Unitarity test of lepton mixing via energy dependence of neutrino oscillation

Abstract

We study the method to test the unitarity of the lepton mixing matrix by using only the long baseline neutrino oscillation experiments, such as the combination of the T2HK experiment and the one with the $ν_e$ beam from a future neutrino factory at J-PARC. Without a specific parametrization, one can directly extract the elements of the lepton mixing matrix by observing the energy dependence of the oscillation probabilities. A non-trivial test of the unitarity under the three-generation assumption can thus be made possible by examining the orthogonality in a similar manner to the unitarity triangle in the quark sector. As the first trial, we perform the analysis based on the simplified situation where the matter effects in the neutrino oscillation can be neglected. Under this simplified analysis, we demonstrate the observation of the unitarity violation in the $3\times3$ part of the lepton mixing matrix for a parameter set in the four-generation model. The statistically most significant measurement can be provided by the energy dependences of the combination of the CP conjugate modes, $ν_μ\to ν_e$ and $\bar ν_μ\to \bar ν_e$, at T2HK and, independently, by the T conjugate modes, $ν_μ\to ν_e$ and $ν_e \to ν_μ$, with the latter measured at the neutrino factory experiments.

Figures (9)

• Figure 1: The orange solid line is the energy dependence of the oscillation probability and the dotted blue line is the approximated one in Eq. \ref{['eq:prob-apx']}.
• Figure 2: The contribution of each energy-dependent function to the oscillation probability. Figure on the left shows each of the energy-dependent functions. Figure on the right shows the contributions of each function with the coefficients multiplied. The solid red line, dotted blue line, dashed green line, and dash-dot orange line represent $\sin^2(\Delta_{31})$, $\Delta_{21}\sin(2\Delta_{31})$, $\Delta_{21}^2$, and $\Delta_{21}\sin^2(\Delta_{31})$, or the ones with the coefficients applied, respectively.
• Figure 3: Number of events in the T2HK experiment. The left and right figures show the fluxes of $\nu_{\mu \to e}$ and $\bar{\nu}_{\mu \to e}$ at the far detector, respectively. Here, the CP phase is assumed to be $\delta_{\rm CP}=\ang{270}$. These expected number of events are calculated based on Hyper-Kamiokande:2018ofw.
• Figure 4: Neutrino flux measured at the Hyper-Kamiokande detector. The anti-muon beam energy is set to $1.5~\mathrm{GeV}$, and calculations are performed for four polarizations ($P_\mu=-1.0,\ -0.5,\ 0.0$). Here we set $\delta_{\rm CP}=\ang{270}$. The total number of muons is set to $10^{22}$.
• Figure 5: Unitarity test in terms of $\xi$. These figures show some comparisons of various channel combinations. These figures also compare different values of anti-muon beam polarization $P_\mu$ and charge identification efficiency $C_{\mathrm{id}}$. From top to bottom, the figures show the cases with $P_\mu=-1.0,\ -0.5,\ 0.0$. From left to right, the figures show the cases with $C_{\mathrm{id}}=1.0,\ 0.7,\ 0.0$. In these figures, the total number of muons is set to $10^{22}$. The blue regions represent the results of the fitting three-generation model to three-generation events, with the color intensity indicating the allowed region up to the $3\sigma$ level. The red solid vertical lines represent $\xi=0$.