A 2025 JHEP simulation study (Garcia Trzeciak, Nunokawa, Arguello Quiroga) assessed how non-unitary leptonic mixing, parametrized as N=ξUPMNSN=\xi U_{\rm PMNS} with a lower-triangular ξ\xi, affects the sensitivity to the Dirac CP phase δCP\delta_{CP} at the next-generation long-baseline experiments T2HK, T2HKK (Hyper-Kamiokande) and DUNE, simulating both near and far detectors. It found the Hyper-K configurations robust (above 5σ5\sigma CP-violation significance in all scenarios) while DUNE drops below 5σ5\sigma for some δCP\delta_{CP} depending on the non-unitarity scenario, and it obtained only weak sensitivity to the tau-row parameters ξ33\xi_{33}, ∣ξ31∣|\xi_{31}|, ∣ξ32∣|\xi_{32}|. The study itself acknowledges simplifications and limitations that it does not treat: only νe\nu_e appearance and νμ\nu_\mu disappearance samples were simulated, so ξ33\xi_{33} remains poorly constrained (it couples to the τ\tau channel, which requires τ\tau-neutrino detection and currently has poor statistics) and the sensitivity to ∣ξ31∣|\xi_{31}|, ∣ξ32∣|\xi_{32}| comes exclusively from the Cauchy-Schwarz inequality, whereas external neutral-current (NC) data such as MINOS/MINOS+ have been shown to achieve better limits; identical signal and background rejection efficiencies, bin sizes and energy resolutions were assumed for the near and far detectors for simplicity, an assumption the study flags as one that "may not hold universally, and discrepancies could arise due to variations in detector technology or design"; the regime of sterile mass-squared splittings Δm2∼\Delta m^2\sim atmospheric or solar is explicitly not treated, where "severe model dependence must be expected when fitting data"; and the 2.7%2.7\% νe/νˉe\nu_e/\bar\nu_e cross-section-ratio uncertainty is adopted as an assumed future constraint motivated by the Hyper-K near-detector programme rather than derived. The problem is to complete this forecast quantitatively by relaxing these acknowledged simplifications.

Background

Long-baseline (LBL) neutrino oscillation experiments send an intense accelerator-produced νμ\nu_\mu beam hundreds of kilometers to a far detector (FD) and measure the νμ→νe\nu_\mu\to\nu_e appearance and νμ→νμ\nu_\mu\to\nu_\mu disappearance channels, in neutrino and antineutrino mode, to determine the oscillation parameters of the three-flavor Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix -- in particular the Dirac CP phase δCP\delta_{CP}, whose violation would manifest as an asymmetry between neutrino and antineutrino oscillation probabilities. T2HK (a 295 km baseline upgrade of T2K with a 187 kton water Cherenkov detector) and its two-detector variant T2HKK (adding a second detector in Korea at about 1100 km) are the Hyper-Kamiokande program's oscillation configurations; DUNE (1300 km baseline, 40 kton liquid-argon time-projection chambers, 1.3 MW beam) is its main competitor. Each experiment also operates a near detector (ND) close to the source that constrains the unoscillated flux and cross sections. If additional neutral leptons (sterile'' neutrinos or heavy neutral leptons generated in seesaw models -- frameworks in which the smallness of neutrino masses follows from mixing with much heavier neutral fermions) mix with the three active flavors, the effective $3\times 3$ active-flavor mixing matrix $N$ is no longer unitary. A standard model-independent description is the triangular parametrization $N=\xi U_{\rm PMNS}$, where $\xi$ is lower triangular with real diagonal $\xi_{ii}\le 1$ and complex off-diagonal entries $\xi_{ij}=|\xi_{ij}|e^{i\varphi_{ij}}$; the new phases $\varphi_{ij}$ are extra sources of CP violation. The Cauchy-Schwarz inequalities on the rows of $N$ imply, for example, that a strong bound on $1-\xi_{33}^2$ induces bounds on $|\xi_{31}|$ and $|\xi_{32}|$. Unitarity violation affects oscillation probabilities at zero distance (zero-distance effects'') as well as over long baselines, and whether it is visible at the ND depends on the new-state mass scale: oscillations driven by the extra states average out at the ND only if Δm2≳10 eV2\Delta m^2\gtrsim 10\,{\rm eV}^2 for Hyper-K and ≳100 eV2\gtrsim 100\,{\rm eV}^2 for DUNE (the ND developed'' scenario); for $0.1\,{\rm eV}^2\lesssim\Delta m^2\lesssim 1\,{\rm eV}^2$ they average out only at the FD (ND undeveloped''), and near the atmospheric or solar splittings the description becomes strongly model dependent. The source study (Garcia Trzeciak, Nunokawa and Arguello Quiroga, JHEP 11 (2025) 059) simulated both ND and FD for T2HK, T2HKK and DUNE under these two scenarios, with systematic uncertainties implemented as normalization and energy-calibration errors, identical detector response assumed for ND and FD, and an uncertainty on the νe/νˉe\nu_e/\bar\nu_e cross-section ratio of 4.9%4.9\% (current) or 2.7%2.7\% (a future target motivated by the Hyper-K near-detector programme, Naseby 2021). Its findings: the ND developed scenario improves non-unitarity bounds; Hyper-K is robust (above 5σ5\sigma CP-violation significance in all cases); DUNE loses sensitivity below 5σ5\sigma for some δCP\delta_{CP} values depending on the scenario, with non-unitarity (rather than cross-section uncertainty) the dominant degradation; and the tau-row parameters ξ33\xi_{33}, ∣ξ31∣|\xi_{31}|, ∣ξ32∣|\xi_{32}| remain weakly constrained because they couple mainly to ντ\nu_\tau channels and neutral-current (NC) interactions, which the analysis did not include. Forero, Giunti, Ternes and Tórtola (Phys. Rev. D 104 (2021) 075030) previously derived stronger ξ33\xi_{33}-related limits using NC data from MINOS/MINOS+, showing that such data can matter. Separately, the correct normalization of oscillation probabilities in the non-unitary case -- whether near-detector data should be used to normalize away zero-distance effects, as in Blennow et al. (JHEP 04 (2017) 153) -- is disputed; the source study argues against the normalization procedure of that earlier work, and the recent clarification by Blennow, Coloma, Fernández-Martínez, Hernández-García, López-Pavón, Marcano, Naredo-Tuero and Urrea (Nucl. Phys. B 2025, ``Misconceptions in neutrino oscillations in presence of non-unitary mixing'') systematizes these subtleties without redoing the T2HK/T2HKK/DUNE forecasts.

