A Model for the decay of the D_s⁺ meson into three pions,

We propose a phenomenological two component model describing the decay amplitude of the process $D_s^{+} \ra 3 \pi$, whose rate has been found surprisingly large. The first component is a constant background $F_{NR}$, and the second one is a Breit-Wigner type amplitude associated to a quasi two body $f_0(980)$ $\pi^{+}$ state. We show that it is possible to reproduce the observed rate for $D_s^{+} \ra \pi^{+}\pi^{+}\pi^{-}$ as well as the two other measured branching ratios for the non resonant part and the resonant $f_0\pi^{+}$ one, with a common parameter $F_{NR}$. Predictions are given for the $D_s^{+} \ra \pi^{0}\pi^{0}\pi^{+}$ rates, as well as for the various $\pi^{+}$ and $\pi^{-}$, or $\pi^{0}$ and $\pi^{+}$ energy distributions for the two possible final states.