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

Abstract.

We investigate the twist-3 light-cone distribution amplitudes (LCDAs) of the scalar mesons a₀, $K^{\ast}_{0}$ and f₀ 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 is 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 $\phi^{s,\sigma}_{a_{0}}$ : $\langle \xi_{s,a_0}^{2(4)}\rangle=0.369\;(0.245)$ and $\langle \xi_{\sigma,a_{0}}^{2(4)}\rangle=0.203 \;(0.093)$ ; those of the twist-3 LCDAs $\phi_{K^{\ast}_{0}}^{s,\sigma}$ : $\langle \xi_{s,K^{\ast}_{0}}^{1(2)}\rangle=0.004\;(0.355)$ and $\langle \xi_{\sigma,K^{\ast}_{0}}^{1(2)}\rangle =0.018\;(0.207)$ ; and those of the twist-3 LCDAs $\phi_{f_{0}}^{s,\sigma}$ : $\langle \xi_{s,f_{0}}^{2(4)}\rangle=0.335\;(0.212)$ and $\langle \xi_{\sigma,f_{0}}^{2(4)}\rangle=0.196\;(0.088)$ , respectively. As an application of those twist-3 LCDAs, we study the $B\rightarrow S$ 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 $B\rightarrow S$ 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.