Testing residual-symmetry-fixed columns of $U_{\rm PMNS}$ at DUNE and T2HK with initial JUNO constraints

TL;DR

The paper investigates fixed-column predictions for the leptonic mixing matrix arising from residual discrete and modular symmetries, examining how JUNO’s precise measurement of $\sin^{2}\theta_{12}$ constrains these predictions. It derives correlations in the $\sin^{2}\theta_{23}$–$\delta_{\rm CP}$ plane implied by various fixed-column patterns and tests them with simulated DUNE and T2HK data, marginalising over remaining oscillation parameters. The analysis shows that the combined JUNO+DUNE+T2HK setup provides strong, model-dependent constraints and can decisively test and often exclude many symmetry-driven scenarios, with exclusion power depending on the true $\theta_{23}$ and the specific symmetry pattern. Overall, the work demonstrates a high discriminatory potential for residual-symmetry-based lepton flavor models in the near future by leveraging complementary measurements from JUNO, DUNE, and T2HK.

Abstract

We study fixed-column predictions of the lepton mixing matrix that arise from residual symmetries originating in a class of discrete flavour and modular symmetries. While the recent high-precision determination of $\sin^{2}θ_{12}$ by JUNO already constrains part of these predictions, the remaining ones are primarily characterized by non-trivial correlations between $\sin^{2}θ_{23}$ and the Dirac CP phase $δ_{\rm CP}$, which are currently only weakly constrained. This motivates a detailed investigation using next-generation long-baseline neutrino experiments. For the viable scenarios, we derive precise $\sin^{2}θ_{23}$-$δ_{\rm CP}$ correlations and use them to generate test-event samples, marginalising over the remaining oscillation parameters. We perform detailed simulations for DUNE and T2HK, presenting allowed regions in the $\sin^{2}θ_{23}$-$δ_{\rm CP}$ plane and evaluating the CP-violation fraction as a function of exposure. Our results show that the combined sensitivity of DUNE and T2HK provides a robust test of fixed-column lepton-mixing predictions.

Figures (10)

• Figure 1: Allowed regions in the $\sin^2\theta_{23}$--$\delta_{\rm CP}$ plane for the fixed-column predictions $C1[1]$ of Table \ref{['tab:1']}. The left panels show the sensitivities of DUNE and T2HK with and without the $\theta_{12}$ prior, while the right panels display their combined analysis. The yellow band represents the theoretical correlations with the lower and higher $\theta_{13}$ values, as calculated using Eqs. (\ref{['Eqn:7']}) and (\ref{['Eqn:11']}). Shaded regions and black solid contours indicate the expected $3\sigma$ sensitivities. The grey contour lines show the $3\sigma$ allowed region from NuFIT 6.1. The pink and cyan regions correspond to DUNE without and with the $\theta_{12}$ prior, respectively. At the same time, the black solid and indigo dashed contours denote the T2HK allowed regions without and with the $\theta_{12}$ prior. In the right panels, the light-blue and light-green regions represent the combined DUNE+T2HK sensitivities without and with the $\theta_{12}$ prior, respectively.
• Figure 2: Allowed regions in the $\sin^2\theta_{23}$--$\delta_{\rm CP}$ plane for the fixed column predictions $C1[2]$ (upper) and $C1'[2]$ (lower) from Table \ref{['tab:1']}. The experimental sensitivities and theoretical correlations are displayed using the same conventions as in Fig. \ref{['fig1']}.
• Figure 3: Allowed regions in the $\sin^2\theta_{23}$--$\delta_{\rm CP}$ plane for the fixed column predictions $C1[3]$ (upper) and $C1'[3]$ (lower) from Table \ref{['tab:1']}. The experimental sensitivities and theoretical correlations are displayed using the same conventions as in Fig. \ref{['fig1']}.
• Figure 4: Allowed regions in the $\sin^2\theta_{23}$--$\delta_{\rm CP}$ plane for the fixed column predictions $C1[4]$ (upper) and $C1'[4]$( lower) from Table \ref{['tab:1']}. The experimental sensitivities and theoretical correlations are displayed using the same conventions as in Fig. \ref{['fig1']}.
• Figure 5: Allowed regions in the $\sin^2\theta_{23}$--$\delta_{\rm CP}$ plane for the fixed column prediction $C1[5]$ (upper) and $C1'[5]$ (lower) from Table \ref{['tab:1']}, shown using the same experimental and theoretical conventions as in Fig. \ref{['fig1']}.