Analytic approach to pion-kaon scattering and strange resonances

We review our analysis of $\pi K$ scattering using forward dispersion relations. The method yields a set of simple parameterizations that are compatible with forward dispersion relations up to 1.6 GeV while still describing the data. Once the partial waves are obtained, we calculate the poles in the complex plane by means of Pad\'e approximants, thus avoiding a particular model for the pole parameterization. The resonances calculated below 1.8 GeV are the much debated scalar $\kappa$-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 $K^*_3(1780)$.