Rare $\Lambda_b \rightarrow \Lambda l^+ l^- $ decay in the Bethe-Salpeter equation approach

We study the rare decays $\Lambda_b \rightarrow \Lambda l^+ l^-~(l=e,\mu, \tau)$ in the Bethe-Salpeter equation approach. We find that depending on the values of parameters in our model the branching ratio $Br(\Lambda_b \rightarrow \Lambda \mu^+ \mu^-)\times 10^{6}$ varies from $0.812$ to $1.445$ when $\kappa = 0.050 \sim 0.060$ GeV$^3$ and the binding energy $E_0=-0.14$ GeV while $Br(\Lambda_b \rightarrow \Lambda \mu^+ \mu^-)\times 10^{6}$ varies from $1.051$ to $1.098$ when $\kappa = 0.055$ 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 $Br(\Lambda_b \rightarrow \Lambda e^+ e^-(\tau^+ \tau^-) )\times 10^{6}$ varies in the range $0.660-1.028$ ($0.252-0.392$) and $0.749-1.098$ ($0.286-0.489$), respectively.