Pion-muon mass ratio and classical electron models

Abstract

At present, one regards the muon and electron as closely related particles because of their quantum electrodynamie and leptonie similarities. In contrast to this very reasonable view, this note will describe a model in which the pion and muon are treated as closely related particles, while the ordinary electron is left to a future development of the theory. The pion-muon model is based part ly on the classical Lorentz electron, but certain ambiguities involved in compensating the self-stress are utilized to introduee nonclassical ideas. The basic advantages of the model are the simplicity with which it resolves the charged pion-muon mass ratio, utilizes isospin in the eompensation mechanism, introduces the neutral pion, and admits of possible extrapolation to other particles. We recall the standard noneovariant expressions for the transformation of the energy and momentmn of the Lorentz electron, with the understanding that the divergent electrostatic self-energy in the rest frame has been cut off, and the finite quantity is denoted by U0, then with c = 1, we have