Electroweak Effects in the Double Dalitz Decay $B_s \to l^+ l^- l'^+ l'^-$

Abstract

We investigate the double Dalitz decays $B_s \to l^+ l^- l'^+ l'^-$ 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 $B_s \to e^+ e^- μ^+ μ^-$ is derived in an efficient way, using a QED result for meson decays mediated by two virtual photons: $B_s \to γ^* γ^* \to e^+ e^- μ^+ μ^-$. A comment is made on the correlation between the planes of the two lepton pairs. The conversion ratios $ρ_{lll'l'}= \frac{Γ(B_s \to l^+ l^- l'^+ l'^-)}{Γ(B_s \to γγ)}$ are estimated to be $ρ_{eeee}=3 \times 10^{-4}, ρ_{eeμμ}=9 \times 10^{-5} \text{and} ρ_{μμμμ}=3 \times 10^{-5}$, and are enhanced relative to pure QED by $10-30 %$.