Elementary Charge and Neutrino’s Mass from Planck Length

Abstract

It is shown that the postulation of a minimum length for the horizons of a black hole leads to lower bounds for the electric charges and magnetic moments of elementary particles. If the minimum length has the order of the Planck scale, these bounds are given, respectively, by the electronic charge and by $\mu \sim 10^{-21} \mu_B$. The latter implies that the masses of fundamental particles are bounded above by the Planck mass, and that the smallest non-zero neutrino mass is $m_{\nu} \sim 10^{-2}$eV. A precise estimation in agreement to the area quantisation of Loop Quantum Gravity predicts a mass for the lightest massive state in concordance with flavor oscillation measurements, and a Barbero-Immirzi parameter in accordance to horizon entropy estimations.