Substructures of quarks and leptons and origins of internal quantum numbers

A motivation of the subquark models is to seek for the origin of the internal quantum numbers of the quarks and leptons in their substructures. There, it is implicitly assumed that the particles with common internal quantum numbers are originated from the common substructures which exhibit the quantum number, which is called 'single origin hypothesis' of the internal quantum number. It is satisfied by the quantum numbers whose origins were already disclosed. The authors seek for composite models where the internal quantum numbers of quarks and leptons, i.e., the color, weak isospin, electric charge and the generation quantum number are all single-originated. To realize the requirement, the 'fundamental charge' k is introduced besides w, h, c and c0, taking them mutually dependent. The electric charges of the w, h, c and c0 are given as: Q(w1) = y + 1/2, Q(w2) = y - 1/2, Q(h) = x, Q(c) = 1/6-x-y and Q(c0) = -1/2±x±y, where x and y are arbitrary constants. Since Q's are multiples of the fundamental charge, their ratios should be simple integers. Thus, models for each charge assignment can be constructed, as far as the quantum numbers are concerned. In order for these 'models' really to be models, the dynamics should be specified which explains those peculiar selection rules, though no answer to this problem is available at present. If it exists, it should be a saturative and non-confining short-distance force. Subcolor may not be a good candidate. (Nogami, K.)