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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→SB \to S transition form factors

Abstract

We investigate the twist-3 light-cone distribution amplitudes (LCDAs) of the scalar mesons a0a_0, K0βˆ—K^{\ast}_0 and f0f_0 within the QCD sum rules. The QCD sum rules are improved by a consistent treatment of the sizable ss-quark mass effects within the framework of the background field approach. Adopting the valence quark component (qΛ‰1q2)(\bar{q}_1 q_2) as the dominant structure of the scalar mesons, our estimation for their masses are close to the measured a0(1450)a_0(1450), K0βˆ—(1430)K^{\ast}_0(1430) and f0(1710)f_0(1710). From the sum rules, we obtain the first two non-zero moments of the twist-3 LCDAs Ο•a0s,Οƒ\phi^{s,\sigma}_{a_0}: ⟨ξs,a02(4)⟩=0.369β€…β€Š(0.245)\langle \xi_{s,a_0}^{2(4)} \rangle=0.369 \;(0.245) and βŸ¨ΞΎΟƒ,a02(4)⟩=0.203β€…β€Š(0.093)\langle \xi_{\sigma,a_0}^{2(4)} \rangle=0.203 \;(0.093); those of the twist-3 LCDAs Ο•K0βˆ—s,Οƒ\phi_{K^*_0}^{s,\sigma}: ⟨ξs,K0βˆ—1(2)⟩=0.004β€…β€Š(0.355)\langle \xi_{s,K^{\ast}_0}^{1(2)} \rangle =0.004\;(0.355) and βŸ¨ΞΎΟƒ,K0βˆ—1(2)⟩=0.018β€…β€Š(0.207)\langle \xi_{\sigma,K^{\ast}_0}^{1(2)} \rangle =0.018\;(0.207); and those of the twist-3 LCDAs Ο•f0s,Οƒ\phi_{f_0}^{s,\sigma}: ⟨ξs,f02(4)⟩=0.335β€…β€Š(0.212)\langle \xi_{s,f_0}^{2(4)} \rangle=0.335 \;(0.212) and βŸ¨ΞΎΟƒ,f02(4)⟩=0.196β€…β€Š(0.088)\langle \xi_{\sigma,f_0}^{2(4)} \rangle=0.196 \; (0.088), respectively. As an application of those twist-3 LCDAs, we study the Bβ†’SB \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 Bβ†’SB \to S transition form factors at the large recoil region q2≃0q^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

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