Constraining the Neutrino Mixing Matrix via Single-Sector Charged-Lepton Rotations in the JUNO Precision Era

Abstract

The unprecedented precision now being achieved in the measurement of the Pontecorvo--Maki--Nakagawa--Sakata (PMNS) lepton mixing matrix opens a new window onto the underlying structure of the neutrino mass matrix and the possibly associated flavor symmetries. In this work, we investigate the constraints imposed on the unitary matrix $U_ν$ that diagonalises the neutrino mass matrix, under the hypothesis that the charged-lepton mixing matrix $U_l$ consists of a single two-by-two rotation in one of the three sectors: (1,2), (1,3), or (2,3). For this analysis, we considered the latest global fit which incorporates the precision measurement of $θ_{12}$ from the JUNO experiment. For each scenario, we also derive analytical expressions for the entries of $U_ν$ in terms of the measured PMNS parameters to obtain compact sum-rule-like formulae.

Figures (8)

• Figure 1: Neutrino mixing angles $\sin^2\theta^{\nu}_{13}$ (red), $\sin^2\theta^{\nu}_{12}$ (green), and $\sin^2\theta^{\nu}_{23}$ (blue) as functions of $\theta^{l}_{12}$, with the PMNS angles fixed to the NuFit 6.1 best-fit values (UO) in NO.
• Figure 2: Distributions of the neutrino mixing angles $\sin^2\theta^{\nu}_{13}$, $\sin^2\theta^{\nu}_{12}$, and $\sin^2\theta^{\nu}_{23}$ obtained by varying the PMNS angles as Gaussian distributions with $1\sigma$ widths and scanning $\theta^{l}_{12}\in[0^\circ,45^\circ]$ uniformly. The correlation plots show the regions containing 90% of the neutrino mixing angle pairs $(\sin^2\theta^{\nu}_{12},\sin^2\theta^{\nu}_{23})$, $(\sin^2\theta^{\nu}_{13},\sin^2\theta^{\nu}_{23})$, and $(\sin^2\theta^{\nu}_{13},\sin^2\theta^{\nu}_{12})$, obtained by varying PMNS parameters and scanning $\theta^{l}_{12}$ over its full range. Solid (dashed) curves correspond to NuFit 6.1 (NuFit 6.0) inputs; red (blue) curves refer to the LO (UO) solution of $\theta_{23}$. Stars indicate the most probable point (peak of the distribution) in each dataset.
• Figure 3: Same as Fig. \ref{['fig:angles_vs_theta_12']} but for the (1,3) charged-lepton rotation, as a function of $\theta^{l}_{13}$.
• Figure 4: Same as Fig. \ref{['fig:triangle12']} but for the (1,3) single charged-lepton rotation case.
• Figure 5: Same as Fig. \ref{['fig:angles_vs_theta_12']} but for the (2,3) charged-lepton rotation, as a function of $\theta^{l}_{23}$.