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Rare $Λ_b \rightarrow Λl^+ l^- $ decay in the Bethe-Salpeter equation approach

We study the rare decays $Λ_b \rightarrow Λl^+ l^-~(l=e,μ, τ)$ in the Bethe-Salpeter equation approach. We find that depending on the values of parameters in our model the branching ratio $Br(Λ_b \rightarrow Λμ^+ μ^-)\times 10^{6}$ varies from $0.812$ to $1.445$ when $κ= 0.050 \sim 0.060$ GeV$^3$ and the binding energy $E_0=-0.14$ GeV while $Br(Λ_b \rightarrow Λμ^+ μ^-)\times 10^{6}$ varies from $1.051$ to $1.098$ when $κ= 0.055$ Gev$^3$ and the binding energy $E_0$ changes from $-0.19$ to $-0.09$ GeV. These results agree with the experimental data. In the same parameter regions, we find that the branching ratio $Br(Λ_b \rightarrow Λe^+ e^-(τ^+ τ^-) )\times 10^{6}$ varies in the range $0.660-1.028$ ($0.252-0.392$) and $0.749-1.098$ ($0.286-0.489$), respectively.