Another relation among the neutrino mass-squared differences?

Abstract

Determining the absolute neutrino mass scale remains a compelling challenge in particle physics. Establishing precise mathematical connections among the neutrino masses could significantly facilitate this task and shed additional light on the underlying mass-generation mechanism. We highlight the possible existence of a simple algebraic relation between the mass-squared differences, $$\frac{\sqrt{\Delta m_{31}^2}+\sqrt{\Delta m_{21}^2}}{\sqrt{\Delta m_{31}^2}-\sqrt{\Delta m_{21}^2}}=\sqrt{2},$$ which agrees remarkably well with the best-fit values of recent global analyses of neutrino oscillation data. We then investigate the implications of adopting this relation and how it decreases the number of independent parameters in the neutrino sector. We demonstrate that there are alternative representations well known in quark and charged-lepton physics. Furthermore, we place a tight constraint on the solar neutrino mass splitting, $\Delta m_{21}^2=(7.445\pm 0.062)\times 10^{-5}{\text{ eV}}^2$, and also obtain $\Delta m_{31}^2=(2.548\pm 0.041)\times 10^{-3}{\text{ eV}}^2$. Next-generation reactor and accelerator neutrino experiments are expected to significantly reduce systematic uncertainties. In particular, the Jiangmen Underground Neutrino Observatory (JUNO) will measure these parameters independently of each other at the sub-percent level, thereby providing a stringent and direct test of our results.

12 pages, 1 table. Version accepted by JHEP. v3: added subsection on applicability, minor text clarifications, and updated references