DIFFERENCE BETWEEN MUON AND ELECTRON MASSES Two Types of Dirac Fields

The idea o f two types o f Dirac fields (in particular, electron and muon fields) conjugate in the sense o f the generalized Konop insk i -Mahmoud hypothesis (e-, #+ particles, e +, # antiparticles, ~ , la + particles, etc.) can more conveniently be presented and interpreted with the aid o f the second order equation for four-component spinors. This is equivalent to the two Dirac equations (ip+m)wi = 0 and (ip--m)lpii = 0 whose field quanta are automatically connected by the Konopinsk i -Mahmoud hypothesis. The quanta o f the "conjt tgate" fields tpi and tpH possess equal bare masses. The theory is invariant wi th respect to the ~p --~ 7,sip transformation. The interactions which violate tp --~ 7,s~0 invariance can remove the mass degeneracy, e.g., the case o f the weak interaction through symmetrical neutral currents G (Vpeyp~0e~eypV' e ~Tp~ot,~yo~0~). 1. Electron and Muon Many years ago a second order equation was proposed for the spinor field (of electrons), with a I_~grangian in the form 1) = 1⁄2m E (1) .p oxp OX~ Both energy and charge in this theory are non-positive definite. Such a theory can describe the electron as a particle of positive energy and negative charge eand the positon as a hole in occupied electron states of negative energies. The theory also allows for another particle of positive charge and positive energy and for its antiparticle. The latter is a hole in the distribution of levels occupied by particles of positive charges and negative energies. An electron may annihilate with a positon (hole), but not with another, positively charged, particle. According to this equation, there should exist a "second" electron. Its properties must be, in a sense, opposite to those of the electron: the particle is a field quantum, charged positively, while the antiparticle is charged negatively. Since there seem to be no "second" electron in nature a question arises whether the #+ meson could be interpreted as the second particle in this theory. Interest in the old Konopinski-Mahmoud hypothesis concerning the muon and electron 2) has recently revived in connection with experimental evidence in favour of the existence of muon and electron neutrinos. 130 MUON AND ELECTRON 131 According to this hypothesis the eelectron and #+ meson are treated as particles and the e + positon and # meson as antiparticles. This is the situation described by the above equation. It appears of interest to investigate which kinds of the known (or experimentally allowable) interactions can remove the mass degeneracy of the free equation describing these particles, i.e., lead to m s # me; to what extent the muon and electron neutrinos can naturally be included in this scheme; and in general how universal is such a classification of bare Fermi particles: can this scheme incorporate baryons, for example. The second order equation for the four-component spinor is equivalent to the first-order equation for the eight-component function. This equation can be written in the form of two separated equations where (ip+m)~k I = 0, (2) (ip-m)~kll = 0, (3) a p = iTZaxu , or, introducing the eight row matrices F ~ = 0 ?~ # 1,2,3,4, F 0 (4) eqs. (2) and (3) can be written as "one" equation ( iP + Fm) = O, = I , e = ( 5 ) i