Theoretical analysis of direct $CP$ violation and differential decay width in $D^\pm\to \pi^\pm \pi^+\pi^-$ in phase space around the resonances $\rho^0(770)$ and $f_0(500)$

TL;DR

This paper provides a theoretical analysis of direct $CP$ violation and decay width differences in $D^ o ho^0(770), f_0(500)$ resonant regions, highlighting the role of interference and phase choices.

Contribution

It introduces a theoretical framework considering interference effects and free phase parameters to explain experimental observations of $CP$ violation in charm decays.

Findings

Proper phase choices can reproduce experimental $CP$ violation levels.

Interference between $ ho^0(770)$ and $f_0(500)$ resonances affects decay asymmetries.

The model aligns with observed differential decay widths.

Abstract

We perform a theoretical study on direct $CP$ violation in $D^\pm\to \pi^\pm \pi^+\pi^-$ in phase space around the intermediate states $\rho^0(770)$ and $f_0(500)$. The possible interference between the amplitudes corresponding to the two resonances is taken into account, and the relative strong phase of the two amplitudes is treated as a free parameter. Our analysis shows that by properly chosen the strong phase, both the $CP$ violation strength and differential decay width accommodate to the experimental results.