Heavy-flavor-conserving hadronic weak decays of charmed and bottom baryons

Abstract

Three decades ago, heavy-flavor-conserving (HFC) weak decays of heavy baryons such as ${\mathrm{\ensuremath{\Xi}}}_{Q}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{Q}\ensuremath{\pi}$ and ${\mathrm{\ensuremath{\Omega}}}_{Q}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{Q}\ensuremath{\pi}$ 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 ${\mathcal{B}}_{\overline{3}}\ensuremath{\rightarrow}{\mathcal{B}}_{\overline{3}}+\ensuremath{\pi}$, with ${\mathcal{B}}_{\overline{3}}$ being an antitriplet heavy baryon, will vanish in the heavy quark limit. Indeed, this is the case for ${\mathrm{\ensuremath{\Xi}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\pi}$ decays. For ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\pi}$ decays, they receive additional nonspectator contributions arising from the $W$-exchange diagrams through the $cs\ensuremath{\rightarrow}dc$ transition. Spectator and nonspectator $W$-exchange contributions to the $S$-wave amplitude of ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\pi}$ 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 ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\pi}$ 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 ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\pi}$ decays are indeed dominated by the parity-conserving transition induced from nonspectator $W$-exchange and that they receive largest contributions from the intermediate ${\mathrm{\ensuremath{\Sigma}}}_{c}$ pole terms. We also show that the $S$-wave of ${\mathrm{\ensuremath{\Omega}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{b}\ensuremath{\pi}$ decays vanishes in the heavy quark limit, while ${\mathrm{\ensuremath{\Omega}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\pi}$ receive additional $W$-exchange contributions via $cs\ensuremath{\rightarrow}dc$ transition. The $P$-wave contribution to ${\mathrm{\ensuremath{\Omega}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\pi}$ is enhanced by the ${{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{'}}}_{c}$ pole, though it is not so dramatic as in the case of ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\pi}$. The asymmetry parameter $\ensuremath{\alpha}$ is found to be positive, of order 0.70 and 0.74 for ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{\ensuremath{\pi}}^{0}$, respectively. The predicted branching fraction is of order $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ for ${\mathrm{\ensuremath{\Omega}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ for ${\mathrm{\ensuremath{\Omega}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\ensuremath{\pi}}^{0}$ both with the asymmetry parameter close to $\ensuremath{-}1$.