S wave Kπscattering and effects of κin J/ψ\to {\bar K}^{*0}(892)K^+π^-

Abstract

$Kπ$ $S$ wave scattering is studied using a chiral unitary approach (ChUT) taking into account coupled channels. With the amplitudes derived from the lowest order chiral Lagrangian as the kernel of a set of coupled channel Bathe-Salpeter equations, the $I=1/2$ $S$ wave $Kπ$ scattering phase shifts below 1.2 GeV can be fitted by one parameter, a subtraction constant, and a scalar resonance corresponding to the controversial $κ$ ($K^*_0(800)$) can be generated dynamically. A good description of the $I=3/2$ $S$ wave $Kπ$ scattering phase shifts below 1.2 GeV can also be obtained. An artificial singularity in the conventional cut-off method of the 2-meson loop integral of the ChUT is found. The formalism is applied to deal with the $S$ wave $Kπ$ final state interaction (FSI) in the decay $J/ψ\to {\bar K}^{*0}(892)K^+π^-$, and a qualitatively good fit to the data is achieved. The role of $κ$ in the decay is discussed.