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

Abstract

We investigate the direct $CP$ violation in the decay $D^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ incorporating the $a_0^0(980)$-$f_0(980)$ mixing mechanism. The integrated mixing intensities ${\overline{\xi }}_{fa}$ and ${\overline{\xi }}_{af}$ 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 ${\pi }^{+}{\pi }^{-}$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 $\sigma (600)$ 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.

Comments: 13 pages, 4 figures