Two-body hadronic weak decays of antitriplet charmed baryons

Abstract

We study Cabibbo-favored (CF) and singly Cabibbo-suppressed (SCS) two-body hadronic weak decays of the antitriplet charmed baryons ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}$, and ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}$ with more focus on the last two. Both factorizable and nonfactorizable contributions are considered in the topologic diagram approach. The estimation of nonfactorizable contributions from $W$-exchange and inner $W$-emission diagrams relies on the pole model and current algebra. The nonperturbative parameters in both factorizable and nonfactorizable parts are calculated in the MIT bag model. Branching fractions and up-down decay asymmetries for all the CF and SCS decays of antitriplet charmed baryons are presented. The prediction of $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{c}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{0}{\ensuremath{\pi}}^{+})$ agrees well with the measurements inferred from Belle and CLEO, while the calculated $\mathcal{B}({\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})$ is too large compared to the recent Belle measurement. We conclude that these two ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Xi}}{\ensuremath{\pi}}^{+}$ modes cannot be simultaneously explained within the current-algebra framework for $S$-wave amplitudes. This issue needs to be resolved in future study. The long-standing puzzle with the branching fraction and decay asymmetry of ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}^{0}{K}^{+}$ is resolved by noting that only the type-II $W$-exchange diagram contributes to this mode. We find that not only does the calculated rate agree with experiment but also the predicted decay asymmetry is consistent with the SU(3)-flavor symmetry approach in sign and magnitude. Likewise, the CF mode ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{+}{K}^{\ensuremath{-}}$ and the SCS decays ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}$, ${\mathrm{\ensuremath{\Sigma}}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ proceed only through type-II $W$ exchange. They are predicted to have large and positive decay asymmetries. These features can be tested in the near future.