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

TL;DR

This paper explores how the mixing between scalar mesons $a_0^0(980)$ and $f_0(980)$ can enhance direct $CP$ violation in $D^ ightarrow o ext{pi} ext{pi} ext{pi}$ decays, especially near the $f_0(980)$ resonance.

Contribution

It introduces the $a_0^0(980)$-$f_0(980)$ mixing mechanism into $CP$ violation analysis in $D$ decays and calculates the mixing intensities from theoretical and experimental data.

Findings

Mixing mechanism can significantly enhance $CP$ asymmetry near the $f_0(980)$ resonance.

The enhancement is larger when $f_0(980)$ has a strong $nar{n}$ component.

A mixing angle of approximately 26° maximizes the effect.

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.