πK Scattering in Three Flavour ChPT

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We present the scattering lengths for the πK processes in the three flavour Chiral Perturbation Theory (ChPT) framework at next-to-next-to-leading order (NNLO). The calculation has been performed analytically but we only include analytical results for the dependence on the low-energy constants (LECs) at NNLO due to the size of the expressions. These results, together with resonance estimates of the NNLO LECs are used to obtain constraints on the Zweig rule suppressed LECs at NLO, L₄ʳ and L₆ʳ. Contrary to expectations from NLO order calculations we find them to be compatible with zero. We do a preliminary study of combining the results from ππ scattering, πK scattering and the scalar form-factors and find only a marginal compatibility with all experimental/dispersive input data.