Direct $CP$ violation in $D^\pm \to π^\pm π^+ π^-$ with $a_0^0(980)-f_0(980)$ mixing

Abstract

We investigate the direct $CP$ violation in the decay $D^\pm \to π^\pm π^+ π^-$ incorporating the $a_0^0(980)$-$f_0(980)$ mixing mechanism. The integrated mixing intensities $\overline ξ_{fa}$ and $\overline ξ_{af}$ are calculated using meson masses and coupling constants extracted from various theoretical models and experimental data, yielding values of appreciable magnitude. We find that when the invariant mass of the $π^+π^-$pair lies near the $f_0(980)$ resonance, this isospin breaking mechanism can enhance the $CP$ asymmetry. The enhancement is particularly pronounced when $f_0(980)$ carries a significant $n\bar{n}$ quark component and the $f_0(980)$ and $σ(600)$ mixing angle is approximately $26^\circ$. It is emphasized that the $a_0^0(980)$-$f_0(980)$ mixing mechanism can be taken into account in both theoretical and experimental studies of $CP$ violation in $B$ or $D$ meson decays.

Figures (3)

• Figure 1: The Feynman diagram for $X\to Y f_0(980) \to Y a_0^0(980) \to Y \pi^{0}\eta$ (left) and $X\to Y f_0(980) \to Y \pi\pi$ (right) Wu:2008hx.
• Figure 2: The Feynman diagram for $X \to Y a_0^0(980) \to Y f_0(980) \to Y \pi\pi$ (left) and $X \to Y a_0^0(980) \to Y \pi^{0}\eta$ (right).
• Figure 3: The differential $CP$-violating asymmetry as a function of $\sqrt{s}$ in the decay $D^\pm \rightarrow f_0(980)[a_0^0(980)]\pi^\pm \rightarrow \pi^+\pi^-\pi^\pm$.