Study ofK+π−scattering in the reactionK+p→K+π−Δ++at12 GeVc

Abstract

We have studied ${K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ elastic scattering in the reaction ${K}^{+}p\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\Delta}}^{++}$ at $12 \frac{\mathrm{GeV}}{c}$ and in the $K\ensuremath{\pi}$ mass interval 800 to 1000 MeV. We have performed a partial-wave analysis in this $K\ensuremath{\pi}$ mass region, dominated by the $p$-wave resonance ${K}^{*}(890)$, in order to obtain information about the $s$-wave amplitude. We have extrapolated the ${K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ moments, the total cross section, and $p$-wave cross section to the pion pole. The $p$-wave cross section is close to the unitarity limit and can be described by a Breit-Wigner resonance form, with parameters $M=896\ifmmode\pm\else\textpm\fi{}2$ MeV and $\ensuremath{\Gamma}=47\ifmmode\pm\else\textpm\fi{}3$ MeV. We then perform an energy-independent phase-shift analysis of the extrapolated moments and total cross section using this Breit-Wigner form for the $p$ wave and a previously determined small negative phase shift for the $I=\frac{3}{2}s$ wave. For the $I=\frac{1}{2}s$-wave phase shift we find the so called down solution, which has a phase shift that rises slowly from 20\ifmmode^\circ\else\textdegree\fi{} at $M(K\ensuremath{\pi})=800$ MeV to 60\ifmmode^\circ\else\textdegree\fi{} at $M(K\ensuremath{\pi})=1000$ MeV. The energy dependence of this phase shift is well described by an effective range form, with a scattering length ${a}_{0}^{1}=\ensuremath{-}0.33\ifmmode\pm\else\textpm\fi{}0.05$ F. The so-called up solution is eliminated or has large ${\ensuremath{\chi}}^{2}$ everywhere except for two overlapping mass intervals at $M(K\ensuremath{\pi})=890 \mathrm{and} 900$ MeV. However, due to limited statistics, we expect two solutions for the $s$ wave very near the mass where the $p$ wave is resonant. We then perform an energy-dependent partial-wave analysis and find again no evidence for an $s$-wave resonance although, due to limited statistics, we could not exclude one at 890 MeV with $\ensuremath{\Gamma}l7$ MeV.