Semileptonic decays of doubly charmed baryons with $Ξ_c-Ξ_c'$ mixing
We study the $Ξ_c- Ξ_c'$ mixing effects in the semileptonic decays the doubly charm baryons of $Ξ_{cc}$. We focus on the ratio of ${\cal R}(θ_c) \equiv {\cal B}( Ξ_{cc} \to Ξ_c' e^+ ν_e)/ {\cal B}( Ξ_{cc} \to Ξ_c e^+ ν_e) $ and find that $({\cal R}(θ_0),{\cal R}(- θ_0)) =(0.46 \pm 0.01,7.33 \pm 0.23)$ with $θ_0 = 0.137π$, which are in sharp contrast to ${\cal R}(0)=2.15\pm0.11$ without the mixing. The ratio is enhanced~(suppressed) by a factor of four for a negative~(positive) $θ_c$. In addition, the polarization asymmetries of $Ξ_c^{(\prime)}$ are found to be $α(-θ_0) = 0.32 ~(-0.76)$ and $α(θ_0) = -0.82~(-0.38)$. As ${\cal R}$ and $α$ are highly sensitive to $θ_c$ and unaffected by the $W$-exchange contributions, they provide excellent opportunities to determine $θ_c$ in the ongoing experiments.