A Model for the decay of the $D_s^{+}$ meson into three pions,

Abstract

We propose a phenomenological two component model describing the decay amplitude of the process $D_s^{+} \ra 3 π$, 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 $f_0(980)$ $π^{+}$ state. We show that it is possible to reproduce the observed rate for $D_s^{+} \ra π^{+}π^{+}π^{-}$ as well as the two other measured branching ratios for the non resonant part and the resonant $f_0π^{+}$ one, with a common parameter $F_{NR}$. Predictions are given for the $D_s^{+} \ra π^{0}π^{0}π^{+}$ rates, as well as for the various $π^{+}$ and $π^{-}$, or $π^{0}$ and $π^{+}$ energy distributions for the two possible final states.