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Motivated by the observations of the decays $B^0 \to K_0^{*}(1430)^0f_0(980)$ and $ B^0 \to K_2^{*}(1430)^0 f_0(980)$ from BaBar collaboration, westudy the $B^{0(+)} \to K_{0,2}^{*}(1430)^{0(+)} f_0(980)/\sigma$ decays in theperturbative QCD approach for the first time. In the absence of reliablenonperturbative wave functions we only assume the scalar meson $f_0(980)$ and$\sigma$ are two-quark ground states. In our calculations, these decays are alldominated by the hard-scattering emission and annihilation diagrams, while thefactorizable emission diagrams are forbidden or suppressed heavily by thevector decay constants. Furthermore, the branching fractions are sensitive tothe mixing between $f_0(980)$ and $\sigma$. Comparing our results with theexperimental data, a large mixing angle $\theta$ is favored. Taking$\theta=145^\circ$, the orders of branching fractions of $B \to K_0^{*}(1430)^0\sigma$, $B \to K_{2}^{*}(1430)^0 \sigma$ and $B \to K_{0,2}^{*}(1430)^0f_0(980)$ are predicted to be $10^{-4}$, $10^{-5}$ and $10^{-6}$, respectively,which can be measured in the current experiments such as LHCb and Belle-2. Inaddition, although these decays are penguin dominant, the mixing also leads tolarge direct $CP$ asymmetries in these decays. With the precise data in future,our results could shed light on the inner structure of the scalar mesons andcan be used to determine the mixing angle of the $\sigma-f_0(980)$ system.

Calculation of the $B\to K_{0,2}^*(1430)f_0(980)/\sigma$ decays in the Perturbative QCD Approach