Slowly but surely, the precision with which we know the neutrino oscillation parameters is improving, with one of the five parameters now reaching the subpercent level.
We perform an updated global analysis of the known and unknown parameters of the standard 3ν framework as of 2025. The known oscillation parameters include three mixing angles (θ12,θ23,θ13) and two squared mass gaps, chosen as δm^2=m2^2−m1^2>0 and Δm^2=m23−1/2(m1^2+m2^2), where α=sign(Δm^2) distinguishes normal ordering (NO, α=+1) from inverted ordering (IO, α=−1).
With respect to our previous 2021 update, the combination of oscillation data leads to appreciably reduced uncertainties for θ23, θ13 and |Δm^2|. In particular, |Δm^2| is the first 3ν parameter to enter the domain of subpercent precision (0.8% at 1σ). 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 2.2σ), for CP violation versus conservation in NO (1.3σ) and for the first θ23 octant versus the second in NO (1.1σ). We discuss the status and qualitative prospects of the mass ordering hint in the plane (δm^2,Δm(ee)^2), where Δm(ee)^2=|Δm^2|+1/2α(cos(θ12)^2−sin(θ12)^2)δm^2, to be measured by the JUNO experiment with subpercent precision.
We also discuss upper bounds on nonoscillation observables, including the effective νe mass mβ in β-decay, the effective Majorana mass mββ in 0νββ decay, and the total ν mass Σ in cosmology.
We report mβ < 0.50 eV (2σ) from 3H [KATRIN] data and mββ < 0.086 eV (2σ) from 76Ge, 130Te and 136Xe data, accounting for parametrized nuclear matrix element covariances.
Concerning Σ, current results show tensions within the standard ΛCDM cosmological model, pulling Σ towards unphysical values and suggesting possible model extensions. We discuss representative combinations of data, with or without augmenting the ΛCDM model with extra parameters accounting for possible systematics (lensing anomaly) or new physics (dynamical dark energy). The resulting 2σ upper limits are roughly spread around the bound Σ < 0.2 eV within a factor of three (both upwards and downwards), with different implications for NO and IO scenarios. Bounds from oscillation and nonoscillation data are also discussed in the planes charted by pairs of (mβ, mββ,Σ) parameters.
Francesco Capozzi, et al., "Neutrino masses and mixing: Entering the era of subpercent precision" arXiv:2503.07752 (March 10, 2025).
Analysis
The estimates of the preference for a normal mass ordering of the three neutrino masses, and of CP violation in neutrino oscillation are probably low considering all of the data and hints out there in the literature. I have very little doubt that both of those will ultimately turn out to be correct, with the CP violation parameter likely to be near maximal.
Other reviews have favored a second octant v. a first octant value for θ23. The true quadrant is very much an open question.
As I understand it, mβ < 0.50 eV is the upper bound on the absolute value of the lightest neutrino mass from heavy hydrogen decades directly measured in the KATRIN experiment, and mββ < 0.086 eV is the upper bound on the Majorana mass of the lightest neutrino mass state from neutrinoless double beta decay experiments. The KATRIN result is now outdated as previously reported at this blog. The new limit is actually 0.45 eV. This pushes the limit on the sum of the three neutrino masses to 1.41 eV in a normal hierarchy and 1.46 eV in an inverted hierarchy, a bound which is more than ten times weaker than the cosmology based bounds, but is much less model dependent and has fewer sources of potential systemic error.
The details of the paper's findings are spelled out in greater detail in its tables.
The bounds on the minimum frequency of neutrinoless double beta decay (which implies Majorana neutrinos and has not yet been detected) also continues to get longer.
The limit on the sum of neutrino masses Σ is conservative with many other papers reaching a lower value. This data also tends to favor a normal ordering of neutrino masses in which the sum of neutrino masses Σ is less than about 0.1 eV, which several data combinations placing two sigma bounds below that threshold.
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