Light-Cone Sum Rules Analysis of $\Xi_{QQ^{\prime}q}\to\Sigma_{Q^{\prime}}^{*}$ Weak Decays

In this work, we investigate the semi-leptonic weak decays of spin-1/2 doubly-heavy baryons $\Xi_{QQ^{\prime}}$ into spin-3/2 singly-heavy baryons $\Sigma_{Q^{\prime}}^*$ within light-cone sum rules. Using the parallel components of the light-cone distribution amplitudes of $\Sigma_{Q^{\prime}}^*$, the transition form factors for these decays are calculated both analytically and numerically. The numerical results for these semi-leptonic weak decays widths and branching ratios are also predicted, which are compared with the same predictions by other theoretical approaches in the literatures. These phenomenology predictions can be tested by the experiments in the future.