Estimations of Neutrino and Graviton Masses by a Phenomenological Mass Relation for Stable Particles

The ratio between the proton and electron masses was shown to be close to the ratio between the shortest lifetimes of particles, decaying by the electromagnetic and strong interactions. The inherent property of each fundamental interaction is defined, namely the Minimal Lifetime of the Interaction (MLTI). The rest mass of the Lightest Free Massive Stable Particle (LFMSP), acted upon by a particular interaction, is shown to be inversely proportional to MLTI. The found mass relation unifies the masses of four stable particles of completely different kinds (proton, electron, electron neutrino and graviton) and covers an extremely wide range of values, exceeding 40 orders of magnitude. On the basis of this mass relation, the electron neutrino and graviton masses have been approximately estimated to 6.5×10^-4 eV and ℏH/c² ≈ 1.5×10^-33 eV, respectively. Besides, the last value has been obtained independently by dimensional analysis by means of three fundamental constants, namely the speed of light in vacuum (c), reduced Planck constant (ℏ) and Hubble constant (H). The presence of an exceptionally small, yet nonzero mass of the graviton implies Yukawa potential of the gravitational field and a finite range of the gravity close to the Hubble distance cH^-1. Therefore, the graviton mass determines a finite size of gravitationally connected (observable) universe for an arbitrary observer. It was shown that the rest energy of LFMSP, acted upon by a particular interaction, is close to Breit-Wigner’s energy width of the shortest living state, decaying by the respective interaction.