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 $\phi^{s,\sigma}_{a_0}$:
$\langle \xi_{s,a_0}^{2(4)} \rangle=0.369 \;(0.245)$ and $\langle
\xi_{\sigma,a_0}^{2(4)} \rangle=0.203 \;(0.093)$; those of the twist-3 LCDAs
$\phi_{K^*_0}^{s,\sigma}$: $\langle \xi_{s,K^{\ast}_0}^{1(2)} \rangle
=0.004\;(0.355)$ 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 $B \to S$ 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.Comment: 14 pages, 12 figures, 7 table