Accelerator Neutrinos

Accelerator neutrino beams are produced by directing a high-energy proton beam (typically 30–120 GeV) onto a graphite or beryllium target. The collisions produce pions and kaons, which are then focused into a long decay pipe where they decay in flight: ${\pi }^{+}\to {\mu }^{+}+{\nu }_{\mu },K^{+}\to {\mu }^{+}+{\nu }_{\mu },\dots$ A magnetic focusing horn selects ${\pi }^{+}$ or ${\pi }^{-}$, producing a beam of predominantly ${\nu }_{\mu }$ or ${\bar{\nu }}_{\mu }$ with small electron-flavor contamination from three-body kaon decays and residual muon decays in the pipe.

Key operating beams

• NuMI at Fermilab (USA) — 700 kW upgraded to 1 MW, feeding NOvA at 810 km and the short-baseline MicroBooNE / ICARUS programs
• J-PARC at Tokai (Japan) — 500 kW upgrading to 1.3 MW, feeding T2K at 295 km to Super-Kamiokande and eventually Hyper-K
• CERN SPS — historically CNGS to Gran Sasso; now part of the SHiP program design
• LBNF under construction at Fermilab — 1.2 MW upgrading to 2.4 MW, feeding DUNE at 1300 km (expected late 2020s)

Intensity is the key figure of merit. A “megawatt beam” produces a few times $10^{20}$ protons on target per year, yielding oscillation event samples in the thousands at the far detector.

Near and far detectors

Every long-baseline experiment pairs a near detector measuring the unoscillated beam spectrum and composition with a far detector measuring the oscillated spectrum at the relevant baseline. The ratio of far to near cancels many common systematic uncertainties including beam flux, cross-section, and target-mass effects.

Near detectors have become sophisticated cross-section and flavor-composition measurement machines in their own right. The T2K near detectors (ND280, INGRID) have produced definitive measurements of $\nu$-nucleus cross-sections in the GeV range. The DUNE near detector will combine liquid argon TPC, gaseous argon TPC, and water-Cherenkov modules in a movable configuration.

Oscillation physics from beams

At typical accelerator energies and baselines ($L/E\sim 500$ km/GeV), the dominant oscillation is ${\nu }_{\mu }\to {\nu }_x$ driven by $\Delta m_{31}^2$. Two channels matter most:

Disappearance. The ${\nu }_{\mu }$ survival probability is $P({\nu }_{\mu }\to {\nu }_{\mu })\approx 1-{\sin }^{2}2{\theta }_{23}{\sin }^2\left(\frac{\Delta m_{31}^{2}L}{4E}\right)$ This provides the cleanest measurement of ${\sin }^{2}2{\theta }_{23}$ and $|\Delta m_{31}^2|$.

Appearance. The ${\nu }_{\mu }\to {\nu }_e$ probability $P({\nu }_{\mu }\to {\nu }_e)\approx {\sin }^{2}2{\theta }_{13}{\sin }^2{\theta }_{23}{\sin }^2\left(\frac{\Delta m_{31}^{2}L}{4E}\right)+\text{sub-leading terms involving }{\delta }_{CP}$ carries the CP-violation signal. Comparing neutrino-mode and antineutrino-mode appearance rates yields the CP asymmetry.

Current results

T2K has accumulated ~80% of its design exposure. Current best-fit ${\delta }_{CP}$ is near $-\pi /2$, with CP conservation (${\delta }_{CP}=0$ or $\pi$) disfavored at the two-sigma level. The ${\theta }_{23}$ octant preference is weak.

NOvA has an essentially symmetric neutrino / antineutrino exposure. Its best fit favors normal ordering and non-maximal ${\theta }_{23}$, with a mild preference for ${\delta }_{CP}\ne 0$. Tensions between T2K and NOvA in the extracted ${\delta }_{CP}$ value are being studied; they may reflect statistical fluctuations, systematic effects, or genuine new physics.

DUNE (first data in the late 2020s) is designed to resolve both the mass ordering and ${\delta }_{CP}$ at the five-sigma level with a few years of running.

Hyper-Kamiokande will complement DUNE with a different baseline (295 km) and off-axis configuration, providing an independent measurement.

Short-baseline programs

A parallel effort operates at much shorter baselines (hundreds of meters) and addresses different physics. The Fermilab Short-Baseline Neutrino Program — SBND, MicroBooNE, ICARUS — targets potential eV-scale sterile neutrino signals in both ${\nu }_{\mu }$ disappearance and ${\nu }_e$ appearance channels. MicroBooNE’s results have disfavored some interpretations of the earlier MiniBooNE low-energy excess without fully resolving its origin.

Outlook

Accelerator neutrino physics is entering its highest-precision decade. The combination of DUNE, Hyper-K, and JUNO — each probing different parameter combinations with different systematics — will complete the oscillation parameter picture: all three mixing angles, both mass-squared differences, the mass ordering, and ${\delta }_{CP}$. Further beyond, neutrino factories and muon colliders would provide pure flavor beams of ${\nu }_{\mu }$ and ${\bar{\nu }}_e$ (or vice versa) with much reduced systematics, enabling precision tests that the current pion-decay technique cannot reach.