Analysis ofKπScattering from the ReactionK+n→K+π−p

We have analyzed $K^{+}{\pi }^{-}$ elastic scattering in the reaction $K^{+}n\to K^{+}{\pi }^{-}p$ at 12 $\frac{\mathrm{GeV}}{c}$. We have extrapolated to the pion pole in order to obtain the on-mass-shell $K^{+}{\pi }^{-}$ elastic-scattering cross section and angular distributions as functions of $K\pi$ mass in the range from threshold to 2 GeV. Using a simple model of $K\pi$ elastic scattering we have determined solutions of the $I=\frac{1}{2}$ $S$-wave phase shift for $M\left(K\pi \right)<\mathrm{}1.7\mathrm{}$ GeV. We find that the $I=\frac{1}{2}$ $S$-wave amplitude performs at least one complete loop in the Argand plot ("down" solution). In addition, if one chooses the appropriate "up" solutions, two rapidly varying loops at $M\left(K\pi \right)$ near the $K^{*}\mathrm{}\left(890\right)\mathrm{}$ and $K^{*}\mathrm{}\left(1420\right)\mathrm{}$, respectively, are also allowed by our data.