Lepton-flavor violation in light hadron decays

Abstract

The lepton-flavor-violating decays of light pseudoscalar mesons and light baryons are investigated within extensions of the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}U(1)$ model. These models contain heavy Dirac or Majorana neutrinos and allow large lepton--heavy-neutrino mixings. The free-parameter space of these models is carefully studied. Special care is devoted to the comparison of results of different models. A large ``nondecoupling'' window is found, and the decoupling of extremely heavy neutrinos is explicitly shown in all models except one, for which the free-parameter space is bounded. Among the decays studied, the experimentally most interesting decays are ${K}_{L}\ensuremath{\rightarrow}e\ensuremath{\mu}$ and ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}e\ensuremath{\mu}$. The ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}e\ensuremath{\mu}$ decay is found to be equally interesting for the study of lepton-flavor violation as ${K}_{L}\ensuremath{\rightarrow}e\ensuremath{\mu}$ decay. The constraint on the model parameters, coming from the nonobservation of the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma}$ decay, leads to the maximal decay rates ${B(K}_{L}\ensuremath{\rightarrow}e\ensuremath{\mu})\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ and $B({\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}e\ensuremath{\mu})\ensuremath{\lesssim}{(2n}_{R}\ensuremath{-}2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, where ${n}_{R}$ is number of heavy neutrinos, much smaller than the present experimental upper limits.