Neutrinos Are Very Likely Very Light

Adopting the cosmological bounds on the sum of the neutrino masses and making some other unambitious assumptions, this paper argues that the lightest of the three neutrino masses is less than 2.3 meV and considers a possible phenomenological relations between the three neutrino masses. Direct measurements of the electron neutrino mass at the Katrin experiment bound it at less than 450 meV with good prospects of reducing the bound to 200 meV, but that is still at least two orders of magnitude less than the likely true value.

By way of comparison, the mass of an electron is about 511,000,000 meV, and the first generation quarks are in the low single digit billions of meVs. 

Determining the absolute neutrino mass scale remains one of the most compelling challenges in particle physics. To constrain theoretical models, establishing precise relations among neutrino masses is essential. We propose a simple integral representation of the neutrino mass-squared differences Δm(ij)^2 that provides a complementary perspective on these oscillation parameters. We then demonstrate its utility through several examples. 

Specifically, assuming stringent cosmological bounds that confine the sum of neutrino masses near the normal ordering floor, we derive an analytical condition for the lightest neutrino mass, m(1) < √(61Δm(21)^2)/30. Using recent data from the JUNO experiment, this yields a competitive upper limit of m(1) < 0.0023 eV (95% C.L.). 

We also formulate practical analytical bounds for m(2) and m(3) adaptable to future data, and translate the results into allowed ranges for the effective electron and Majorana neutrino masses m(νe) and m (ββ). Finally, we show that neutrino mass relations of the Gatto-Sartori-Tonin type emerge directly from the proposed integral representation.

I. Alikhanov, "Integral representation of the neutrino mass-squared differences" arXiv:2607.19340 (July 21, 2026).