2158 Letters to the Editor that q-q scattering amplitude for the case of the heavier quark mass is found to become smaller by one order than that for the case of the ordinary quark mass m"-'0.3(GeV) (compare the results obtained in I). As well, one can show that a set of ap- proximate solution to Eqs. (5) and (6) (i.e., S-S and V-S parts) takes the follow- ing expression; f(p, k) = (ao' +a// (m 2 - k2) )f(p, k; VA), (13) Prog. The or. Phys. Vol. 57 (1977), June Two Kinds of Muon Number N onconserva tion Kenzo lSHIKA W A, Shoichi MIDORIKA W A, Takeshi MORIYA and Motohiko YOSHIMURA Department of Physics Tohoku UnizJersity, Sendai 980 March 28, 1977 Long time ago Feinberg and Weinbergu pointed out that there may exist two dis- tinct classes of muon number conservation consistent with the available experimental data. One of them, the additive law, states that the total electron and muon number be separately conserved, while in the other case of the multiplica- tive law the weaker form of conservation of '5_j CNe + NJ and ( -1) l;N 1 ' is assumed. Surprisingly, no sensitive test of additive vs multiplicative laws has been conducted to date. Experimental upper limits of equivalent (V-A) Fermi couplings for the +(co' +c/ /(m 2 -k 2 ))k"]f(p, k; vJ..). (14) Here the unknown parameters a 0 ' (A, A 0 , P', m, fl), b 0 ' (A, A 0 , p 2 , m, fJ), etc. are to be determined in the same manner as a, b, etc. of (9) and (10). The solutions (9), (10), (13) and (14) indicate that the above- mentioned two sets of simultaneous integral equations have the same structure of the solutions in our approximation. 1) R Hayashi, Prog. Theor. Phys. 57 (1977). 1104. processes allowed by the multiplicative law, jJ+e---'7jJ-e", 2 l e-e---'?fJ-fJ-, 3 > !1'.--'7e+VeV 1 ,!> are 5800 Gp, 610 Gp, 0.6 Gp, respectively with GF the S-decay constant. More re- cently, much theoretical discussion has been presented on possible existence of muon number nonconserving processes, being stimulated by unpublished reports of the observation fJ--'7er. 5 > This process violates at once both forms of the conservation law, hence there still remains an important question of which should be maintained in an approximate world ignoring the pre- sumably small violation. Before the unpublished reports of ob- served fJ--'?er were circulated, we presented detailed calculations 6 > for muon number nonconserving processes in certain vector- like gauge models. 7 >,s> In these vectorlike models an approximate multiplicative law is maintained. By 'approximate' we mean that in processes involving the known four leptons the multiplicative law is violated only by higher order weak interactions. Violation of the additive law, on the other hand, is caused by an exchange of unusual Higgs boson called r-- that couples to Downloaded from https://academic.oup.com/ptp/article-abstract/57/6/2158/1940325 by guest on 01 June 2020