Bounds on the slope and the curvature of the scalar K\pi form factor at zero momentum transfer

We derive and calculate unitarity bounds on the slope and curvature of the strangeness-changing scalar form factor at zero momentum transfer, using low-energy constraints and Watson final state interaction theorem. The results indicate that the curvature is important and should not be neglected in the representation of experimental data. The bounds can be converted also into an allowed region for the constants $C\mathrm{\_}{12}^r$ and $C\mathrm{\_}{34}^r$ of Chiral Perturbation Theory. Our results are consistent with, but weaker than the predictions made by Jamin, Oller and Pich in a coupled channel dispersion approach basedon chiral resonance model. We comment on the differences between the two dispersive methods and argue that the unitarity bounds are useful as an independent check involving different sources of information