Two-body hadronic weak decays of antitriplet charmed baryons

TL;DR

This paper analyzes two-body hadronic weak decays of antitriplet charmed baryons using a topological diagram approach, incorporating factorizable and nonfactorizable effects, and compares predictions with experimental data to resolve existing puzzles.

Contribution

It provides a comprehensive calculation of branching fractions and decay asymmetries for CF and SCS decays, highlighting the role of W-exchange diagrams and addressing previous discrepancies.

Findings

Predicted branching fraction for $ o o o$ agrees with Belle and CLEO.

Calculated rate for $ o o$ is larger than Belle measurement.

Certain decay modes are explained by type-II W-exchange contributions.

Abstract

We study Cabibbo-favored (CF) and singly Cabibbo-suppressed (SCS) two-body hadronic weak decays of the antitriplet charmed baryons $\Lambda_c^+$, $\Xi_c^0$ and $\Xi_c^+$ 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 non-perturbative 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 $\mathcal{B}(\Xi_c^+\to \Xi^0\pi^+ )$ agrees well with the measurements inferred from Belle and CLEO, while the calculated ${\cal B}(\Xi_c^0\to \Xi^-\pi^+)$ is too large compared to the recent Belle measurement. We conclude that these two $\Xi_c\to\Xi \pi^+$ 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 $\Lambda_c^+\to\Xi^0 K^+$ is resolved by noting that only type-II $W$-exchange diagram will contribute to this mode. We find that not only the calculated rate agrees 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 $\Xi_c^0\to \Sigma^+K^-$ and the SCS decays $\Xi_c^0\to pK^-,\Sigma^+\pi^-$ proceed only through type-II $W$-exchange. They are predicted to have large and {\it positive} decay asymmetries. These features can be tested in the near future.