Weak decays of $B_c$ into two hadrons under flavor SU(3) symmetry

A large number of $B_c$ meson events have been recorded at the LHCb detector, especially some two-body hadronic decay modes. We analyzed the weak decays of the $B_c$ meson into two hadron states under the flavor SU(3) symmetry. The relations among amplitudes of $B_c$ into $D+P(V)$, $B+P(V)$, $P(V)+P(V)$, $T_8+{\bar{T}}_8$ and $T_{10}+{\bar{T}}_{10}$ were investigated systematically, where $P$ ( $V$) denotes a light pseudoscalar (vector) meson and $T_{8,10}$ denotes a light baryon. The $\eta -{\eta }^{\mathrm{\prime }}$ mixing and $\omega -\varphi$ mixing effects are also considered for the phenomenological discussions. We obtained the relations among decay widths of different $B_c$ decay channels. These results are helpful to study the two-body decay properties of the $B_c$ meson and test the flavor SU(3) symmetry.