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With the discovery of the doubly heavy $\Xi_{cc}$ baryon, comprehensivestudies of the properties of the doubly heavy baryons are started. In thepresent work, we examine the $\Xi_{bb} \to \Sigma_b \ell^+ \ell^-$ and$\Xi_{cc} \to \Sigma_c \ell^+ \ell^-$ decays induced by flavor-changing neutralcurrents (FCNC) in the framework of the light-cone sum rules. After obtainingthe sum rules for the form factors induced by the tensor current, the branchingratios of the relevant transitions are estimated. We found that the branchingratio for the $c \to u$ transition is around five orders smaller than the $b\to d$ transition. Our findings are also compared with other approaches.

Weak $\Xi_{QQ} \to \Sigma_Q \ell^+ \ell^-$ decays induced by FCNC in QCD