Neutrino masses and mixing: Entering the era of subpercent precision

Abstract

We perform an updated global analysis of the known and unknown parameters of the standard $3\nu$ framework as of 2025. The known oscillation parameters include three mixing angles $(\theta_{12},\,\theta_{23},\,\theta_{13})$ and two squared mass gaps, chosen as $\delta m^2=m^2_2-m^2_1>0$ and $\Delta m^2=m^2_3-{\textstyle\frac{1}{2}}(m^2_1+m^2_2)$, where $\alpha=\mathrm{sign}(\Delta m^2)$ distinguishes normal ordering (NO, $\alpha=+1$) from inverted ordering (IO, $\alpha=-1$). With respect to our previous 2021 update, the combination of oscillation data leads to appreciably reduced uncertainties for $\theta_{23}$, $\theta_{13}$ and $|\Delta m^2|$. In particular, $|\Delta m^2|$ is the first $3\nu$ parameter to enter the domain of subpercent precision (0.8\% at $1\sigma$). We underline some issues about systematics, that might affect this error estimate. Concerning oscillation unknowns, we find a relatively weak preference for NO versus IO (at $2.2\sigma$), for CP violation versus conservation in NO (1.3$\sigma$) and for the first $\theta_{23}$ octant versus the second in NO ($1.1\sigma$). We discuss the status and qualitative prospects of the mass ordering hint in the plane $(\delta m^2,\,\Delta m^2_{ee})$, where $\Delta m^2_{ee}=|\Delta m^2|+{\textstyle\frac{1}{2}}\alpha(\cos^2\theta_{12}-\sin^2\theta_{12})\delta m^2$, to be measured by the JUNO experiment with subpercent precision. We also discuss upper bounds on nonoscillation observables. We report $m_\beta<0.50$~eV and $m_{\beta\beta}<0.086$~eV ($2\sigma$). Concerning the sum of neutrino masses $\Sigma$, we discuss representative combinations of data, with or without augmenting the $\Lambda$CDM model with extra parameters accounting for possible systematics or new physics. The resulting $2\sigma$ upper limits are roughly spread around the bound $\Sigma < 0.2$~eV within a factor of three. [Abridged]