T2K and NOvA: The Current Hunt for CP Violation

The three-flavor oscillation framework has, since Daya Bay’s 2012 measurement of ${\theta }_{13}$, had one headline parameter left to measure: the Dirac CP-violating phase ${\delta }_{CP}$. Whether this phase is zero (CP is conserved in the lepton sector) or substantially non-zero (CP is violated) has profound implications for our understanding of why the universe contains matter rather than antimatter.

Two long-baseline accelerator neutrino experiments are currently carrying the measurement forward: T2K in Japan, and NOvA at Fermilab. Both have accumulated about a decade of data. Both show hints — but not definitive evidence — of a non-trivial ${\delta }_{CP}$. Both will hand the baton to next-generation experiments in the late 2020s.

This article explains what each experiment is, what they have measured so far, and why leptonic CP violation has remained just out of reach at the 5σ discovery level despite growing statistical precision.

The physics they measure

In long-baseline accelerator experiments, an intense beam of muon neutrinos (or antineutrinos) is produced by pion decay downstream of a proton target, and sent through the Earth to a far detector hundreds of kilometres away. The observable is the appearance of electron neutrinos in a detector that is otherwise dominated by muon neutrinos.

The oscillation probability for ${\nu }_{\mu }\to {\nu }_e$ at the relevant baseline and energy is approximately: $P({\nu }_{\mu }\to {\nu }_e)\approx {\sin }^{2}2{\theta }_{13}{\sin }^2{\theta }_{23}{\sin }^2\left(\frac{\Delta m_{31}^{2}L}{4E}\right)+\text{(CP-dependent terms)}$ The “CP-dependent terms” are small corrections proportional to $\sin {\delta }_{CP}$. Critically, they flip sign between neutrinos and antineutrinos: $\Delta P=P({\nu }_{\mu }\to {\nu }_e)-P({\bar{\nu }}_{\mu }\to {\bar{\nu }}_e)\propto \sin {\delta }_{CP}$ If CP is conserved (${\delta }_{CP}=0$ or $\pi$), neutrinos and antineutrinos oscillate at the same rate. If CP is violated (any other value of ${\delta }_{CP}$), they differ. Measuring this difference is the core of both experiments.

T2K

T2K — Tokai to Kamioka — sends a muon neutrino beam from the J-PARC accelerator complex on Japan’s Pacific coast to the Super-Kamiokande detector 295 kilometres to the west, in a mountain near Kamioka.

Key design choices:

• Off-axis geometry: The beam is aimed 2.5° off the direct line to Super-K. This off-axis angle narrows the energy spectrum to a sharp peak around 0.6 GeV — precisely at the first oscillation maximum for ${\theta }_{13}$-driven ${\nu }_{\mu }\to {\nu }_e$ at 295 km baseline. The narrow beam suppresses backgrounds from higher-energy neutral-current events.
• Near detector (ND280): 280 metres from the beam source, characterises the unoscillated flux and constrains neutrino-cross-section systematics.
• Far detector (Super-K): 50 kilotons of water Cherenkov, but with only 22.5 kt fiducial volume used for T2K analysis due to systematic uncertainty control.

T2K began data-taking in 2010 and has now accumulated approximately $4\times 10^{21}$ protons-on-target in combined neutrino and antineutrino modes. As of 2023, the experiment has observed ~100 ${\nu }_{\mu }\to {\nu }_e$ appearance events in neutrino mode and ~20 ${\bar{\nu }}_{\mu }\to {\bar{\nu }}_e$ events in antineutrino mode.

The current T2K analysis gives a best-fit ${\delta }_{CP}$ near $-1.7$ radians (approximately $-\pi /2$) and excludes CP conservation at about 2.5σ significance. The preferred region lies firmly in the lower half-plane. Normal mass ordering is mildly preferred.

NOvA

NOvA — NuMI Off-axis ${\nu }_e$ Appearance — sends a muon neutrino beam from Fermilab in Illinois to a 14-kiloton liquid scintillator detector in Ash River, Minnesota, 810 kilometres away.

Key design choices:

• Longer baseline: 810 km vs. T2K’s 295 km. This gives the experiment stronger sensitivity to matter effects, which is useful for mass-ordering determination but complicates the CP extraction.
• Off-axis geometry: 0.8° off-axis, producing a peaked energy spectrum around 2 GeV — matched to the first oscillation maximum for the longer baseline.
• Liquid scintillator tracking: 344,000 PVC cells filled with liquid scintillator, read out by wavelength-shifting fibres and avalanche photodiodes. The geometry gives good tracking for GeV-scale events and distinguishes electrons from photons with reasonable efficiency.
• Near detector: A smaller 0.3-kt version of the same detector technology at Fermilab, identical in material composition — cross-section and flux systematics largely cancel between near and far detectors.

