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

Abstract

We study the nonleptonic three-body charmed baryon weak decays of ${\mathbf{B}}_c\to {\mathbf{B}}_{n}P{P}^{\prime }$ under the $SU(3{)}_F$ flavor symmetry, where ${\mathbf{B}}_c$ denotes the anti-triplet charmed baryon, comprising $({\Xi }_c^0,-{\Xi }_c^{+},{\Lambda }_c^{+})$, 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 $H(\bar{6})$, there are 4 parameters from the color-symmetric one, $H(15)$, 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 $H(15)$. With the better fitting values, we evaluate the branching ratios and up-down asymmetries of ${\mathbf{B}}_c\to {\mathbf{B}}_{n}P{P}^{\prime }$, which present some interesting results such as $\mathcal{B}({\Lambda }_c^{+}\to (\Xi (1690{)}^0\to {\Sigma }^{+}{K}^{-})K^{+})\equiv (1.5\pm 0.4)\times 10^{-3}$ and potential $SU(3)$ breaking effects in ${\Xi }_c^{+}\to p{\pi }^{+}{K}^{-}$ and ${\Lambda }_c^{+}\to {\Sigma }^{+}{\pi }^{-}{K}^{+}$ to be verified by the experiments at BESIII, Belle-II and LHCb.

Comments: 21 pages, 2 figures,14 tables