Rare Decays of $${D_{s}}$$ Mesons to Three Charged Leptons and a Neutrino within the Standard Model

The branching ratios of the four-lepton decays $$D_{s}^{-}\to\mu^{+}\mu^{-}{\bar{\nu}}_{e}e^{-}$$ and $$D_{s}^{-}\to e^{+}e^{-}{\bar{\nu}}_{\mu}\mu^{-}$$ are found on the basis of the Standard Model, and the respective single-differential distributions are obtained and analyzed within this framework. The contributions of virtual-photon emission by the $$s$$ and $$c$$ quarks of the $$D_{s}^{-}$$ meson and virtual-photon bremsstrahlung by a final-state charged lepton are taken into account in the calculations. Virtual-photon emission by the $$s$$ quark is described on the basis of the vector-meson-dominance model.