NOvA began data-taking in 2014 and has accumulated approximately $3\times 10^{21}$ protons-on-target. The experiment has observed ~82 ${\nu }_e$ appearance events in neutrino mode and ~33 ${\bar{\nu }}_e$ events in antineutrino mode.

The 2022 NOvA analysis prefers the upper half-plane for ${\delta }_{CP}$ (around $+\pi /2$) in its antineutrino appearance data, while the combined analysis is consistent with CP conservation at 1σ. Normal mass ordering is preferred. The significance against CP conservation is approximately 1.5σ, weaker than T2K.

The tension

T2K and NOvA overlap significantly in their best-fit regions but differ in emphasis: T2K prefers ${\delta }_{CP}$ firmly in the lower half-plane, NOvA’s antineutrino appearance tilts upper half-plane. The tension is not statistically significant (the combined analysis is consistent with the data from both), but it is noticeable enough to have generated substantial theoretical and experimental discussion.

Several explanations have been offered:

• Statistical fluctuation: With ~100 events per experiment, significant variance is expected. More data should resolve the tension either way.
• Unknown systematics: One or both experiments might have cross-section or flux uncertainties that produce the apparent tension. Both collaborations are actively improving near-detector constraints.
• New physics: Non-standard interactions or a fourth (sterile) neutrino with different oscillation behaviour in matter versus vacuum could produce subtle differences between a 295 km / 0.6 GeV experiment and an 810 km / 2 GeV experiment. No compelling model currently fits both the tension and all other oscillation constraints simultaneously.

The most likely resolution is the first: statistical fluctuation. Both experiments are still accumulating data, and the tension should either sharpen into a real discrepancy or gradually fade as statistics improve.

Combined analysis

Global fits combine T2K, NOvA, and reactor-experiment data (Daya Bay, RENO, Double Chooz) to extract the best values of all PMNS parameters simultaneously. As of 2024, the combined fits give:

• ${\delta }_{CP}/\pi =1.19\pm 0.22$ (i.e., close to $-\pi /2$)
• ${\sin }^2{\theta }_{23}=0.451$ (lower octant) or $0.570$ (upper octant) — the octant remains unresolved
• Normal mass ordering preferred at ~2σ
• CP conservation excluded at ~2.5σ

These numbers are heavily driven by T2K in the neutrino-mode CP analysis, and by NOvA’s longer-baseline matter effects for the mass-ordering hint. They are insufficient for 5σ discovery of either CP violation or the mass ordering.

Why these experiments matter

T2K and NOvA occupy a specific role in the history of neutrino physics: they are the first experiments that genuinely tried to measure ${\delta }_{CP}$, and they did so after the Daya Bay measurement of ${\theta }_{13}$ (2012) made the enterprise feasible.

Their results have demonstrated:

1. The experimental programme works: CP-sensitive ${\nu }_{\mu }\to {\nu }_e$ appearance measurements are statistically viable in long-baseline beam experiments.
2. ${\delta }_{CP}$ is probably not zero: Both experiments show non-trivial asymmetries at $\sim 2\sigma$ confidence, and the combined data excludes CP conservation at ~2.5σ.
3. The next generation is necessary: 5σ discovery requires an order-of-magnitude increase in statistics, achievable only with Hyper-Kamiokande and DUNE.

The baton-passing is already happening. T2K’s successor Hyper-Kamiokande begins physics operation in 2027 on the same J-PARC beam. NOvA’s successor DUNE begins operation in 2029 on an upgraded Fermilab beam. Both of the current experiments will have contributed their data to the worldwide combined fits that will, sometime in the 2030s, deliver a definitive answer on whether the lepton sector violates CP.

Lessons learned

Several methodological lessons from T2K and NOvA will inform the next generation:

Near-detector systematics dominate at high statistics. Both experiments have found that as event counts grow, the limiting uncertainty becomes knowledge of neutrino-nucleus cross-sections. DUNE and Hyper-K are investing heavily in near-detector instrumentation precisely because of this lesson.

Matter effects + CP violation + mass ordering are entangled. The three effects enter the oscillation probability in non-orthogonal ways, and separating them requires either multiple baselines, multiple energy spectra, or both. The two current experiments, run in parallel, have shown that neither alone can cleanly separate all three.

Long timescales are unavoidable. CP-violation hunting requires large event samples, which require beam exposure measured in years. Any single experiment takes a decade to produce a mature result, and the community must plan for this timescale rather than expect rapid answers.

As of 2026, T2K and NOvA together hold about 250 ${\nu }_e$ appearance events. By 2035, DUNE and Hyper-Kamiokande combined should hold several thousand. At that sample size, the CP violation question will be settled.