Study of two-body doubly charmful baryonic $B$ decays with $SU(3)$ flavor symmetry

Within the framework of $SU(3)$ flavor symmetry, we investigate two-body doubly charmful baryonic $B\to {\mathbf{B}}_c{\bar{\mathbf{B}}}_c^{\mathrm{\prime }}$ decays, where ${\mathbf{B}}_c{\bar{\mathbf{B}}}_c^{\mathrm{\prime }}$ represents the anti-triplet charmed dibaryon. We determine the $SU(3{)}_f$ amplitudes and calculate $\mathcal{B}(B^{-}\to {\mathrm{\Xi }}_c^0{\bar{\mathrm{\Xi }}}_c^{-})=(3.4_{-0.9}^{+1.0})\times {10}^{-5}$ and $\mathcal{B}({\bar{B}}_s^0\to {\mathrm{\Lambda }}_c^{+}{\bar{\mathrm{\Xi }}}_c^{-})=(3.9_{-1.0}^{+1.2})\times {10}^{-5}$ induced by the single $W$-emission configuration. We find that the $W$-exchange amplitude, previously neglected in studies, needs to be taken into account. It can cause a destructive interfering effect with the $W$-emission amplitude, alleviating the significant discrepancy between the theoretical estimation and experimental data for $\mathcal{B}({\bar{B}}^0\to {\mathrm{\Lambda }}_c^{+}{\bar{\mathrm{\Lambda }}}_c^{-})$. To test other interfering decay channels, we calculate $\mathcal{B}({\bar{B}}_s^0\to {\mathrm{\Xi }}_c^{0(+)}{\bar{\mathrm{\Xi }}}_c^{0(+)})=(3.0_{-1.1}^{+1.4})\times {10}^{-4}$ and $\mathcal{B}({\bar{B}}^0\to {\mathrm{\Xi }}_c^0{\bar{\mathrm{\Xi }}}_c^0)=(1.5_{-0.6}^{+0.7})\times {10}^{-5}$. We estimate non-zero branching fractions for the pure $W$-exchange decay channels, specifically $\mathcal{B}({\bar{B}}_s^0\to {\mathrm{\Lambda }}_c^{+}{\bar{\mathrm{\Lambda }}}_c^{-})=(8.1_{-1.5}^{+1.7})\times {10}^{-5}$ and $\mathcal{B}({\bar{B}}^0\to {\mathrm{\Xi }}_c^{+}{\bar{\mathrm{\Xi }}}_c^{-})=(3.0\pm 0.6)\times {10}^{-6}$. Additionally, we predict $\mathcal{B}(B_c^{+}\to {\mathrm{\Xi }}_c^{+}{\bar{\mathrm{\Xi }}}_c^0)=(2.8_{-0.7}^{+0.9})\times {10}^{-4}$ and $\mathcal{B}(B_c^{+}\to {\mathrm{\Lambda }}_c^{+}{\bar{\mathrm{\Xi }}}_c^0)=(1.6_{-0.4}^{+0.5})\times {10}^{-5}$, which are accessible to experimental facilities such as LHCb.