Problem Statement

Complete, quantitatively, the assessment of how non-unitary leptonic mixing affects the sensitivity to the CP phase δCP\delta_{CP} and the reconstruction of the non-unitarity parameters at T2HK, T2HKK and DUNE, by extending the source study's joint near-and-far-detector simulation in the four directions corresponding to the simplifications and limitations the study itself acknowledges but does not treat, which are all parts of one objective -- replacing the study's idealized channel content, systematic model, parametrization and cross-section assumptions with realistic ones and determining how the conclusions change. Concretely, within one coherent forecasting framework: (i) add dedicated ντ\nu_\tau appearance and/or neutral-current samples -- either channel type is an acceptable route -- and determine whether the weak sensitivity to ξ33\xi_{33}, ∣ξ31∣|\xi_{31}| and ∣ξ32∣|\xi_{32}| is closed for these experiments, judged against the best existing tau-row constraints (such as the MINOS/MINOS+ NC limits the source study itself invokes), where closing the gap means these experiments' own joint sensitivity reaches that benchmark, not that the external bound is imported as an input; (ii) replace the idealized near-detector treatment (identical ND/FD efficiencies, binning and resolutions; normalization and energy-calibration errors scaled from the FD) with realistic, detector-technology-specific near-detector systematics, including correlated and event-level ND/FD differences, and quantify their impact on the joint non-unitarity and δCP\delta_{CP} sensitivity; (iii) test whether alternative consistent parametrizations of non-unitarity, and explicit sterile-state oscillation models with mass-squared splittings spanning from the atmospheric and solar scales up to splittings so large that the extra states cannot be kinematically produced in meson and muon decays, including the regimes where oscillations from the extra states are partially or fully averaged at the near detector, change the quantitative conclusions about CP sensitivity or parameter reconstruction; and (iv) quantify how the assumed improvement of the νe/νˉe\nu_e/\bar\nu_e cross-section-ratio uncertainty from the present 4.9%4.9\% to the 2.7%2.7\% level adopted as a future constraint in the source study -- an assumption motivated by the Hyper-K near-detector programme, whose experimental achievability is not itself part of this problem -- together with the residual correlated near-detector cross-section systematics, propagates into the joint non-unitarity and δCP\delta_{CP} fits. The deliverable is the corrected set of sensitivity forecasts (which tau-row gaps close, and how the CP-violation reach of each experiment, including DUNE's below-5σ5\sigma regions, shifts), with the relative effect of each extension identified by evaluating each of (i)--(iv) individually against the source study's baseline in addition to the joint forecast.

References

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