Direct CP violation in multi-body $B$ decays with the $a_0^0(980)$--$f_0(980)$ mixing

Abstract

We predict that the $a_0^0(980)$-$f_0(980)$ mixing would lead to large CP violation. We calculate the localized direct CP asymmetry in the decays $B^{\pm }\to f_0(980)[a_0^0(980)]{\pi }^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ via the $a_0^0(980)$-$f_0(980)$ mixing mechanism based on the hypothetical $q\bar{q}$ structures of $a_0^0(980)$ and $f_0(980)$ in the QCD factorization. It is shown that there is a peak for CP violation, which could be as large as 58%, when the invariance mass of $\pi \pi$ is near the masses of $a_0^0(980)$ and $f_0(980)$. Since the CP asymmetry is sensitive to the $a_0^0(980)$-$f_0(980)$ mixing, measuring the CP violating parameter in the aforementioned decays could provide a new way to verify the existence of the $a_0^0(980)$-$f_0(980)$ mixing and be helpful in clarifying the configuration nature of the light scalar mesons.

Comments: 12 pages, 2 figures; accepted by Phys. Rev. D