Neutrino masses and mixings: Status of known and unknown 3ν parameters

Abstract Within the standard 3 ν mass–mixing framework, we present an up-to-date global analysis of neutrino oscillation data (as of January 2016), including the latest available results from experiments with atmospheric neutrinos (Super-Kamiokande and IceCube DeepCore), at accelerators (first T2K ν ‾ and NO ν A ν runs in both appearance and disappearance modes), and at short-baseline reactors (Daya Bay and RENO far/near spectral ratios), as well as a reanalysis of older KamLAND data in the light of the “bump” feature recently observed in reactor spectra. We discuss improved constraints on the five known oscillation parameters ( δ m 2 , | Δ m 2 | , sin 2 ⁡ θ 12 , sin 2 ⁡ θ 13 , sin 2 ⁡ θ 23 ), and the status of the three remaining unknown parameters: the mass hierarchy [ sign ( ± Δ m 2 ) ], the θ 23 octant [ sign ( sin 2 ⁡ θ 23 − 1 / 2 ) ], and the possible CP-violating phase δ . With respect to previous global fits, we find that the reanalysis of KamLAND data induces a slight decrease of both δ m 2 and sin 2 ⁡ θ 12 , while the latest accelerator and atmospheric data induce a slight increase of | Δ m 2 | . Concerning the unknown parameters, we confirm the previous intriguing preference for negative values of sin ⁡ δ (with best-fit values around sin ⁡ δ ≃ − 0.9 ), but we find no statistically significant indication about the θ 23 octant or the mass hierarchy (normal or inverted). Assuming an alternative (so-called LEM) analysis of NO ν A data, some δ ranges can be excluded at > 3 σ , and the normal mass hierarchy appears to be slightly favored at ∼ 90 % C.L. We also describe in detail the covariances of selected pairs of oscillation parameters. Finally, we briefly discuss the implications of the above results on the three non-oscillation observables sensitive to the (unknown) absolute ν mass scale: the sum of ν masses Σ (in cosmology), the effective ν e mass m β (in beta decay), and the effective Majorana mass m β β (in neutrinoless double beta decay).