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

摘要

We investigate the twist-3 light-cone distribution amplitudes (LCDAs) of the scalar mesons a_0, K_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 (-bar1q2) as the dominant structure of the scalar mesons, our estimation for their masses is close to the measured a_0(1450), K_0~? (1430) and f_0(1710). From the sum rules, we obtain the first two non-zero moments of the twist-3 LCDAs φ_(a_0)~s,σ: 〈ξ_(s,a_0)~(2(4))〉 = 0.369 (0.245) and 〈ξ_(σ,a_0)~(24))〉 = 0.203 (0.093); those of the twist-3 LCDAs φ_(K_0~?)~(s,σ): 〈ξ_(s,K_0~?)~(1(2))〉 = 0.004 (0.355) and 〈ξ_(σ,K_0~?)~(1(2))〉 = 0.018 (0.207); and those of the twist-3 LCDAs φ_(f_0)~(s,σ): 〈ξ_(s,f_0)~(2(4))〉 = 0.335 (0.212) and 〈ξ_(σ,f_0)~(2(4))〉 = 0.196 (0.088), respectively. As an application of those twist-3 LCDAs, we study the B → 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 → S transition form factors at the large recoil region q~2 ? 0 are consistent with those obtained in the literature, which inversely shows the present twist-3 LCDAs are acceptable.