Two-body weak decays of doubly charmed baryons

Abstract

The hadronic two-body weak decays of the doubly charmed baryons ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++},{\mathrm{\ensuremath{\Xi}}}_{cc}^{+}$, and ${\mathrm{\ensuremath{\Omega}}}_{cc}^{+}$ are studied in this work. To estimate the nonfactorizable contributions, we work in the pole model for the $P$-wave amplitudes and current algebra for $S$-wave ones. For the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}{\ensuremath{\pi}}^{+}$ mode, we find a large destructive interference between factorizable and nonfactorizable contributions for both $S$- and $P$-wave amplitudes. Our prediction of $\ensuremath{\sim}0.70%$ for its branching fraction is smaller than the earlier estimates in which nonfactorizable effects were not considered, but agrees nicely with the result based on an entirely different approach, namely, the covariant confined quark model. On the contrary, a large constructive interference was found in the $P$-wave amplitude by Dhir and Sharma, leading to a branching fraction of order (7--16)%. Using the current results for the absolute branching fractions of $({\mathrm{\ensuremath{\Lambda}}}_{c}^{+},{\mathrm{\ensuremath{\Xi}}}_{c}^{+})\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ and the LHCb measurement of ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}{\ensuremath{\pi}}^{+}$ relative to ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}$, we obtain $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}{\ensuremath{\pi}}^{+}{)}_{\text{expt}}\ensuremath{\approx}(1.83\ifmmode\pm\else\textpm\fi{}1.01)%$ after employing the latest prediction of $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}_{c}^{++}{\overline{K}}^{*0})$. Our prediction of $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}{\ensuremath{\pi}}^{+})\ensuremath{\approx}0.7%$ is thus consistent with the experimental value but in the lower end. It is important to pin down the branching fraction of this mode in future study. Factorizable and nonfactorizable $S$-wave amplitudes interfere constructively in ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\ensuremath{\pi}}^{+}$. Its large branching fraction of order 4% may enable experimentalists to search for the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}$ through this mode. That is, the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}$ is reconstructed through the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\ensuremath{\pi}}^{+}$ followed by the decay chain ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$. Besides ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\ensuremath{\pi}}^{+}$, the ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}({\ensuremath{\pi}}^{0},\ensuremath{\eta})$ modes also receive large nonfactorizable contributions to their $S$-wave amplitudes. Hence, they have large branching fractions among ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathcal{B}}_{c}+P$ channels. Nonfactorizable amplitudes in ${\mathrm{\ensuremath{\Xi}}}_{cc}^{++}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}{\ensuremath{\pi}}^{+}$ and ${\mathrm{\ensuremath{\Omega}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}{\overline{K}}^{0}$ are very small compared to the factorizable ones owing to the Pati-Woo theorem for the inner $W$-emission amplitude. Likewise, nonfactorizable $S$-wave amplitudes in ${\mathrm{\ensuremath{\Xi}}}_{cc}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}({\ensuremath{\pi}}^{0},\ensuremath{\eta})$ decays are also suppressed by the same mechanism.