Trimaximal Mixing Patterns Meet the First JUNO Result

TL;DR

JUNO's refined measurement of $\theta_{12}$ and $\Delta m^2_{21}$ challenges simple trimaximal (TM1/TM2) realizations of TBM. The authors explore whether RG running from a high-energy TM pattern can restore compatibility with the data in both Majorana and Dirac frameworks, finding that quasi-degenerate neutrino masses can reconcile TM1/TM2 with JUNO, though Majorana TM2 is largely excluded by $m_{ββ}$ bounds. In contrast, Dirac TM1 remains viable and typically preferred, while Dirac TM2 faces tighter constraints from KATRIN. The results highlight the complementary role of oscillation and non-oscillation experiments in testing flavor-symmetry-based mixing patterns and point to future measurements as decisive tests of these scenarios.

Abstract

The JUNO experiment has recently released its first measurement results based on 59.1 days of data, achieving unprecedented precision in measuring the lepton mixing angle $θ_{12}$. This significant improvement places stringent constraints on certain neutrino mass models and flavor mixing patterns. In this work, we examine the impact of the latest JUNO results on the two trimaximal (i.e., TM1 and TM2) mixing patterns. They are two well-motivated variants of the tri-bimaximal mixing pattern and predict specific correlations between $θ_{12}$ and $θ_{13}$, which lie outside the experimentally allowed $1σ$ and $3σ$ regions, respectively, after taking into account JUNO's results. Then, attempting to reconcile these TM mixing patterns with the latest experimental data, we further investigate the renormalization group (RG) running effects on them in the both Majorana and Dirac neutrino cases. Our analytical and numerical results show that RG corrections can bring the two TM mixing patterns into excellent agreement with the latest JUNO data if neutrino masses are quasi-degenerate. However, the Majorana case faces severe constraints from neutrinoless double beta decay limits, and particularly, the TM2 mixing pattern with Majorana neutrinos has been essentially ruled out. In the Dirac case, the TM1 mixing pattern is fully consistent with current data including beta decay results, whereas the TM2 pattern is strongly constrained by the KATRIN limit and even could be largely ruled out if the KATRIN experiment reaches its final sensitivity without any discovery. Future high-precision measurements of lepton mixing parameters and absolute neutrino masses in both oscillation and non-oscillation experiments will provide decisive tests of these mixing patterns.

Figures (8)

• Figure 1: Correlations between $\theta^{}_{12}$ and $\theta^{}_{13}$ in the TM1 and TM2 mixing patterns. The black (grey) stars, dashed lines, and dashed-dotted lines stand for the best-fit point, $1\sigma$ region, and $3\sigma$ region of $\theta^{}_{12}$ and $\theta^{}_{13}$, respectively, in the NMO (IMO) case. In the left panel, the central values of $\theta^{}_{12}$ and $\theta^{}_{13}$ together with their uncertainties are both taken from the NuFIT 6.0 results, while in the right panel, the central value and uncertainty of $\theta^{}_{12}$ are from the latest JUNO measurement.
• Figure 2: Contour plots for $\delta$ and $\rho \left( \sigma \right)$ in the $\theta^{}_{23}$-$\theta^{}_{13}$ plane in both NMO and IMO cases. The black stars, dashed lines, and dashed-dotted lines stand for the best-fit point, $1\sigma$ range, and $3\sigma$ range of $\theta^{}_{13}$ and $\theta^{}_{23}$ from the NuFIT 6.0 global analysis, respectively.
• Figure 3: The values of running factors $I^{}_{M,D}$ and $\Delta^{}_\tau$ against the energy scale $\mu$ from $\Lambda=10^{16}$ GeV down to the electroweak scale $\Lambda^{}_{\rm EW} = 200$ GeV.
• Figure 4: Correlations among observables at $\Lambda^{}_{\rm EW}$ in the NMO case with Majorana neutrinos. The cyan star and the red and blue regions correspond to $\chi^2 = \chi^2_{\rm min}$, $\chi^2 \leq 1$, and $\chi^2 \leq 9$, respectively. Further details are provided in the main text.
• Figure 5: The same as Fig. \ref{['fig:nmo']} but in the IMO case.