The problem of the “anomalous” mass of muons

Abstract

Ir is supposed t h a t there exists ah intermediately strong interaction between muons and kaons having the same f o r m a s that between nucleons and kaons. This interaetion explains the relatively large mass of the muons. After fixing the values of the parameters appearing in the interaetion other observable consequenees, e. g. elastie and inelastic muonnucleon seattering, anomalous muon magnetie moment etc. ate analysed. These "anomalous" effects caused by the supposed interaction turn out to be small and thus do not seem to contradict the present experimental facts. Finally, other kaonic interactions are briefly analysed. The universal k a o n interactionIr is well known that a satisfactory theory which would explain the experimentally observed mass spectrum of the elementary particles does not exist. The attractive idea of the field theoretical origin of the masses of particles proposed by MAX ABRAHAM at the turn of the century cannot be followed through in a consistent w a y ; according to the philosophy of the renormalizatŸ theory problems such as determining the observable masses from other data have no meaning. Recent experimental and theoretical arguments, however, seem to suggest t h a t the interactions show some kind of non-local character which may be expressed roughly and provisionally by introducing some cut-off method, thus we have a possibility of calculating finite field theoretical self-masses. Essentially almost all mass values can be calculated in good agreement with the experimental values by means of the simple perturbation theory, introducing a separate cut-off parameter for each type of interaction. We refer here e. g. to FEYMANN'S beautiful estiroate [1] of the neutron-proton masses.* Thus these provisional calculations (which ate far from being without further problems, e. g. 7£etc.) may give also some information about the systematization of the elementary particles.* The :t+--:r ~ mass difference is a combined effeet of the electromagnetie and strong interactions, so it is natural that in the course of zt+, zt 0 mass calculations we have to take into account such cut-off parameter value (i. e. t h a t of the strong interaction ~ N M <~ m e 137) whieh the combined interaction shows. (C. f. [2]). The same is the situation in FV~YMAr~'S calculation for the neutron-proton mass differenee.