We present simple and predictive realizations of neutrino masses in theories based on the $SU(6)$ grand unifying group. At the level of the lowest-dimension operators, this class of models predicts a skew-symmetric flavor structure for the Dirac mass term of the neutrinos. In the case that neutrinos are Dirac particles, the lowest-order prediction of this construction is then one massless neutrino and two degenerate massive neutrinos. Higher-dimensional operators suppressed by the Planck scale perturb this spectrum, allowing a good fit to the observed neutrino mass matrix. A firm prediction of this construction is an inverted neutrino mass spectrum with the lightest neutrino hierarchically lighter than the other two, so that the sum of neutrino masses lies close to the lower bound for an inverted hierarchy. In the alternate case that neutrinos are Majorana particles, the mass spectrum can be either normal or inverted. However, the lightest neutrino is once again hierarchically lighter than the other two, so that the sum of neutrino masses is predicted to lie close to the corresponding lower bound for the normal or inverted hierarchy. Near future cosmological measurements will be able to test the predictions of this scenario for the sum of neutrino masses. In the case of Majorana neutrinos that exhibit an inverted hierarchy, future neutrinoless double beta experiments can provide a complementary probe.

• Received 20 May 2020
• Accepted 30 July 2020

DOI:https://doi.org/10.1103/PhysRevD.102.035020

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society