# Direct $CP$ violation in multi-body $B$ decays with ${a}_{0}^{0}\left(980\right)-{f}_{0}\left(980\right)$ 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 ${B}^{±}\to {f}_{0}\left(980\right)\left[{a}_{0}^{0}\left(980\right)\right]{\pi }^{±}\to {\pi }^{+}{\pi }^{-}{\pi }^{±}$ 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)