The impact of $a_0^0(980)-f_0(980)$ mixing on the localized $CP$ violations of the $B^-\rightarrow K^- \pi^+\pi^-$ decay

TL;DR

This paper investigates how the mixing between $a_0^0(980)$ and $f_0(980)$ affects localized CP violations in the decay $B^- ightarrow K^-\pi^+\pi^-$, showing that the mixing enhances CP violation near the $f_0(980)$ resonance.

Contribution

It introduces the consideration of $a_0^0(980)$-$f_0(980)$ mixing in analyzing CP violation in B meson decays, providing theoretical predictions consistent with experimental data.

Findings

CP violation is enhanced near the $f_0(980)$ resonance due to mixing.

Predicted CP asymmetries range from 0.24 to 0.52.

Branching fraction results align with experimental measurements.

Abstract

In the framework of the QCD factorization approach, we study the localized $CP$ violations of the $B^-\rightarrow K^- \pi^+\pi^-$ decay with and without $a_0^0(980)-f_0(980)$ mixing mechanism, respectively, and find that the localized $CP$ violation can be enhanced by this mixing effect when the mass of the $\pi^+\pi^-$ pair is in the vicinity of the $f_0(980)$ resonance. The corresponding theoretical prediction results are $\mathcal{A}_{CP}(B^-\rightarrow K f_0 \rightarrow K^-\pi^+\pi^-)=[0.24, 0.36]$ and $\mathcal{A}_{CP}(B^-\rightarrow K^- f_0(a_0) \rightarrow K^-\pi^+\pi^-)=[0.33, 0.52]$, respectively. Meanwhile, we also calculate the branching fraction of the $B^-\rightarrow K^-f_0(980)\rightarrow K^-\pi^+\pi^-$ decay, which is consistent with the experimental results. We suggest that $a_0^0(980)-f_0(980)$ mixing mechanism should be considered when studying the $CP$ violation of the $B$ or $D$ mesons decays theoretically and experimentally.