A Phenomenological Analysis of Non-resonant Charm Meson Decays

We analyse the consequences of the usual assumption of a constant function to fit non-resonant decays from experimental Dalitz plot describing charmed meson decays. We first show, using the $D^+\to \bar{K}^0\pi^+\pi^0$ decay channel as an example, how an inadequate extraction of the non-resonant contribution could yield incorrect measurements for the resonant channels. We analyse how the correct study of this decay will provide a test for the validity of factorization in D meson decays. Finally, we show how form factors could be extracted from non-resonant decays. We particularly discuss about the form factor that can be measured from the $D^+_s\to \pi^-\pi^+\pi^+$ decay. We emphasize on its relevance for the study of the decay $\tau \to \nu_{\tau} 3\pi$ and the extraction of the $a_1$ meson width.