Electroweak Effects in the Double Dalitz Decay $B_s\to l^{+}{l}^{-}{l}^{\prime +}{l}^{\prime -}$

Abstract

We investigate the double Dalitz decays $B_s\to l^{+}{l}^{-}{l}^{\prime +}{l}^{\prime -}$ on the basis of the effective Hamiltonian for the transition $b\bar{s}\to l^{+}{l}^{-}$, and universal form factors suggested by QCD. The correlated mass spectrum of the two lepton pairs in the decay $B_s\to e^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$ is derived in an efficient way, using a QED result for meson decays mediated by two virtual photons: $B_s\to {\gamma }^{\ast }{\gamma }^{\ast }\to e^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$. A comment is made on the correlation between the planes of the two lepton pairs. The conversion ratios ${\rho }_{ll{l}^{\prime }{l}^{\prime }}=\frac{\Gamma (B_s\to l^{+}{l}^{-}{l}^{\prime +}{l}^{\prime -})}{\Gamma (B_s\to \gamma \gamma )}$ are estimated to be ${\rho }_{eeee}=3\times 10^{-4},{\rho }_{ee\mu \mu }=9\times 10^{-5}\text{and}{\rho }_{\mu \mu \mu \mu }=3\times 10^{-5}$, and are enhanced relative to pure QED by $10-30$.

Comments: Two typos corrected: (i) factor $1/{\Gamma }_{\gamma \gamma }$ inserted in Eq. (14), (ii) co-ordinate labels $x_{12},x_{34}$ inserted in Figs. 1-3. To appear in Physics Letters B