J-PARC Neutrino Factory

• The neutrino factory at J-PARC is a facility that uses stored muon decays to generate intense, well-collimated electron neutrino beams for precision oscillation measurements.
• It employs advanced techniques such as muon cooling and neutron tagging at Hyper-Kamiokande to enhance the accuracy of oscillation probability and charge identification.
• The design uniquely enables robust tests of T-reversal and CP violation with minimal influence from matter effects, offering critical insights into the three-neutrino paradigm and CPT symmetry.

A neutrino factory at J-PARC is conceived as a next-generation accelerator-based facility designed to produce intense, well-controlled beams of electron neutrinos through the decay of stored muons, enabling precision studies of neutrino oscillation and symmetry violation in the lepton sector. Leveraging the J-PARC accelerator complex, the concept foresees high-flux, low-energy muon beams circulating in a storage ring and producing collimated νₑ fluxes aimed at far detectors such as Hyper-Kamiokande. The unique structure of neutrino and antineutrino beams thus generated, along with a carefully coordinated detection strategy, positions a J-PARC neutrino factory to probe time-reversal (T) and CP violation with unprecedented sensitivity and minimal impact from matter-induced systematic uncertainties (Kitano et al., 8 Jul 2024, Kitano et al., 6 Dec 2024).

1. Neutrino Oscillation Probability Measurement

The neutrino factory at J-PARC proposes using stored, cooled μ⁺ beams to generate intense, highly collimated νₑ (and  ̄νμ) beams. These neutrinos are directed at the Hyper-Kamiokande detector (295 km baseline), where event counting in both near and far detectors allows precise measurement of the oscillation probability for νₑ → νμ. The event count-based extraction formula, incorporating detector response and charge identification efficiency (C_id), is given by:

$$P(\nu_e \rightarrow \nu_\mu) = \frac{1}{\kappa} \left\{ [\kappa N^{(\nu_e \rightarrow \nu_\mu)}_\text{far} + (1-\kappa) N^{(\bar{\nu}_\mu \rightarrow \bar{\nu}_\mu)}_\text{far}] - (1-\kappa) N^{(\bar{\nu}_\mu \rightarrow \bar{\nu}_\mu)}_\text{far}|_{\text{T2HK}} \cdot \tilde{N}^{(\nu_e \rightarrow \nu_e)}_\text{near} \right\}$$

where κ is a known function of C_id and N_far and Ñnear denote event counts for oscillated and unoscillated components, properly normalized for detector size and distance. This approach uses neutron tagging in the water Cherenkov detector to achieve charge separation between νμ and  ̄ν_μ charged-current events, an area under active experimental R&D for enhanced efficiency.

2. T-Reversal Measurement and Analysis

A key element in the neutrino factory program is the ability to contrast oscillation channels related by time-reversal symmetry. By measuring νₑ → νμ transitions (neutrino factory) and comparing them to νμ → νₑ transitions (T2K/T2HK, using conventional beams), one forms the T-violating asymmetry observable:

$$P^{\text{(TV)}}_j = P_j(\nu_e \rightarrow \nu_\mu) - P_j(\nu_\mu \rightarrow \nu_e)$$

where the index j denotes binning in reconstructed neutrino energy. This differential is directly sensitive to the CP phase δ in the PMNS matrix. The time-reversal observable is constructed for each energy bin and is robust against most systematics not associated with T violation, allowing extraction of δ with statistically optimized χ² fits.

3. Sensitivity to Matter Effects and Extraction of the CP Phase

T violation, as quantified by the above asymmetry, exhibits near immunity to uncertainties in the Earth's matter density profile. While the CP-violating observable constructed from P(νμ → ν_e) vs. P( ̄νμ → ̄ν_e) acquires significant dependence on matter density, the χ² for T violation remains almost unaffected. This is a consequence of the effective symmetry of earth matter for source-detector exchange and the structure of the oscillation Hamiltonian. The insensitivity carries substantial experimental value: extraction of the CP phase δ from T violation is minimally impacted by matter effect uncertainties, enabling clean tests of leptonic CP violation even with imperfect knowledge of density along the baseline.

