Charge dependent relation between the masses of different generations and Neutrino masses

Abstract

Despite the enormous achievements, the Standard model of Particle physics can not be consider as complete theory of fundamental interactions. Among other things, it can not describe the gravitational interaction and it depends on 19 parameters. The Standard model includes 12 fermions (matter elementary particles with spin $\frac{1}{2}$) which are divided in three generations, groups with same interactions but different masses. Each generation can be classified into two leptons (with electric charges $Q=-1$, electron-like and $Q=0$, neutrino) and two quarks (with electric charges $Q=-\frac{1}{3}$, down-type and $Q=\frac{2}{3}$, up-type). However, the understanding of the relationship between generations and ratio of masses of different generations are unknown. Here we show that there exists the simple relation between masses of different generations which depend only on the electric charges for $Q=-1,\, \, Q=-\frac{1}{3}$ and $Q=\frac{2}{3}$. It is in pretty good agreement with experimental data. Assuming that the same relation valid for $Q=0$, we are able to calculate neutrino masses. Therefore, our results could pave the way for further investigations beyond Standard model.