Lepton-number violating meson decays in theories beyond the Standard Model

After discussion of mechanisms of lepton number violation, we consider meson decays $K^+ \to\pi^ - \ell ^ + \ell '^ +$ and $D^ + \to K^ - \ell ^ + \ell '^ +$ ($\ell,\ell ' = e,\mu$) with $\Delta L= 2$ in the Standard Model extended by massive Majorana neutrinos and in a supersymmetric extension of the Standard Model with explicit breaking of R-parity by trilinear or bilinear Yukawa couplings in the superpotential. We give estimates of the branching ratios for these decays and compare the effectiveness of various decay mechanisms taking into account present experimental bounds on lepton mixing, masses of neutrinos and superparticles, and R-parity violating couplings.