Heavy-Flavor-Conserving Hadronic Weak Decays of Charmed and Bottom Baryons

Three decades ago, heavy-flavor-conserving (HFC) weak decays of heavy baryons such as $\Xi_Q\to\Lambda_Q\pi$ and $\Omega_Q\to\Xi_Q\pi$ for $Q=c,b$ had been studied within the framework that incorporates both heavy-quark and chiral symmetries. It was pointed out that if the heavy quark in the HFC process behaves as a spectator, then the $P$-wave amplitude of ${\cal B}_{\bar 3}\to {\cal B}_{\bar 3}+\pi$ with ${\cal B}_{\bar 3}$ being an antitriplet heavy baryon will vanish in the heavy quark limit. Indeed, this is the case for $\Xi_b\to\Lambda_b \pi$ decays. For $\Xi_c\to\Lambda_c\pi$ decays, they receive additional nonspectator contributions arising from the $W$-exchange diagrams through the $cs\to dc$ transition. Spectator and nonspectator $W$-exchange contributions to the $S$-wave amplitude of $\Xi_c\to\Lambda_c\pi$ are destructive, rendering the $S$-wave contribution even smaller. However, the nonspectator effect on the $P$-wave amplitude was overlooked in all the previous model calculations until a very recent investigation within the framework of a constituent quark model in which the parity-conserving pole terms were found to be dominant in $\Xi_c\to\Lambda_c\pi$ decays. Since the pion produced in the HFC process is soft, we apply current algebra to study both $S$- and $P$-wave amplitudes and employ the bag and diquark models to estimate the matrix elements of four-quark operators. We confirm that $\Xi_c\to\Lambda_c\pi$ decays are indeed dominated by the parity-conserving transition induced from nonspectator $W$-exchange and that they receive largest contributions from the intermediate $\Sigma_c$ pole terms. We also show that the $S$-wave of $\Omega_b\to \Xi_b \pi$ decays vanishes in the heavy quark limit, while $\Omega_c\to \Xi_c\pi$ receive additional $W$-exchange contributions via $cs\to dc$ transition.