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 ${\mathrm{\Xi }}_Q\to {\mathrm{\Lambda }}_Q\pi$ and ${\mathrm{\Omega }}_Q\to {\mathrm{\Xi }}_Q\pi$ 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 ${\mathcal{B}}_{\overline{3}}\to {\mathcal{B}}_{\overline{3}}+\pi$, with ${\mathcal{B}}_{\overline{3}}$ being an antitriplet heavy baryon, will vanish in the heavy quark limit. Indeed, this is the case for ${\mathrm{\Xi }}_b\to {\mathrm{\Lambda }}_b\pi$ decays. For ${\mathrm{\Xi }}_c\to {\mathrm{\Lambda }}_c\pi$ 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 ${\mathrm{\Xi }}_c\to {\mathrm{\Lambda }}_c\pi$ 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 ${\mathrm{\Xi }}_c\to {\mathrm{\Lambda }}_c\pi$ 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 ${\mathrm{\Xi }}_c\to {\mathrm{\Lambda }}_c\pi$ decays are indeed dominated by the parity-conserving transition induced from nonspectator $W$-exchange and that they receive largest contributions from the intermediate ${\mathrm{\Sigma }}_c$ pole terms. We also show that the $S$-wave of ${\mathrm{\Omega }}_b\to {\mathrm{\Xi }}_b\pi$ decays vanishes in the heavy quark limit, while ${\mathrm{\Omega }}_c\to {\mathrm{\Xi }}_c\pi$ receive additional $W$-exchange contributions via $cs\to dc$ transition. The $P$-wave contribution to ${\mathrm{\Omega }}_c\to {\mathrm{\Xi }}_c\pi$ is enhanced by the ${{\mathrm{\Xi }}^{\prime }}_c$ pole, though it is not so dramatic as in the case of ${\mathrm{\Xi }}_c\to {\mathrm{\Lambda }}_c\pi$. The asymmetry parameter $\alpha$ is found to be positive, of order 0.70 and 0.74 for ${\mathrm{\Xi }}_c^0\to {\mathrm{\Lambda }}_c^{+}{\pi }^{-}$ and ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Lambda }}_c^{+}{\pi }^0$, respectively. The predicted branching fraction is of order $5\times {10}^{-4}$ for ${\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}_c^{+}{\pi }^{-}$ and $3\times {10}^{-4}$ for ${\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}_c^0{\pi }^0$ both with the asymmetry parameter close to $-1$.

Figure 1

The $W$-exchange diagram for the HFC decay ${\mathrm{\Xi }}_b^{-}\to {\mathrm{\Lambda }}_b^0{\pi }^{-}$ and the corresponding pole diagram.

Figure 2

$W$-exchange diagrams for the HFC decay ${\mathrm{\Xi }}_b^0\to {\mathrm{\Lambda }}_b^0{\pi }^0$.

Figure 3

$W$-exchange diagrams for the HFC decay ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Lambda }}_c^{+}{\pi }^0$.

Figure 4

$W$-exchange diagrams for the HFC decay ${\mathrm{\Xi }}_c^0\to {\mathrm{\Lambda }}_c^{+}{\pi }^{-}$.

Figure 5

$W$-exchange diagrams for the HFC decays: (a) ${\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}_c^{+}{\pi }^{-}$ and (b) ${\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}_c^0{\pi }^0$.