Discrete flavour and CP symmetries in light of JUNO and neutrino global fit

TL;DR

This work assesses how non-Abelian discrete flavour symmetries combined with generalized CP symmetry constrain the PMNS matrix through residual symmetries in charged-lepton and neutrino sectors. By analyzing one- and two-parameter breaking patterns across A_5, Σ(168), Δ(6n^2), and D_n groups, the authors translate group-theoretical structures into precise predictions for the three mixing angles and three CP phases, then confront them with NuFIT v6.0 and JUNO data. JUNO’s first results strongly disfavour several patterns, particularly those with fixed second-column structures, while many two-parameter realizations remain viable, offering rich correlations among θ_{12}, θ_{23}, θ_{13}, and δ_{CP}. The study highlights that the synergy among JUNO, DUNE, and T2HK can provide a comprehensive and decisive test of these symmetry-based explanations for lepton flavour, guiding future model-building toward minimal groups such as S_4, A_5, Δ(6n^2), and related D_n realizations. The results underscore the potential of upcoming precision measurements to discriminate among residual-symmetry patterns and to refine our understanding of the flavour structure in the lepton sector.

Abstract

Working within the reference three-neutrino mixing framework, we confront the lepton mixing predictions derived using non-Abelian discrete flavour and CP symmetries with the first JUNO data on the solar neutrino mixing parameters $\sin^2θ_{12}$ and with the results of the latest global neutrino data analysis. We focus on symmetry breaking patterns for which the lepton PMNS mixing matrix depends only on one or two free real parameters. Performing a comprehensive statistical analysis in each of the considered cases, we report the best fit values, the $3σ$ C.L. allowed ranges and the $χ^2$-distributions of the lepton mixing observables - the three mixing angles and the three CP-violation phases. We find that the JUNO measurements can disfavour or rule out a number of the mixing patterns associated with specific types of breaking of the discrete flavour and CP symmetries. The synergy of JUNO, DUNE and T2HK data can provide an exhaustive test of the considered approach to lepton mixing based on non-Abelian discrete lepton flavour symmetries combined with the CP symmetry.

Figures (7)

• Figure 1: Best-fit predictions of the neutrino mixing angles $\theta_{12}$, $\theta_{13}$, $\theta_{23}$ and the Dirac CPV phase $\delta_{CP}$ for lepton mixing patterns with one parameter in case of NO and IO neutrino masses spectrum. The gray regions in all plots are the current $3\sigma$ ranges of the corresponding observables for NO and IO from Esteban:2024eli. The dashed line is the current best-fit value. The light red and red region for $\sin^{2}\theta_{12}$ are the latest $3\sigma$ range obtained from the first 59.1 days of JUNO data JUNO:2025gmd and the prospective $3\sigma$ range of after 6 years of JUNO running with precision of $0.5\%$JUNO:2022mxj. The red regions shown for $\sin^{2}\theta_{23}$ and $\delta_{CP}$ represent the anticipated future $3\sigma$ sensitivities of next-generation long-baseline experiments such as DUNE DUNE:2020ypp and T2HK Hyper-Kamiokande:2018ofw, assuming the current NuFit best-fit values together with prospective precisions of about $3\%$ for $\sin^{2}\theta_{23}$ and $12^\circ$ for $\delta_{CP}$.
• Figure 2: The predictions of likelihood profiles for $\sin^{2}\theta_{12}$, $\sin^{2}\theta_{23}$ and $\delta_{CP}$ obtained using the current global data on the neutrino mixing parameters for lepton mixing patterns with one parameter. The dashed curves denote the likelihoods obtained from the NuFITEsteban:2024eli. In the $\sin^{2}\theta_{12}$ panel, the red dashed curve shows the likelihood from the recent JUNO 59.1-day data JUNO:2025gmd, while the dotted line indicates the projected $0.5\%$ precision expected after six years of JUNO operation JUNO:2022mxj. The dotted curves in the $\sin^{2}\theta_{23}$ and $\delta_{CP}$ panels correspond to the anticipated sensitivities of DUNE DUNE:2020ypp and T2HK Hyper-Kamiokande:2018ofw, assuming the current NuFit best-fit values together with prospective precisions of about $3\%$ for $\sin^{2}\theta_{23}$ and $12^\circ$ for $\delta_{CP}$. The solid colored lines represent the likelihoods predicted by the individual mixing patterns. The left (right) panels employ the one-dimensional projections $\chi^{2}_{i}(o_{i})$ for NO (IO).
• Figure 3: Best-fit predictions of the neutrino mixing angles $\theta_{12}$, $\theta_{13}$, $\theta_{23}$ and the Dirac CPV phase $\delta_{CP}$ for lepton mixing patterns with two parameter in case of NO and IO neutrino masses spectra. The remaining conventions follow those used in figure \ref{['fig:onepara_bfpoints_plots_NO_IO']}.
• Figure 4: The predictions of likelihood profiles for $\sin^{2}\theta_{12}$, $\sin^{2}\theta_{23}$ and $\delta_{CP}$ obtained using the current global data on the neutrino mixing parameters for two-parameter mixing patterns that originate from $A_{5}\rtimes H_{CP}$ and $\Sigma(168)\rtimes H_{CP}$. The remaining conventions follow those used in figure \ref{['fig:one_para_likelihood_NO_IO']}.
• Figure 5: The predictions of likelihood profiles for $\sin^{2}\theta_{12}$, $\sin^{2}\theta_{23}$ and $\delta_{CP}$ obtained using the current global data on the neutrino mixing parameters for two-parameter mixing patterns $U^{VIII}$ that originate from $\Delta(6n^{2})\rtimes H_{CP}$ and $D_{n}\rtimes H_{CP}$. The remaining conventions follow those used in figure \ref{['fig:one_para_likelihood_NO_IO']}.