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 $Ξ_Q\toΛ_Qπ$ and $Ω_Q\toΞ_Qπ$ 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 ${\cal B}_{\bar 3}\to {\cal B}_{\bar 3}+π$ with ${\cal B}_{\bar 3}$ being an antitriplet heavy baryon will vanish in the heavy quark limit. Indeed, this is the case for $Ξ_b\toΛ_b π$ decays. For $Ξ_c\toΛ_cπ$ 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 $Ξ_c\toΛ_cπ$ 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 $Ξ_c\toΛ_cπ$ 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 $Ξ_c\toΛ_cπ$ decays are indeed dominated by the parity-conserving transition induced from nonspectator $W$-exchange and that they receive largest contributions from the intermediate $Σ_c$ pole terms. We also show that the $S$-wave of $Ω_b\to Ξ_b π$ decays vanishes in the heavy quark limit, while $Ω_c\to Ξ_cπ$ receive additional $W$-exchange contributions via $cs\to dc$ transition.

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