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Home > Physical Review D (APS) > Direct <math><mi>C</mi><mi>P</mi></math> violation in multi-body <math><mi>B</mi></math> decays with <math><msubsup><mi>a</mi><mn>0</mn><mn>0</mn></msubsup><mo>(</mo><mn>980</mn><mo>)</mo><mo>−</mo><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>980</mn><mo>)</mo></math> mixing |

Wang, Chao (Center for Ecological and Environmental Sciences, Key Laboratory for Space Bioscience & Biotechnology, Northwestern Polytechnical University, Xi’an 710072, China) ; Wang, Rui-Wu (Center for Ecological and Environmental Sciences, Key Laboratory for Space Bioscience & Biotechnology, Northwestern Polytechnical University, Xi’an 710072, China) ; Kang, Xian-Wei (College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China) ; Guo, Xin-Heng (College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China)

16 April 2019

**Abstract: **We predict that ${a}_{0}^{0}\left(980\right)-{f}_{0}\left(980\right)$ mixing would lead to large $CP$ violation. We calculate the localized direct $CP$ asymmetry in the decays ${B}^{\pm}\to {f}_{0}\left(980\right)\left[{a}_{0}^{0}\right(980\left)\right]{\pi}^{\pm}\to {\pi}^{+}{\pi}^{-}{\pi}^{\pm}$ via the ${a}_{0}^{0}\left(980\right)-{f}_{0}\left(980\right)$ mixing mechanism based on the hypothetical $q\overline{q}$ structures of ${a}_{0}^{0}\left(980\right)$ and ${f}_{0}\left(980\right)$ in the QCD factorization approach. It is shown that there is a peak for $CP$ violation, which could be as large as 58%, when the invariant mass of $\pi \pi $ is near the masses of ${a}_{0}^{0}\left(980\right)$ and ${f}_{0}\left(980\right)$. Since the $CP$ asymmetry is sensitive to ${a}_{0}^{0}\left(980\right)-{f}_{0}\left(980\right)$ mixing, measuring the $CP$-violating parameter in the aforementioned decays could provide a new way to verify the existence of ${a}_{0}^{0}\left(980\right)-{f}_{0}\left(980\right)$ mixing and be helpful in clarifying the configuration of the light scalar mesons.

**Published in: ****Physical Review D 99 (2019)**
**Published by: **APS

**DOI: **10.1103/PhysRevD.99.074017

**License: **CC-BY-4.0