Semileptonic decays of doubly charmed baryons with $\hat{I}{ž}_c-\hat{I}{ž}_c^{\prime }$ mixing

Abstract

We study the $\hat{I}{ž}_c-\hat{I}{ž}_c^{\prime }$ mixing effects in the semileptonic decays the doubly charm baryons of $\hat{I}{ž}_{cc}$. We focus on the ratio of $\mathcal{R}(\hat{I}{¸}_c)\equiv \mathcal{B}(\hat{I}{ž}_{cc}\to \hat{I}{ž}_c^{\prime }{e}^{+}\hat{I}{½}_e)/\mathcal{B}(\hat{I}{ž}_{cc}\to \hat{I}{ž}_c{e}^{+}\hat{I}{½}_e)$ and find that $(\mathcal{R}(\hat{I}{¸}_0),\mathcal{R}(-\hat{I}{¸}_0))=(0.46\pm 0.01,7.33\pm 0.23)$ with $\hat{I}{¸}_0=0.137\ddot{I}€$, which are in sharp contrast to $\mathcal{R}(0)=2.15\pm 0.11$ without the mixing. The ratio is enhanced~(suppressed) by a factor of four for a negative~(positive) $\hat{I}{¸}_c$. In addition, the polarization asymmetries of $\hat{I}{ž}_c^{(\prime )}$ are found to be $\hat{I}\pm (-\hat{I}{¸}_0)=0.32(-0.76)$ and $\hat{I}\pm (\hat{I}{¸}_0)=-0.82(-0.38)$. As $\mathcal{R}$ and $\hat{I}\pm$ are highly sensitive to $\hat{I}{¸}_c$ and unaffected by the $W$-exchange contributions, they provide excellent opportunities to determine $\hat{I}{¸}_c$ in the ongoing experiments.

6 pages, 2 figures