A MODEL FOR THE CHARMED $D_s^{+}$ MESON DECAYS INTO THREE PIONS

Abstract

We propose a phenomenological three component model describing the decay amplitude of the process $D_s^{+}\text{ra}3\pi$. The first component is a constant background, the second one is a Breit-Wigner amplitude associated to a quasi two-body $f_0(980){\pi }^{+}$ state and the third one another Breit-Wigner amplitude corresponding to a possible quasi two-body $\rho (770)\pi$ state. We show that it is possible to reproduce the observed total rate for $D_s^{+}\text{ra}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ as well as the two other measured branching ratios for the non resonant part and the resonant $f_0{\pi }^{+}$ one. Implication of the $\rho {\pi }^{+}$ state, of which an experimental limit has been given, is discussed. An upper bound in the 10 MeV range for the decay constant $f_{{\pi }^{\prime }}$ of the $\pi (1300)$ meson is obtained . Predictions are given for the $D_s^{+}\text{ra}{\pi }^0{\pi }^0{\pi }^{+}$ rate as well as for the ${\pi }^{+}$ and ${\pi }^{-}$ (${\pi }^0$ and ${\pi }^{+}$) energy distributions for these two decay modes $D_s^{+}\text{ra}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ ($D_s^{+}\text{ra}{\pi }^0{\pi }^0{\pi }^{+}$) respectively.

Comments: 23 pages + 8 pages (attached Postscript file of 9 figures), Latex