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

As a continuation of our previous work, we investigate the weak decays of doubly-heavy baryons $\Xi_{QQ^{\prime}}$ into sextet $\Sigma_{Q^{\prime}}$ with light-cone sum rules. We calculate the form factors for these decays with the parallel light-cone distribution amplitudes of $\Sigma_{Q^{\prime}}$. Numerical results of these form factors are used to predict the decay widths and branching ratios of the corresponding semi-leptonic processes. Parametric uncertainties and theoretical analyses are also given in detail. We find that the decay widths of $\Xi_{cc}$ and $\Xi_{bc}$ decays are several orders of magnitude larger than those of $\Xi_{bb}$ decays.