The three-flavor oscillation probability, in matter, is given in the form

$$P(\nu_\alpha \rightarrow \nu_\beta) = \delta_{\alpha\beta} - 4 \sum_{j>k} \operatorname{Re}\!\left[ \tilde{U}^{(\pm)}_{\alpha j} \tilde{U}^{(\pm)*}_{\beta j} \tilde{U}^{(\pm)*}_{\alpha k} \tilde{U}^{(\pm)}_{\beta k} \right] \sin^2\!\left( \frac{ \Delta \tilde{E}^{(\pm)}_{jk} L }{2} \right) + 2 \sum_{j>k} \operatorname{Im}\!\left[ \tilde{U}^{(\pm)}_{\alpha j} \tilde{U}^{(\pm)*}_{\beta j} \tilde{U}^{(\pm)*}_{\alpha k} \tilde{U}^{(\pm)}_{\beta k} \right] \sin\!\left( \Delta \tilde{E}^{(\pm)}_{jk} L \right)$$

with matter-corrected mixing matrix elements and energy eigenvalues. The dependence of the T-violation term on δ enters via the imaginary part, i.e., a Jarlskog-like invariant, and vanishes for δ = 0 independent of matter effects.

4. Testing the Three-Neutrino Paradigm and CPT Theorem

By combining T and CP observables, the J-PARC neutrino factory program provides stringent checks of foundational QFT symmetries. In the three-neutrino paradigm, the CPT theorem requires

$$P(\nu_e \rightarrow \nu_\mu) - P(\bar{\nu}_\mu \rightarrow \bar{\nu}_e) = P^{\text{(TV)}}_j + P^{\text{(CP)}}_j = 0$$

up to small matter-induced corrections. Measuring both P^{(TV)} and P^{(CP)} independently enables a nontrivial test of this relation and, by extension, of the completeness of the standard neutrino mixing scenario. The independence of T violation from matter effects also decouples this test from uncertainties that challenge CP-only approaches. This program positions a neutrino factory at J-PARC as a precision tool not only for extracting δ but for challenging the entire structure of neutrino mixing and validating the CPT symmetry at accelerator baselines.

5. Experimental Implementation at J-PARC

The facility concept relies on ultra-slow muon technology for muon cooling—a process already applied in the muon g–2/EDM J-PARC program—combined with a racetrack-type storage ring aimed at Hyper-Kamiokande. Expected annual fluxes are of order 10²¹ muons, yielding abundant event rates. The baseline of 295 km matches that of T2HK, facilitating channel comparisons and systematics control.

A technical challenge is the efficient discrimination between μ⁻ and μ⁺ charged-current events in the detector. Hyper-Kamiokande, using neutron tagging and water Cherenkov signatures, is expected to achieve C_id in the 70–100% range. Even at less-than-perfect charge ID performance, the oscillation maximum strongly suppresses antineutrino backgrounds, maintaining the efficacy of the T violation test.

6. Future Directions and Experimental Challenges

Further development of this program focuses on improving detector charge identification efficiencies, optimizing neutron tagging, and systematically quantifying experimental uncertainties. While current analyses focus on statistical errors, extension to comprehensive error budgets—including those linked to detector modeling, background subtraction, and residual matter profile uncertainties—is an open avenue.

Additionally, the potential integration with a staged muon collider scenario, as discussed in the context of J-PARC site planning, could offer pathways to even more intense neutrino sources and opportunities for muon collider physics. The broader application of these techniques to test CPT and potential BSM (e.g., non-unitarity scenarios) is anticipated.

7. Significance for Precision Oscillation Physics

The J-PARC neutrino factory initiative aligns with contemporary objectives in neutrino physics: precise, systematics-robust extraction of the CP phase, model-independent validation of the three-neutrino framework, and unambiguous discrimination of fundamental symmetry violations. By combining advanced accelerator capabilities, developments in detector charge tagging, and a dual approach to T and CP observables, it lays out a technically feasible and theoretically robust roadmap for deepening the understanding of leptonic mixing and its foundational symmetries (Kitano et al., 8 Jul 2024, Kitano et al., 6 Dec 2024).