Study of heavy quark conserving weak decays in the quark model

Within the framework of a constituent quark model, we investigate the heavy quark conserving weak decays of $\Xi_c$ and $\Xi_b$. This process involves elementary transitions of $us\to du$ or $s\to ud \bar u$ with the heavy quark as a spectator, while for the charmed baryon in the initial state it can also occur via $cs\to dc$ to conserve the heavy quark flavor in the weak decays. It shows that the heavy quark symmetry (HQS) plays an essential role in the processes where the heavy quark acts as a spectator. For the $\Xi_c$ decays, the dominance of the pole terms in the parity-conserving transitions is evident. This can naturally explain the sizeable branching ratio for $\Xi_c^0\to\Lambda_c\pi^-$ as recently reported by LHCb. The same mechanism predicts a large branching ratio for $\Xi_c^+\to\Lambda_c\pi^0$. In contrast, the decays of $\Xi_b$ will only go through the parity-violating processes because of the HQS. In addition, the branching ratios of the $\Xi_c^+\to \Lambda_c \pi^0$ and $\Xi_b^0\to \Lambda_b \pi^0$ processes are also predicted for the further experimental measurement.