Rare ${\Lambda }_b\to \Lambda l^{+}{l}^{-}$ decay in the Bethe-Salpeter equation approach

Abstract

We study the rare decays ${\Lambda }_b\to \Lambda l^{+}{l}^{-}(l=e,\mu ,\tau )$ in the Bethe-Salpeter equation approach. We find that depending on the values of parameters in our model the branching ratio $Br({\Lambda }_b\to \Lambda {\mu }^{+}{\mu }^{-})\times 10^6$ 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 $Br({\Lambda }_b\to \Lambda {\mu }^{+}{\mu }^{-})\times 10^6$ 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 $Br({\Lambda }_b\to \Lambda e^{+}{e}^{-}({\tau }^{+}{\tau }^{-}))\times 10^6$ varies in the range $0.660-1.028$ ($0.252-0.392$) and $0.749-1.098$ ($0.286-0.489$), respectively.