A model-independent partial-wave analysis of the $S$-wave component of the $K\pi$ system from decays of $D^{+}$ mesons to the three-body $K^{-}{\pi }^{+}{\pi }^{+}$ final state is described. Data come from the Fermilab E791 experiment. Amplitude measurements are made independently for ranges of $K^{-}{\pi }^{+}$ invariant mass, and results are obtained below $825\mathrm{MeV}/c^2$, where previous measurements exist only in two mass bins. This method of parametrizing a three-body decay amplitude represents a new approach to analyzing such decays. Though no model is required for the $S$-wave, a parametrization of the relatively well-known reference $P$- and $D$-waves, optimized to describe the data used, is required. In this paper, a Breit-Wigner model is adopted to describe the resonances in these waves. The observed phase variation for the $S$-, $P$-, and $D$-waves do not match existing measurements of $I=\frac{1}{2}$ $K^{-}{\pi }^{+}$ scattering in the invariant mass range in which scattering is predominantly elastic. If the data are mostly $I=\frac{1}{2}$, this observation indicates that the Watson theorem, which requires these phases to have the same dependence on invariant mass, may not apply to these decays without allowing for some interaction with the other pion. The production rate of $K^{-}{\pi }^{+}$ from these decays, if assumed to be predominantly $I=\frac{1}{2}$, is also found to have a significant dependence on invariant mass in the region above $1.25\mathrm{GeV}/c^2$. These measurements can provide a relatively model-free basis for future attempts to determine which strange scalar amplitudes contribute to the decays.

• Received 27 July 2005
• Corrected 24 August 2006

DOI:https://doi.org/10.1103/PhysRevD.73.032004