Nonleptonic three-body charmed baryon weak decays with H(15)

We study the nonleptonic three-body charmed baryon weak decays of $\mathbf{B}_{c}\rightarrow\mathbf{B}_{n}PP^{\prime}$ under the $SU(3)_{F}$ flavor symmetry, where $\mathbf{B}_{c}$ denotes the anti-triplet charmed baryon, comprising $(\Xi^{0}_{c},-\Xi^{+}_{c},\Lambda^{+}_{c})$, and $\mathbf{B}_{n}$ and $P(P^{\prime})$ represent octet baryon and pseudoscalar meson states, respectively. In addition to 12 parameters from the contributions of the color-antisymmetric part of the effective Hamiltonian, denoted as $H(\bar{\mathbf{6}})$, there are 4 parameters from the color-symmetric one, $H(\mathbf{15})$, which were not included in the previous study. With 16 parameters in total and 28 experimental data points, we obtain the minimal $\chi^2$ over degree of freedom of $\chi^{2}/d.o.f=1.5$, which is a great improvement comparing to that without $H(\mathbf{15})$. With the better fitting values, we evaluate the branching ratios and up-down asymmetries of $\mathbf{B}_{c}\rightarrow\mathbf{B}_{n}PP^{\prime}$, which present some interesting results such as $\mathcal{B}\,(\Lambda^{+}_{c}\rightarrow(\Xi(1690)^{0}\rightarrow\Sigma^{+}K^{-})\,K^{+})\equiv(1.5\pm0.4)\times10^{-3}$ and potential $SU(3)$ breaking effects in $\Xi^{+}_{c}\rightarrow p\pi^{+}K^{-}$ and $\Lambda^{+}_{c}\rightarrow \Sigma^{+}\pi^{-}K^{+}$ to be verified by the experiments at BESIII, Belle-II and LHCb.