Why three generations?

Abstract

We discuss an anthropic explanation of why there exist three generations of fermions. If one assumes that the right-handed neutrino sector is responsible for both the matter-antimatter asymmetry and the dark matter, then anthropic selection favors three or more families of fermions. For successful leptogenesis, at least two right-handed neutrinos are needed, while the third right-handed neutrino is invoked to play the role of dark matter. The number of the right-handed neutrinos is tied to the number of generations by the anomaly constraints of the $U(1)_{B-L}$ gauge symmetry. Combining anthropic arguments with observational constraints, we obtain predictions for the $X$-ray observations, as well as for neutrinoless double-beta decay.