Neutrino masses and mass hierarchy: Evidence for the normal hierarchy

The latest cosmological constraints on the sum of neutrino masses, in combination with the latest laboratory measurements on oscillations, provide "decisive" Bayesian evidence for the normal neutrino mass hierarchy. We show that this result holds across very different prior alternatives by exploring two extremes on the range of prior choices. In fact, while the specific numerical value for the Evidence depends on the choice of prior, the Bayesian odds remain greater than 140:1 across very different prior choices. For Majorana neutrinos this has important implications for the upper limit of the neutrino-less double beta decay half life and thus for the technology and resources needed for future double beta decay experiments.KS acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 713673. KS is also supported by an INPhINIT fellowship from “la Caixa” Foundation (ID 100010434), grant code LCF/BQ/DI17/11620047. Funding for this work was partially provided by project PGC2018-098866-B-I00 MCIN/AEI/10.13039/501100011033 y FEDER “Una manera de hacer Europa”, and the “Center of Excellence Maria de Maeztu 2020-2023” award to the ICCUB (CEX2019-000918M funded by MCIN/AEI/10.13039/501100011033). LV acknowledges support of European 4In a otherwise standard ΛCDM cosmological model.– 14Union’s Horizon 2020 research and innovation programme ERC (BePreSysE, grant agreement 725327).Peer reviewe