Asymmetries of anti-triplet charmed baryon decays

We analyze the decay processes of ${\mathbf{B}}_c\to {\mathbf{B}}_{n}M$ with the $SU(3{)}_F$ flavor symmetry and spin-dependent amplitudes, where ${\bf B}_c({\bf B}_n)$and$M$ are the anti-triplet charmed (octet) baryon and nonet meson states, respectively. In the $SU(3{)}_F$ approach, it is the first time that the decay rates and up-down asymmetries are fully and systematically studied without neglecting the $\mathcal{O}(\overline{15})$ contributions of the color anti-symmetric parts in the effective Hamiltonian. Our results of the up-down asymmetries based on $SU(3{)}_F$ are quite different from the previous theoretical values in the literature. In particular, we find that the up-down symmetry of $\alpha ({\mathrm{\Lambda }}_c^{+}\to {\mathrm{\Xi }}^0{K}^{+}{)}_{SU(3)}=0.94_{-0.11}^{+0.06}$, which is consistent with the recent experimental data of $0.77\pm 0.78$ by the BESIII Collaboration, but predicted to be zero in the literature. We also examine the $K_S^0-K_L^0$ asymmetries between the decays of ${\bf B}_c \to {\bf B}_n K_S^0$and${\bf B}_c \to {\bf B}_n K_L^0$ with both Cabibbo-allowed and doubly Cabibbo-suppressed transitions.