Charmed baryon decays in $SU(3)_F$ symmetry

In the recent years, fruitful results on charmed baryons are obtained by BESIII, Belle and LHCb. We investigate the two-body non-leptonic decays of charmed baryons in the flavor $SU(3)$ symmetry. Hundreds of amplitude relations are clearly provided, and are classified according to the $I$-, $U$- and $V$-spin symmetries. Among them, some amplitude relations are tested by the experimental data, or used to predict the branching fractions based on the exact flavor symmetry without any other approximation. Some relations of $K^0_S-K^0_L$ asymmetries and $CP$ asymmetries are obtained under the $U$-spin symmetry in the modes of charmed baryon decaying into neutral kaons. Besides, the $U$-spin breaking effect is explored in the $\Lambda_c^+\to \Sigma^+K^{*0}$ and $\Xi_c^+\to p\bar{K}^{*0}$ modes.