Abstract
We discuss the existence of the light scalar meson K* 0(800) (also called κ) in a rigorous way, by showing the presence of a pole in the πK→πK amplitude on the second Riemann sheet. For this purpose, we study the domain of validity of two classes of Roy–Steiner representations in the complex energy plane. We prove that one of them is valid in a region sufficiently broad in the imaginary direction. From this representation, we compute the l=0 partial wave in the complex plane neither making any additional approximation nor having model dependence, relying only on experimental data. A scalar resonance with strangeness S=1 is found with the following mass and width: Mκ=658±13 MeV and Γκ=557±24 MeV.
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