Impact of unitarity violation on sensitivity of the leptonic CP phase at Hyper-Kamiokande and DUNE

TL;DR

The paper investigates how violations of unitarity in the leptonic mixing matrix affect the sensitivity to the CP-violating phase $\delta_{CP}$ in the next-generation long-baseline experiments HK and DUNE. It introduces a non-unitary framework with the effective matrix $N$ and a parameterization $N = \begin{pmatrix} \xi_{11} & 0 & 0 \\ \xi_{21} & \xi_{22} & 0 \\ \xi_{31} & \xi_{32} & \xi_{33} \end{pmatrix} U_{PMNS}$, along with Cauchy–Schwarz bounds to constrain off-diagonal elements, and analyzes two detector scenarios: ND developed (non-unitarity visible at the near detector) and ND undeveloped (non-unitarity appears only at the far detector). Using GLoBES-based simulations with near and far detectors for HK and DUNE, the study finds that HK maintains sensitivity above $5\sigma$ to $\delta_{CP}$ across all considered non-unitarity cases, while DUNE shows more vulnerability to unitarity violation, though robustness can be recovered in the ND developed scenario. The near detector significantly improves constraints on $|\xi_{21}|$, whereas the phase $\phi_{21}$ is constrained mainly by the far detector; cross-section uncertainties are a dominant systematic affecting CP sensitivity, particularly for HK-like setups. Overall, the work highlights the critical role of near-detector effects and a rigorous non-unitarity treatment in accurately assessing CP-violation sensitivity in future experiments.

Abstract

We study the impact of unitarity violation on the sensitivity of the leptonic CP phase, $δ_{CP}$, considering the next generation of long-baseline neutrino experiments, Hyper-Kamiokande and DUNE. By simulating near and far detectors and assuming different scenarios for non-unitarity, we verify how it can affect the sensitivity to measure the $δ_{ CP}$ violating phase. We also probe the capability of these experiments to constrain the non-unitarity parameters and how their capability could be improved if the impact of non-unitarity at both near and the far detectors were properly taken into account. We find that the Hyper-Kamiokande experiment is robust in the presence of non-unitarity mixing, achieving a sensitivity above $5σ$ for our all considered cases. On the other hand, DUNE suffers somewhat more impact due to unitarity violation, reaching a sensitivity below 5$σ$ for some values of $δ_{CP}$. However, depending on the scenario adopted for non-unitarity, DUNE demonstrates robustness in the sensitivity to $δ_{ CP}$ phase.

Figures (17)

• Figure 1: Iso-contour of difference $\Delta P$ in the $L-E$ plane. The left (right) panel represents the deviation from unitary due to $\xi_{21}$ ($\xi_{31}$). See text for details.
• Figure 2: The neutrino-antineutrino asymmetry as a function of $\delta_{CP}$ values for $L = 295$ km and $E_{\nu} = 0.6$ GeV (left) and $L = 1300$ km and $E_{\nu} = 2.5$ GeV (right). Unitary case is represented by black lines (solid, dashed and dotted). Non-unitary case is represented by colored lines (solid, dashed and dotted) with $\xi_{21} = 0.025$ and four values for $\phi_{21}$ (see legend).
• Figure 3: CP ellipses in the bi-probability plane for unitary scenario with varying $\delta_{CP}$ (black line) and unitarity violation scenario with $\delta_{CP}$ fixed and varying $\phi_{21}$ (colored lines) for a setup with $E_{\nu} = 0.6$ GeV - $L = 295$ km (left) and $E_{\nu} = 2.5$ GeV - $L = 1300$ km (right). The solid lines correspond to $\sin^{2}\theta_{23} = 0.574$, dashed lines to $\sin^{2}\theta_{23} = 0.434$ and dotted lines to $\sin^{2}\theta_{23} = 0.608$.
• Figure 4: Expected sensitivity on non-unitary parameters to be achieved by the T2HK, T2HKK and DUNE experiments. The upper panels show the sensitivity to the off-diagonal parameters and lower panels to the diagonal parameters. The case where non-unitarity only appears in the far detector (ND undeveloped) is represented by solid lines. The case where unitarity violation already appears in the near detector (ND developed) is represented by dashed lines. The dashed horizontal line represents the $\Delta \chi^2$ value corresponding to 90% CL.
• Figure 5: 1$\sigma$ and 3$\sigma$ (2 d.of.) C.L. contours in the ($|\xi_{21}|, \phi_{21}$) plane for T2HK, assuming ND undeveloped scenario (green line) and ND developed scenario (purple line). We have fixed $|\xi_{21}|^{\text{true}}$ = 0.025 and four values for $\phi_{21}^{\mathrm{true}}$. The values for other non-unitary parameters are described in Section \ref{['sec:simu']}.