Description of the Four-Particle Decays \(\bar{B}_{d,s}\to\mu^{+}\mu^{-}e^{+}e^{-}\) on the Basis of the Standard Model

Partial widths and double- and single-differential distributions are calculated on the framework of the Standard Model for the four-lepton decays \(\bar{B}_{q}\to\mu^{+}\mu^{-}e^{+}e^{-}\) , where \(q\) = \(d\) and \(s\) . The contribution of virtual-photon emission by a light \(q\) quark and a heavy \(b\) quark, the bremsstrahlung contribution from charged leptons in the final state, the weak-annihilation contribution, and the contribution of wide vector \(c\bar{c}\) resonances are taken into account. The contribution of narrow \(J/\psi\) and \(\psi(2S)\) resonances is excluded. Virtual-photon emission by the light quark of a \(\bar{B}_{q}\) meson is described on the framework of the vector-meson-dominance model, within which only the contributions of the lightest vector mesons containing \(q\bar{q}\) pairs are taken into account. For the \(\bar{B}_{s}\) meson, this is the \(\varphi(1020)\) resonance. For the \(\bar{B}_{d}\) meson, the contributions of the \(\rho^{0}(770)\) and \(\omega(782)\) resonances are taken into account. Two possibilities are considered in the present study. The first is that where the contributions of the narrow \(\varphi(1020)\) and \(\omega(782)\) mesons are excluded from the partial widths with respect to the corresponding decays. The second is that where the contributions of narrow resonances are taken into account in partial widths. The problem of the influence of the subtraction procedure on the partial widths with respect to the decays \(\bar{B}_{q}\to\mu^{+}\mu^{-}e^{+}e^{-}\) is studied individually.