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Light scalar mesons and charmless hadronic $B_c \to SP, SV$ decays in the perturbative QCD approach

In this work, based on the assumption of two-quark structure of the scalars, the charmless hadronic $B_c \to SP, SV$ decays(here, $S$, $P$, and $V$ denote the light scalar, pseudoscalar, and vector mesons, respectively) are investigated by employing the perturbative QCD(pQCD) factorization approach.From our numerical evaluations and phenomenological analysis, we find that (a) the pQCD predictions for the {\it CP}-averaged branching ratios(BRs) of the considered $B_c$ decays vary in the range of $10^{-5}$ to $10^{-8}$, which will be tested in the ongoing LHCb and forthcoming Super-B experiments, while the {\it CP}-violating asymmetries for these modes are absent naturally in the standard model because only one type tree operator is involved; %% (b) analogous to $B \to K^* η^{(\prime)}$ decays, $Br(B_c \to κ^+ η) \sim 5 \times Br(B_c \to κ^+ η^\prime)$ in the pQCD approach, which can be understood by the constructive and destructive interference between the $η_q$ and $η_s$ contributions to the $B_c \to κ^+ η$ and $B_c \to κ^+ η^\prime$ decays, however, $Br(B_c \to K_0^*(1430) η)$ is approximately equal to $Br(B_c \to K_0^*(1430) η')$ in both scenarios because the factorizable contributions from $η_s$ term play the dominant role in the considered two channels; %% (c) if $a_0(980)$ and $κ$ are the $q\bar q$ bound states, the pQCD predicted BRs for $B_c \to a_0(980) (π, ρ)$ and $B_c \to κK^{(*)}$ decays will be in the range of $10^{-6} \sim 10^{-5}$, which are within the reach of the LHCb experiments and could be measured in the near future; and %% (d) for the $a_0(1450)$ and $K_0^*(1430)$ channels, the BRs for $B_c \to a_0(1450) (π, ρ)$ and $B_c \to K_0^*(1430) K^{(*)}$ modes in the pQCD approach are found to be $(5 \sim 47) \times 10^{-6}$ and $(0.7 \sim 36) \times 10^{-6}$, respectively.