Analytical dispersive parameterization for S-wave $\pi \pi$ and $\pi K$ scattering

In this proceeding, we illustrate the applicability of a new parameterization of the S-wave amplitude on the example of the $\pi \pi \to \pi \pi$ and $\pi K\to \pi K$ lattice data ($m_{\pi }\sim 240$ MeV) from the HadSpec collaboration. The applied parameterization follows from the dispersive representation for the inverse scattering amplitude. The left-hand cut contribution is parametrized by the series in a suitably constructed conformal variable. The crucial input in the analysis is the Adler zero, whose position we extracted from the chiral perturbation theory at next-to-leading order with the uncertainties propagated from the low-energy constants.