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.

Mapping states with explicit gluonic degrees of freedom in the light sector is a challenge, and has led to controversies in the past. In particular, the experiments have reported two different hybrid candidates with spin-exotic signature, π1(1400) and π1 (1600), which couple separately to ηπ and η π. This picture is not compatible with recent Lattice QCD estimates for hybrid states, nor with most phenomenological models. We consider the recent partial wave analysis of the η ( ) π system by the COMPASS collaboration. We fit the extracted intensities and phases with a coupled-channel amplitude that enforces the unitarity and analyticity of the S-matrix. We provide a robust extraction of a single exotic π1 resonant pole, with mass and width 1564 ± 24 ± 86 MeV and 492 ± 54 ± 102 MeV, which couples to both η ( ) π channels. We find no evidence for a second exotic state. We also provide the resonance parameters of the a2(1320) and a 2 (1700).

In this work we present a determination of the mass, width, and coupling of the resonances that appear in kaon-pion scattering below 1.8 GeV. These are: the much debated scalar κ-meson, nowadays known as K * 0 (800), the scalar K * 0 (1430), the K * (892) and K * 1 (1410) vectors, the spin-two K * 2 (1430) as well as the spin-three K * 3 (1780). The parameters will be determined from the pole associated to each resonance by means of an analytic continuation of the K π scattering amplitudes obtained in a recent and precise data analysis constrained with dispersion relations, which were not well satisfied in previous analyses. This analytic continuation will be performed by means of Padé approximants, thus avoiding a particular model for the pole parameterization. We also pay particular attention to the evaluation of uncertainties.

We provide global parameterizations of scattering S0 and P partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of , both in the real axis up to 1.12 and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 . Above that energy we just describe the available experimental data. Moreover, the analytic continuations of these global parameterizations also describe accurately the dispersive determinations of the , and pole parameters.

In this work we provide a dispersive analysis of ππ → KK scattering. For this purpose we present a set of partial-wave hyperbolic dispersion relations using a family of hyperbolas that maximizes the applicability range of the hyperbolic dispersive representation, which we have extended up to 1.47 GeV. We then use these equations first to test simple fits to different and often conflicting data sets, also showing that some of these data and some popular parameterizations of these waves fail to satisfy the dispersive analysis. Our main result is obtained after imposing these new relations as constraints on the data fits. We thus provide simple and precise parameterizations for the S, P and D waves that describe the experimental data from KK threshold up to 2 GeV, while being consistent with crossing symmetric partialwave dispersion relations up to their maximum applicability range of 1.47 GeV. For the S-wave we have found that two solutions describing two conflicting data sets are possible. The dispersion relations also provide a representation for S, P and D waves in the pseudo-physical region.