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We study the {\it CP}-averaged branching fractions and the {\it CP}-violatingasymmetries in the pure annihilation decays of $B_s^0 \to a_0^+ a_0^-$ and$B_d^0 \to K_0^{*+} K_0^{*-}$, where $a_0\;[K_0^*]$ denotes the scalar$a_0(980)$ and $a_0(1450)$ [$K_0^*(800) ( {\rm or}\; \kappa)$ and$K_0^*(1430)$], with the perturbative QCD factorization approach under theassumption of two-quark structure for the $a_0$ and $K_0^*$ states. Thenumerical results show that the branching ratios of the $B_d^0 \to K_0^{*+}K_0^{*-}$ decays are in the order of $10^{-6}$, while the decay rates of the$B_s^0 \to a_0^+ a_0^-$ modes are in the order of $10^{-5}$. In light of themeasured modes with the same quark components in the pseudoscalar sector,namely, $B_d^0 \to K^+ K^-$ and $B_s^0 \to \pi^+ \pi^-$, the predictions forthe considered decay modes in this work are expected to be measured at theLarge Hadron Collider beauty and/or Belle-II experiments in the (near) future.Meanwhile, it is of great interest to find that the twist-3 distributionamplitudes $\phi^{S}$ and $\phi^{T}$ with inclusion of the Gegenbauerpolynomials for the scalar $a_0(1450)$ and $K_0^*(1430)$ states in scenario 2contribute slightly to the branching ratios while significantly to the {\it CP}violations in the $B_d^0 \to {K_0^*}(1430)^+ {K_0^*}(1430)^-$ and $B_s^0 \toa_0(1450)^+ a_0(1450)^-$ decays, which indicates that, compared to theasymptotic $\phi^S$ and $\phi^T$, these Gegenbauer polynomials could change thestrong phases evidently in these pure annihilation decay channels. Thesepredictions await for the future confirmation experimentally, which couldfurther provide useful information to help explore the inner structure of thescalars and shed light on the annihilation decay mechanism.

Pure annihilation decays of $B_s^0 \to a_0^+ a_0^-$ and $B_d^0 \to K_0^{*+} K_0^{*-}$ in the PQCD approach

Pure annihilation decays of $B_s^0 \to a_0^+ a_0^-$ and $B_d^0 \to K_0^{+} K_0^{-}$ in the PQCD approach