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.