handed antineutrino and a right-handed antineutrino back into a left-handed neutrino.

But do both processes happen with the same probability? If not, if in fact neutrinos violate CP invariance, the rate at which they do so will have profound implications for how matter and antimatter are related — including the question of whether neutrinos are their own antiparticles — and how neutrinos oscillate, how a great many other fundamental processes proceed, and indeed how the universe came to look the way it does.

Because of this, says Siegrist, "Measuring theta one three will be a pathfinder for future neutrino physics."

Digging an Experiment

Reactors produce copious amounts of antineutrinos from nuclear fission, and the Daya Bay reactors — two at Daya Bay itself, another two at nearby Ling Ao, and a third pair under construction at Ling Ao — are among the most powerful in the world.

Besides a plentiful source of antineutrinos, an experiment to measure θ₁₃ needs big detectors placed at the right distance from that source. At Daya Bay, two detectors in each of two nearby locations will establish a baseline, by measuring the flux and energy of the electron antineutrinos emerging from the Daya Bay and Ling Ao reactors.

Neutrinos oscillate with a certain frequency, which translates into measurable flight paths characteristic of each mixing angle. Due to θ₁₃ oscillation, some proportion of electron antineutrinos "disappear" about two kilometers away from where they are created in the reactors — much as electron neutrinos created in the sun disappear on their way to Earth. The experiment's far detectors, four in all, will be positioned at this distance. The near and far detectors will be exchanged on a regular basis to cancel any systematic detector errors.

Each detector consists of clear acrylic and steel vessels holding different liquids, nested inside each other like Russian dolls. Innermost is the target tank, 20 metric tons of liquid scintillator laced with gadolinium, a heavy metal; the target tank is surrounded by another tank of scintillator without gadolinium, a "gamma-ray catcher." Both of these are surrounded by a steel tank of mineral oil that acts as shielding.

	The powerful reactors at Daya Bay produce a flood of antineutrinos. Shielded from cosmic rays, detectors will be moved from chamber to chamber through tunnels to measure the neutrino mixing angle θ13, comparing the number of antineutrinos detected near the reactors with the number detected over a kilometer away.

"When an electron antineutrino hits a proton in the target, the products are a positron and a neutron, a so-called inverse beta-decay reaction," Luk explains. "The positron deposits energy in the scintillator, which the detector records as a flash of light. A few tens of microseconds later the detector records another flash of light from gamma rays released when the neutron is captured by a gadolinium nucleus." The light is collected by the 200 photomultiplier tubes that line the mineral-oil-filled outer tank.

Each detector sits on a massive, multiwheeled carriage for movement through the tunnel system. Two detectors fit into each experimental hall, where they are shielded from radioactive decays in the surrounding rock by two meters of water on all sides.

By knowing how many electron antineutrinos are produced in the reactors — on the order of a million quadrillion every second! — and the number expected to arrive at each detector — about a thousand per day at the nearby sites, a hundred a day at the far sites — and then comparing how many events are actually detected, sin² 2θ₁₃ can be determined to a precision of better than 0.01.

"To get theta one three, essentially we measure the difference in flux at two points," says Luk. "Basically it comes down to how many antineutrinos disappear." 

"We intend to start taking data in 2010," says U.S. Project Manager Edwards. "Whether Daya Bay happens is up to us."

Additional information

• More about the experiment at Daya Bay
• More about neutrino physics