Phase Motion of the Scalar $\pi \pi$ Amplitudes in $D^+$, $D^+_s \to \pi^-\pi^+\pi^+$ Decays

TL;DR

This paper presents a direct, model-independent measurement of the phase motion of the scalar $\pi ext{-}\pi$ amplitudes in $D^+$ and $D_s^+$ decays, confirming the presence of the $\sigma(500)$ meson and demonstrating the Amplitude Difference method.

Contribution

It introduces a model-independent approach to measure phase motion in charm decays, confirming the $\sigma(500)$ scalar meson and illustrating the method with $f_0(980)$ analysis.

Findings

Strong phase variation compatible with $\sigma(500)$

Confirmation of previous evidence for scalar meson

Demonstration of the Amplitude Difference method

Abstract

We make a direct and model-independent measurement of the low $\pi^+\pi^-$ mass phase motion in the $D^+ \to \pi^-\pi^+\pi^+$ decay. Our preliminary results show a strong phase variation, compatible with the isoscalar $\sigma(500)$ meson. This result confirms our previous result where we found evidence for the existence of this scalar particle using full Dalitz-plot analysis. We apply the Amplitude Difference (AD) method to the same Fermilab E791 data sample used in the preceding analysis. We also give an example of how we extract the phase motion of the scalar amplitude, looking at the $f_0(980)$ in $D^+_s \to \pi^-\pi^+\pi^+$ decay.