Zooming in on `bi-large' neutrino mixing with the first JUNO results

Technical Summary: Zooming in on 'Bi-Large' Neutrino Mixing with the First JUNO Results

Problem Statement
The paper addresses the challenge of testing theoretical frameworks for lepton mixing against increasingly precise experimental data. Specifically, it focuses on "bi-large" mixing patterns, a class of models proposing that the smallest lepton mixing angle is numerically close to the largest quark mixing angle (the Cabibbo angle, $\lambda$). These models suggest the Cabibbo angle acts as a universal seed for both quark and lepton mixings. While previous analyses tested these patterns against global oscillation data, the recent release of high-precision measurements by the Jiangmen Underground Neutrino Observatory (JUNO) for the solar mixing angle ($\sin^2 \theta_{12}$) and the solar mass-squared difference ($\Delta m^2_{21}$) necessitates a re-evaluation. The authors aim to determine the viability of four specific bi-large mixing schemes (T1, T2, T3, and T4) in light of these new constraints and assess JUNO's potential to discriminate between them.

Methodology
The authors examine four bi-large mixing patterns (T1–T4) proposed in recent literature [27–31]. These patterns assume the neutrino diagonalization matrix ($U_\nu$) is constructed from the Cabibbo angle, while the full leptonic mixing matrix ($U = U_\ell^\dagger U_\nu$) includes a charged-lepton correction factor ($U_\ell$) motivated by Grand Unified Theories (GUTs), typically modeled as "CKM-like."

1. Model Definitions:
   • T1 & T2: One-parameter models where mixing angles are functions of the Cabibbo parameter $\lambda$ and a single free phase $\phi$. T1 and T2 differ in their specific correlations between $\theta_{23}$, $\theta_{12}$, and $\theta_{13}$ with $\lambda$.
   • T3 & T4: Two-parameter models introducing an additional free parameter $\psi$ alongside $\phi$. T3 and T4 share the same neutrino sector ($U_{BL3}$) but differ in their charged-lepton corrections ($U_{l1}$ vs. $U_{l2}$).
2. Data Confrontation: The authors confront the predictions of these models with:
   • The latest JUNO results: $\sin^2 \theta_{12} = 0.3092 \pm 0.0087$ and $\Delta m^2_{21} = (7.50 \pm 0.12) \times 10^{-5} \text{ eV}^2$ (Normal Ordering).
   • Updated global fit data (PDG 2025 and Refs. [4, 6, 7]).
3. Analysis Technique: The study employs numerical analysis using exact formulae rather than leading-order approximations. The authors perform $\chi^2$ analyses and random scans to determine allowed regions for the model parameters ($\phi$ and $\psi$) that satisfy experimental constraints within $1\sigma$, $2\sigma$, and $3\sigma$ confidence levels. They generate correlation plots in the $(\sin^2 \theta_{12} - \sin^2 \theta_{23})$, $(\sin^2 \theta_{12} - \delta)$, and $(\sin^2 \theta_{12} - \sin^2 \theta_{13})$ planes.
4. Neutrinoless Double Beta Decay ($0\nu\beta\beta$): The effective Majorana mass parameter $\langle m_{\beta\beta} \rangle$ is calculated as a function of the lightest neutrino mass $m_1$ for the T1 pattern, comparing the constrained region against JUNO's precision and projected sensitivities of future experiments.

Key Results

• Pre-JUNO Status: Before JUNO's specific $\theta_{12}$ measurement, T1 was the most compatible with global data. T2 was consistent at the $2\sigma$ level in the lower octant. T3 was excluded at $3\sigma$, and T4 was marginally consistent but expected to be ruled out with improved $\delta$ precision.
• Impact of JUNO on T1:
  • Atmospheric Octant: T1 is compatible only with the higher atmospheric octant ($\sin^2 \theta_{23} > 0.5$), explicitly excluding maximal mixing ($\sin^2 \theta_{23} = 0.5$). JUNO tightens this prediction to $\sin^2 \theta_{23} \simeq 0.57$.
  • CP Violation: The T1 pattern disfavors both maximal CP violation ($\delta = \pm \pi/2$) and CP conservation ($\delta = \pi$) at the $1\sigma$ level, predicting $\delta \approx 0.7\pi$ or $1.3\pi$.
  • Solar Angle: The model predicts $\sin^2 \theta_{12} \sim 0.30-0.31$, which is consistent with JUNO's $3\sigma$ range but more constrained than the general global fit.
• Impact of JUNO on T2:
  • T2 prefers nearly maximal atmospheric mixing ($\sin^2 \theta_{23} \approx 0.5$).
  • Unlike T1, T2 excludes CP conservation even at the $3\sigma$ level.
• Impact of JUNO on T3 and T4:
  • T3: Predicts exclusively the lower octant ($\sin^2 \theta_{23} < 0.5$). It is marginally compatible with global data at $3\sigma$ but becomes excluded when JUNO's $1\sigma$ constraint on $\sin^2 \theta_{12}$ is applied.
  • T4: Predicts near-maximal atmospheric mixing. Like T3, it is excluded at the $2\sigma$ level by global data and further constrained by JUNO, though it remains compatible at the $3\sigma$ level.
  • Both T3 and T4 are expected to be decisively tested or ruled out by future precision measurements of $\sin^2 \theta_{23}$ and $\delta$.
• Neutrinoless Double Beta Decay: The JUNO precision on $\theta_{12}$ and $\Delta m^2_{21}$ slightly reduces the allowed region for $\langle m_{\beta\beta} \rangle$. The T1 pattern occupies a smaller region within the JUNO-allowed space compared to a generic scheme.

Significance and Claims
The paper claims that the first results from JUNO provide a critical "zoom" on bi-large mixing patterns, transforming them from broadly viable hypotheses into models with sharp, testable predictions. The authors emphasize that:

1. Discrimination Power: JUNO's precision is sufficient to distinguish between different bi-large scenarios. For instance, the octant preference (T1 favors high, T2 favors near-maximal) and CP phase predictions (T1 allows CP conservation at $3\sigma$, T2 does not) offer clear discriminators.
2. Theoretical Constraints: The T1 pattern emerges as particularly distinctive, forbidding maximal atmospheric mixing and specific CP phases, making it a sharp target for future verification or exclusion.
3. Future Outlook: While T1 and T2 remain viable, T3 and T4 are "severely cornered" by existing data and are likely to be excluded by upcoming precision measurements. The study concludes that the bi-large paradigm, particularly the T1 and T2 variants, remains a robust framework worthy of continued scrutiny as JUNO accumulates more data.

The authors do not claim to have discovered a new mixing pattern but rather to have rigorously tested existing theoretical proposals against the new experimental frontier, highlighting how precision data can effectively prune the landscape of flavor models.