Weak decays of doubly heavy baryons: *

The discovery of $\Xi_{cc}^{++}$ has inspired new interest in studying doubly heavy baryons. In this study, the weak decays a charmed baryon ${\cal B}_{cc}$ to light B}$ and charm meson $D^{(*)}$ (either pseudoscalar or vector one) are calculated. Following our previous work, we calculate short distance contributions under factorization hypothesis, whereas long modeled as final state interactions which calculated with one particle exchange model. We find that B}_{cc}\to {\cal B} D^{*}$ decays' branching ratios obviously larger, they receive more polarization states. Among investigate, following have largest fractions: BR}(\Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{*+}) \in [0.46\%, 3.33\%]$ estimated $\tau_{\Xi_{cc}^{++}}=256$ fs; BR}(\Xi_{cc}^{+}\rightarrow\Lambda D^{*+}) [0.38\%, 2.63\%]$ BR}(\Xi_{cc}^{+}\rightarrow\Sigma^{0} [0.45\%, 3.16\%]$ $\tau_{\Xi_{cc}^+}=45$ BR}(\Omega_{cc}^{+}\rightarrow\Xi^{0} [0.27\%, 1.03\%]$, D^{+}) [0.07\%, 0.44\%]$ BR}(\Omega_{cc}^{+}\rightarrow\Sigma^{0} [0.06\%, 0.45\%]$ $\tau_{\Omega_{cc}^+}=75$ fs. By comparing decay widths pure color commensurate channels those bow-tie ones, mechanism plays an important role decays.