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

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.