From topological amplitudes to rescattering dynamics in charmed baryon decays

Charmed baryon decays play an important role in studying the weak and strong interactions. Charmed baryon decays decaying into an octet baryon and a pseudoscalar meson have been studied in the framework of rescattering dynamics at the hadron level and topological amplitudes at the quark level. In this work, we investigate the relation between topological amplitudes and rescattering dynamics in the $B_{c\overline{3}}\to B_8P$ decays. Note that the chiral Lagrangian is constructed using (1,1)-rank octet tensors. The (1,1)-rank amplitudes, which are linear combinations of topological diagrams, are used to match the chiral Lagrangian. Possible meson-meson or meson-baryon coupling configurations are constructed from the (1,1)-rank amplitudes via tensor contractions. The rescattering amplitudes derived from topological amplitudes are consistent with those derived directly from the chiral Lagrangian. Isospin sum rules for all isospin systems in $B_{c\overline{3}}\to B_8P$ decays are checked in terms of $s$- and $t$-channel rescattering amplitudes. Rescattering amplitudes contributing to quark-loop diagrams are found to be comparable to those contributing to tree diagrams, indicating potential observable $CP$ violation in charmed baryon decays. Furthermore, it is found that the K\"orner-Pati-Woo theorem is not consistent with the rescattering dynamics. The proof of the K\"orner-Pati-Woo theorem is questionable when the color changes of quarks arising from gluons are considered. We suggest precisely measuring the branching fraction of the $\Lambda^+_c\to \Sigma^+K^0_S$ mode on Belle (II) to test the K\"orner-Pati-Woo theorem.