Analysis of FCNC ${\mathrm{\Xi }}_{QQ}\to {\mathrm{\Lambda }}_Q{l}^{+}{l}^{-}$ decay in light-cone sum rules

The weak decays of doubly heavy ${\mathrm{\Xi }}_{QQ}$ baryon induced by flavor changing $b\to d$ and $c\to u$ flavor changing neutral current within the light-cone sum rules are studied. The sum rules are constructed and analyzed for the corresponding transition form factors using the parallel components of the light-cone distribution amplitudes for ${\mathrm{\Lambda }}_Q$ baryon. Having the results for the form factors, the corresponding branching ratios for ${\mathrm{\Xi }}_{QQ}\to {\mathrm{\Lambda }}_Q{l}^{+}{l}^{-}$ 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, ${\mathrm{\Xi }}_{bb}\to {\mathrm{\Lambda }}_b{l}^{+}{l}^{-}$ decay has the potential of being discovered at LHCb. However, ${\mathrm{\Xi }}_{bb}\to {\mathrm{\Lambda }}_b{l}^{+}{l}^{-}$ 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.

Figure 1

The variation of form factors (at $q^2=0$) with respect to the Borel mass parameter at the fixed values of $s_{\mathrm{th}}$ is shown.