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Analysis of FCNC $Ξ_{QQ} \to Λ_Q l^+ l^-$ decay in light-cone sum rules

The weak decays of doubly heavy $Ξ_{QQ}$ baryon induced by flavor changing $b \to d$ and $ c \to u$ flavor changing neutral current within the light cone sum rules are studied. Using the parallel components of the light cone distribution amplitudes for $Λ_Q$ baryon, the sum rules are constructed and analyzed for the corresponding transition form factors. Having the results for the form factors, the corresponding branching ratios for $Ξ_{QQ} \to Λ_Q l^+ l^-$ decays are estimated. While the branching ratio due to $b \to d$ transition is around $10^{-9}$, in $c \to u$ transition case, it is found as around $10^{-13}$. Hence, $Ξ_{bb} \to Λ_b l^+ l^-$ decay has the potential of being discovered at LHCb. However, $Ξ_{bb} \to Λ_b l^+ l^-$ is difficult to be measured due to the extremely small values of obtained branching ratio. Our results on the branching ratio are also compared with the results of the light-front approach.