Muon parity conservation and the universality principle

All p re sen t e x p e r i m e n t a l ev idence is cons i s ten t wi th , besides t he conserva t ion of the to ta l lep ton n u m b e r (1), the ex is tence of e i ther an addi t ive conserva t ion law of ninon n u m b e r (N~) or a mul t ip l iea t ive conserva t ion law (2) of muon p a r i t y (P~) (a), and fu r the r tes t s are still needed in order to decide which form of l ep ton conserva t ion law prevails (Ld). The conse rva t ion of P~ is equ iva len t to t he selection rule AN~ = 0, -4-2, ~: 4 . . . . . and so is less res t r i c t ive t h a n the conserva t ion of N ~ (i .e . A N ~ = 0). I t is there fore of much in te res t , b o t h theore t ica l and exper imen ta l , to cons t ruc t a model in te rac t ion Hami l ton ian which re la tes possible AN~ = ~= 2 t rans i t ions to t he welles tab l i shed AN~ = 0 ones and thus enables one to make q u a n t i t a t i v e pred ic t ions abou t t he fo rmer processes. In t he p re sen t note , we w a n t to p ropose a muon-pa r i t y -conse rv ing weakin te rac t ion scheme, based exclusively upon the pr inciple of un iversa l i ty (5.s). F i r s t ly let us confine ourselves to t he pure ly leptonic case and in t roduce lep ton cur ren t s w i th P ~ § 1 and 1 respec t ive ly :