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

Technical Summary: Testing Residual-Symmetry-Fixed Columns of $U_{PMNS}$ at DUNE and T2HK with Initial JUNO Constraints

Problem Statement
The paper addresses the challenge of testing theoretical frameworks based on discrete flavour and modular symmetries, which predict specific "fixed-column" structures for the lepton mixing matrix ($U_{PMNS}$). While recent high-precision measurements of the solar mixing angle $\sin^2 \theta_{12}$ by the JUNO experiment have already constrained the first element of these predicted columns, the remaining elements depend on the atmospheric mixing angle $\theta_{23}$ and the Dirac CP phase $\delta_{CP}$. These parameters currently suffer from significant experimental uncertainties and degeneracies (specifically hierarchy-octant-$\delta_{CP}$ degeneracies). The authors aim to investigate whether the non-trivial correlations between $\sin^2 \theta_{23}$ and $\delta_{CP}$ predicted by residual symmetries can be decisively tested and constrained by next-generation long-baseline neutrino experiments, specifically DUNE and T2HK, in conjunction with JUNO data.

Methodology
The study employs a multi-step analytical and simulation-based approach:

1. Theoretical Framework: The authors consider residual symmetries arising from Discrete Subgroups (DSG) of $U(3)$ and $SU(3)$, as well as modular symmetries. These symmetries (specifically a $Z_2$ symmetry in the neutrino sector and a $Z_m$ ($m \ge 3$) symmetry in the charged-lepton sector) fix one column of $U_{PMNS}$.
2. Model Selection: They identify viable fixed-column candidates ($|c_0|^2$) from groups with order $< 512$ (including $\Delta(6n^2)$, $PSL(2,7)$, $\Sigma(168)$, and modular groups $\Gamma_N$) that are compatible with pre-JUNO global fits (NuFIT 6.0).
3. JUNO Constraint Application: The authors apply the updated NuFIT 6.1 global analysis results, which incorporate JUNO data, to filter these candidates. This step eliminates several scenarios (e.g., $C_1[6]$, $C_1[7]$, $C_2[1]$, $C_2[2]$) where the predicted $\sin^2 \theta_{12}$ falls outside the $3\sigma$ allowed range.
4. Correlation Derivation: For the surviving scenarios, the authors derive analytical correlations between $\delta_{CP}$ and the mixing angles ($\theta_{12}, \theta_{23}, \theta_{13}$). These correlations define specific theoretical bands in the $\sin^2 \theta_{23}$–$\delta_{CP}$ plane.
5. Experimental Simulation: Using GLoBES, the authors simulate prospective data for DUNE (624 kt$\cdot$MW$\cdot$yr exposure) and T2HK (374 kt fiducial mass, 10-year run with 1:3 neutrino-to-antineutrino ratio).
   • Analysis: A $\chi^2$ analysis is performed including systematic uncertainties (normalization, signal, and background) via the pull method.
   • Priors: A Gaussian prior on $\sin^2 \theta_{12}$ (based on JUNO precision) is explicitly included to assess its impact.
   • Marginalization: The analysis marginalizes over $|\Delta m^2_{31}|$, $\theta_{23}$, and $\sin^2 \theta_{13}$ within their $3\sigma$ ranges, while testing specific true values of $\theta_{23}$ and $\delta_{CP}$.
6. Exclusion Metric: The authors define an exclusion fraction, $f_{exclude}$, representing the fraction of true $\delta_{CP}$ values that can be ruled out at the $3\sigma$ confidence level as a function of experimental exposure.

Key Contributions

• Systematic Screening: The paper provides a comprehensive list of viable fixed-column predictions from discrete and modular symmetries that survive the stringent JUNO $\sin^2 \theta_{12}$ constraints (Table II).
• Correlation Mapping: It explicitly maps the theoretical correlations between $\sin^2 \theta_{23}$ and $\delta_{CP}$ for these surviving models, highlighting how they differ from generic phenomenological approaches.
• Sensitivity Analysis: The study quantifies the sensitivity of DUNE and T2HK to these specific correlations, both individually and in combination, demonstrating how the inclusion of the JUNO prior significantly tightens the allowed parameter space.
• Exclusion Potential: It calculates the fraction of the $\delta_{CP}$ parameter space that can be excluded at $3\sigma$ for various models, showing a strong dependence on the true value of $\theta_{23}$ (specifically the octant).

Results

• Viability: Several fixed-column scenarios (e.g., $C_1[1]$ through $C_1[5]$) remain viable after JUNO constraints, while others are completely excluded.
• Allowed Regions: The theoretical correlations appear as narrow bands in the $\sin^2 \theta_{23}$–$\delta_{CP}$ plane. Experimental simulations show that DUNE and T2HK produce broad allowed regions due to systematics and marginalization, but the combination of both experiments significantly reduces these regions.
• Impact of JUNO Prior: Including the JUNO prior on $\sin^2 \theta_{12}$ drastically shrinks the allowed regions for combined DUNE+T2HK analyses. In some cases (e.g., $C_1[6]$), the prior alone drives the minimum $\chi^2$ beyond the $3\sigma$ threshold, leading to total exclusion.
• Exclusion Reach:
  • DUNE vs. T2HK: T2HK generally exhibits a stronger exclusion capability than DUNE, attributed to its larger detector mass and optimized neutrino-to-antineutrino running ratio (1:3), which enhances $\delta_{CP}$ sensitivity.
  • Octant Dependence: The exclusion power is highly dependent on the true value of $\theta_{23}$. Scenarios where $\theta_{23}$ lies in the lower octant (e.g., $42.0^\circ$) generally show stronger exclusion fractions compared to the higher octant ($48.0^\circ$).
  • Model Specifics: For models like $C_1[2]$ and $C_1[5]$, large portions of the $\delta_{CP}$ space (e.g., $60^\circ$–$298^\circ$) can be excluded at $3\sigma$ with realistic exposures, particularly when $\theta_{23}$ is in the lower octant.
  • Combined Power: The combined DUNE+T2HK analysis provides the most robust test, offering the strongest constraints on the parameter space.

Significance
The paper claims that the combined precision of JUNO, DUNE, and T2HK creates a powerful framework for scrutinizing residual-symmetry-based flavour models. The interplay between the precise measurement of $\theta_{12}$ and the long-baseline sensitivity to $\theta_{23}$ and $\delta_{CP}$ allows for the decisive testing—and potential exclusion—of a wide class of discrete-symmetry predictions. The authors conclude that these future experiments will enable precise tests of neutrino mixing frameworks over a wide region of parameter space, moving beyond generic phenomenological fits to test specific group-theoretical origins of lepton mixing.