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Twist-3 light-cone distribution amplitudes of the scalar mesons within the QCD sum rules and their application to the $B \to S$ transition form factors

We investigate the twist-3 light-cone distribution amplitudes (LCDAs) of the scalar mesons $a_0$, $K^{\ast}_0$ and $f_0$ within the QCD sum rules. The QCD sum rules are improved by a consistent treatment of the sizable $s$-quark mass effects within the framework of the background field approach. Adopting the valence quark component $(\bar{q}_1 q_2)$ as the dominant structure of the scalar mesons, our estimation for their masses are close to the measured $a_0(1450)$, $K^{\ast}_0(1430)$ and $f_0(1710)$. From the sum rules, we obtain the first two non-zero moments of the twist-3 LCDAs $ϕ^{s,σ}_{a_0}$: $\langle ξ_{s,a_0}^{2(4)} \rangle=0.369 \;(0.245)$ and $\langle ξ_{σ,a_0}^{2(4)} \rangle=0.203 \;(0.093)$; those of the twist-3 LCDAs $ϕ_{K^*_0}^{s,σ}$: $\langle ξ_{s,K^{\ast}_0}^{1(2)} \rangle =0.004\;(0.355)$ and $\langle ξ_{σ,K^{\ast}_0}^{1(2)} \rangle =0.018\;(0.207)$; and those of the twist-3 LCDAs $ϕ_{f_0}^{s,σ}$: $\langle ξ_{s,f_0}^{2(4)} \rangle=0.335 \;(0.212)$ and $\langle ξ_{σ,f_0}^{2(4)} \rangle=0.196 \; (0.088)$, respectively. As an application of those twist-3 LCDAs, we study the $B \to S$ transition form factors by introducing proper chiral currents into the correlator, which is constructed such that the twist-3 LCDAs give dominant contribution and the twist-2 LCDAs make negligible contribution. Our results of the $B \to S$ transition form factors at the large recoil region $q^2 \simeq 0$ are consistent with those obtained in the literature, which inversely shows the present twist-3 LCDAs are acceptable.