Hierarchy of lepton masses in a vectorlike theory with Majorana particles

We demonstrate that a slightly modified version of the vectorlike weak-interaction theory of Fritzsch, Gell-Mann, and Minkowski can provide a framework for understanding the lepton mass spectrum. We conjecture that electrons and neutrinos are massless in the absence of weak interactions, and acquire masses through radiative corrections. But because there are heavy Majorana leptons in such a theory, electron mass is of the second order and neutrino masses are of the fourth order. One of the more immediate predictions of our theory is that among the dominant three-body decay products of the 1.8-GeV lepton $U$ of Perl et al. there should be a Majorana lepton of intermediate mass (∼100 MeV?) which decays into ${\overline{\nu }}_e\gamma$ and ${\nu }_e\gamma$ with a lifetime ∼${10}^{-5\mathrm{}}$ sec. Heavy Majorana particles and the attendant lepton-number violations are in fact desired for a number of reasons in an S${\mathrm{U}}_2$ ${\times \mathrm{U}}_1$ vectorlike theory where all fundamental fermions transform as doublets. We discuss lepton-number-violation processes such as $\alpha \to \beta {\mu }^{\pm }{\mu }^{\pm }$. We calculate the fourth-order induced neutrino masses. The possibility of their being finite and calculable quantities in a theory with an enlarged gauge group is also examined. We remark that our estimates indicate that the observation of "neutrino beam oscillation" will be hopelessly difficult in a laboratory setting.