Lepton-flavor violation in light hadron decays

The lepton-flavor-violating decays of light pseudoscalar mesons and light baryons are investigated within extensions of the $\mathrm{SU}\left(2\right)\mathrm{}\times U\left(1\right)\mathrm{}$ 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 $K_L\to e\mu$ and ${\pi }^0\to e\mu$. The ${\pi }^0\to e\mu$ decay is found to be equally interesting for the study of lepton-flavor violation as $K_L\to e\mu$ decay. The constraint on the model parameters, coming from the nonobservation of the $\overrightarrow{\mu }e\gamma$ decay, leads to the maximal decay rates ${B(K}_L\to e\mu )\sim 5\times {10}^{-16}$ and $B({\pi }^0\to e\mu )\lesssim {(2n}_R-2)\times {10}^{-15}$, where $n_R$ is number of heavy neutrinos, much smaller than the present experimental upper limits.