Daya Bay and the angle that opened the door to CP violation

Three angles describe how the three neutrino flavours mix into the three mass states: θ₁₂, θ₂₃ and θ₁₃. By the late 2000s the first two were comfortably measured and both turned out to be large. The solar angle θ₁₂, fixed by solar and reactor data, sits around 33°. The atmospheric angle θ₂₃, fixed by atmospheric and accelerator data, sits near 45° — close to maximal. The third angle, θ₁₃, was the stubborn unknown. The CHOOZ reactor experiment in the 1990s had only managed an upper limit, sin²2θ₁₃ < 0.1 or so, and many theorists half-expected it to be exactly zero, perhaps protected by some flavour symmetry.

Whether θ₁₃ was zero or merely small was not a detail. The amount of CP violation observable in neutrino oscillation — the difference between how neutrinos and antineutrinos change flavour — is controlled by the Jarlskog invariant, which contains a factor of sin θ₁₃. If θ₁₃ vanished, the CP-violating phase δ would drop out of every observable and the question of whether leptons violate CP would become experimentally meaningless. The entire scientific case for the next generation of long-baseline experiments hinged on θ₁₃ being non-zero and, ideally, not too small.

Why a reactor is the clean way to measure θ₁₃

There are two ways to get at θ₁₃. Accelerator experiments look for muon neutrinos turning into electron neutrinos over hundreds of kilometres; that appearance probability depends on θ₁₃, but it is tangled up with the CP phase δ, the mass ordering, and matter effects, so a single measurement cannot isolate θ₁₃ cleanly. Reactors take the opposite, surgical approach. A nuclear reactor is a pure source of electron antineutrinos of a few MeV, and over a baseline of one to two kilometres the only oscillation that matters is the fast one driven by the atmospheric splitting. The survival probability of reactor antineutrinos is, to excellent approximation,

P(ν̄_e → ν̄_e) ≈ 1 − sin²2θ₁₃ · sin²(1.267 · Δm²_ee · L / E),

with L in metres, E in MeV and Δm²_ee in eV². There is no δ, no matter effect, no ambiguity — just θ₁₃ and the known atmospheric splitting. The depth of the disappearance dip is set directly by sin²2θ₁₃. The catch is that for a small angle the dip is only a few percent, far smaller than the uncertainty in how many antineutrinos a reactor actually emits. The trick that makes the measurement possible is to use two sets of detectors: a near set, close enough that oscillation has barely begun, and a far set at the oscillation minimum. The ratio of far to near rates cancels the reactor flux and the detector cross-section almost entirely, leaving the oscillation deficit exposed.

Drag the slider and watch the orange far-hall point dive below the blue near-hall point. At the measured value of sin²2θ₁₃ ≈ 0.085 the far detectors register a few percent fewer antineutrinos than a no-oscillation extrapolation from the near detectors would predict. That small, stubborn deficit — robust because the reactor flux cancels in the ratio — is the entire signal.

How Daya Bay caught it

The Daya Bay experiment sits at a nuclear power complex in Guangdong province, southern China, one of the most powerful reactor sites in the world: six cores delivering nearly 18 gigawatts of thermal power. The collaboration installed eight identical antineutrino detectors — each a 20-tonne target of gadolinium-doped liquid scintillator — in three underground halls. Two halls sat close to the reactor cores, a few hundred metres away; the third sat in a far hall around 1.6 to 1.9 kilometres from the cores, near the first oscillation minimum. The detectors were built to be functionally identical so that any difference in their response would cancel when near and far rates were compared. Each antineutrino announced itself by inverse beta decay: a prompt flash from the positron, followed microseconds later by a second flash as the neutron captured on gadolinium, a coincidence that rejects almost all background.

On 8 March 2012 the collaboration announced a result based on just 55 days of data: sin²2θ₁₃ = 0.092 ± 0.017, a non-zero value at 5.2 standard deviations. Subsequent data refined the central value to around 0.085. The Korean experiment RENO and the French-led Double Chooz reported consistent results within the same year. After more than a decade of upper limits, the last mixing angle had a value — and it was big, only a factor of a few below the other two angles rather than vanishingly small.

Why a single number reorganised the field

A large θ₁₃ was the best news the long-baseline community could have received. Because the electron-appearance signal at accelerators scales with sin²2θ₁₃, a value near 0.085 meant that experiments like T2K and NOvA would see hundreds of appearance events rather than a handful — enough to begin probing the CP phase δ and the mass ordering within a realistic running time. Every flagship of the following decade rests on this: the T2K hint of CP violation, NOvA's matter-effect measurements, and the design cases for DUNE and Hyper-Kamiokande all assume a θ₁₃ that only Daya Bay and its peers could supply. Had θ₁₃ come back ten times smaller, those experiments would have been reduced to setting limits for a generation.

Daya Bay went on to deliver more than the discovery. It produced the most precise measurement of the atmospheric splitting Δm²_ee from a reactor, and it observed an unexpected distortion in the reactor antineutrino spectrum around 5 MeV — the so-called "5 MeV bump" — that no flux model had predicted and that remains a live puzzle in reactor physics. But its place in the story is fixed by that one measurement in 2012. The PMNS matrix, whose geometry we explore in the PMNS matrix as a 3D rotation, had its final rotation angle pinned down, and the door to leptonic CP violation — bolted shut if θ₁₃ had been zero — swung open.