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) Regge trajectory, finding the ordinary almost real and linear behavior, typical of q bar{q} resonances. In contrast, for the 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) or sigma 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.
Highlights
The Regge trajectory of an elastic resonance can be calculated from dispersion theory, instead of fitted phenomenologically, using only its pole parameters as input
Let us remark that, due to the analytic properties of amplitudes in the complex plane, in certain cases Regge trajectories can be calculated from the properties of just one resonance [1,2], instead of fitted to several resonances assuming that a straight line should describe them
Regge trajectories and residues [3,4,5,6,7] and is more fundamental and predictive than a pure straight line fit. It does not assume a priori a particular functional form for the trajectories. It includes a consistent treatment of resonance widths, which are usually neglected in the usual phenomenological fits of Regge trajectories
Summary
Let us remark that, due to the analytic properties of amplitudes in the complex plane, in certain cases Regge trajectories can be calculated from the properties of just one resonance [1,2], instead of fitted to several resonances assuming that a straight line should describe them. 3.2 we show that the controversial κ or K ∗(800) meson results in a non-ordinary trajectory, whose imaginary part is larger than the real part, which is not linear and whose slope is much smaller than the universal slope of ordinary trajectories This is a new piece of evidence supporting the non-quark–antiquark nature of this state (tetraquark, meson–meson “molecule”, different admixtures of these, etc.) which has been suggested from many other approaches [13,14,15,16,17,18,19,20,21,22].
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