I understand that the question of the number of generations, while practically settled experimentally, is an open issue from the point of view of theoretical models. I can only think of two theoretical arguments to set bounds in this number:
- to get some CP violation, we need at least 3 generations in the CKM matrix.
- to keep the sign of the beta function of QCD under control, we can not have more than 16.5 flavours, so 8 generations.
Are there more arguments in the theoretical/phenomenology market, bounding the number of generations in some way? And, is there any that fixes it exactly to three?