We study the three-body antitriplet ${\mathbf{B}}_{\mathbf{c}}\to {\mathbf{B}}_{\mathbf{n}}M{M}^{\prime }$ decays with the $SU(3)$ flavor [$SU(3{)}_f$] symmetry, where ${\mathbf{B}}_{\mathbf{c}}$ denotes the charmed baryon antitriplet of $({\mathrm{\Xi }}_c^0,-{\mathrm{\Xi }}_c^{+},{\mathrm{\Lambda }}_c^{+})$, and ${\mathbf{B}}_{\mathbf{n}}$ and $M(M^{\prime })$ represent baryon and meson octets, respectively. By considering only the S-wave $M{M}^{\prime }$-pair contributions without resonance effects, the decays of ${\mathbf{B}}_{\mathbf{c}}\to {\mathbf{B}}_{\mathbf{n}}M{M}^{\prime }$ can be decomposed into irreducible forms with 11 parameters under $SU(3{)}_f$, which are fitted by the 14 existing data, resulting in a reasonable value of ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.=2.8$ for the fit. Consequently, we find that the triangle sum rule of $\mathcal{A}({\mathrm{\Lambda }}_c^{+}\to n{\overline{K}}^0{\pi }^{+})-\mathcal{A}({\mathrm{\Lambda }}_c^{+}\to p{K}^{-}{\pi }^{+})-\sqrt{2}\mathcal{A}({\mathrm{\Lambda }}_c^{+}\to p{\overline{K}}^0{\pi }^0)=0$ given by the isospin symmetry holds under $SU(3{)}_f$, where $\mathcal{A}$ stands for the decay amplitude. In addition, we predict that $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to n{\pi }^{+}{\overline{K}}^0)=(0.9\pm 0.8)\times {10}^{-2}$, which is 3–4 times smaller than the BESIII observation, indicating the existence of the resonant states. For the to-be-observed ${\mathbf{B}}_{\mathbf{c}}\to {\mathbf{B}}_{\mathbf{n}}M{M}^{\prime }$ decays, we compute the branching fractions with the $SU(3{)}_f$ amplitudes to be compared to the BESIII and LHCb measurements in the future.

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• Particle decays
• Particle interactions
• Quark model
• Flavor symmetries