Pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV

Abstract

In this work we provide simple and precise parametrizations of the existing πK scattering data from threshold up to 1.6 GeV, which are constrained to satisfy forward dispersion relations as well as three additional threshold sum rules. We also provide phenomenological values of the threshold parameters and of the resonance poles that appear in elastic scattering.

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 )

“…These two features can be seen in both panels of Fig. 1, where we have represented as a dotted line the modulus of the amplitude obtained in a recent reanalysis [29] of scattering data [30,31] constrained to satisfy Forward Dispersion Relations (FDR). The reason for such a behavior can be attributed to the presence of backgrounds, possibly from other resonances.…”

“…In this case the "PFDR-pole" parameters are: Fig. 1 The dotted line, labeled "FDR-data", corresponds to the modulus of the K π scattering partial wave in the scalar-isospin 1/2 channel, obtained from a fit to data constrained with forward dispersion relations [29]. On the left panel, the dashed line is the Breit-Wigner shape obtained using the resonance parameters in the RPP.…”

“…Actually, the parameterizations in [29] do have several poles [26] and describe the data very accurately. However, if one tries to implement a dispersive formalism with more Regge poles, each one has three more functions to determine (Re α, Im α and β), but still just one elastic unitarity condition for the whole partial wave.…”

“…This sequence is calculated from the values of the amplitude and its derivatives at an energy point near the resonance. The values of the amplitude are taken from the recent analysis of scattering data [29] constrained with forward dispersion relations. This approach is meant to minimize the model dependence.…”

Calculation of Regge Trajectories of Strange Resonances and Identification of the $K_0^*(800)$ as a Non-ordinary Meson

“…These integral equations allow us to obtain a set of precise scattering lengths. There can be observed [6] how this analysis leads to a set of threshold parameters compatible with the experimental measurements of the DIRAC Collaboration [7].…”