The non-ordinary Regge behavior of the $$K^*_0(800)$$ K 0 ∗ ( 800 ) or $$\kappa $$ κ -meson versus the ordinary $$K^*_0(1430)$$ K 0 ∗ ( 1430 )

Abstract The Regge trajectory of an elastic resonance can be calculated from dispersion theory, instead of fitted phenomenologically, using only its pole parameters as input. This also provides a correct treatment of resonance widths in Regge trajectories, essential for very wide resonances. In this work we first calculate the $$K^*_0(1430)$$ K 0 ∗ ( 1430 ) Regge trajectory, finding the ordinary almost real and linear behavior, typical of $$q \bar{q}$$ q q ¯ resonances. In contrast, for the $$K^*_0(800)$$ K 0 ∗ ( 800 ) meson, the resulting Regge trajectory is non-linear and has a much smaller slope than ordinary resonances, being remarkably similar to that of the $$f_0(500)$$ f 0 ( 500 ) or $$\sigma $$ σ meson. The slope of these unusual Regge trajectories seems to scale with the meson masses rather than with scales typical of quark degrees of freedom. We also calculate the range of the interaction responsible for the formation of these resonances. Our results strongly support a non-ordinary, predominantly meson–meson-like, interpretation for the lightest strange and non-strange resonances