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The quadratic scalar radius of the pion and the mixed $π-K$ radius

We consider the quadratic scalar radius of the pion, $<r^2_{{\rm S},π}>$, and the mixed $K-π$ scalar radius, $<r^2_{{\rm S},Kπ}>$. With respect to the second, we point out that the more recent (post-1974) experimental results in $K_{l3}$ decays imply a value, $<r^2_{{\rm S},Kπ}>=0.31\pm0.06 {\rm fm}^2$, which is about $2 σ$ above estimates based on chiral perturbation theory. On the other hand, we show that this value of $<r^2_{{\rm S},Kπ}>$ suggests the existence of a low mass S$\tfrac{1}{2}$ $Kπ$ resonance. With respect to $<r^2_{{\rm S},π}>$, we contest the central value and accuracy of current evaluations, that give $<r^2_{{\rm S},π}>=0.61\pm0.04 {\rm fm}^2$. Based on experiment, we find a robust lower bound of $<r^2_{{\rm S},π}>\geq0.70\pm0.06 {\rm fm}^2$ and a reliable estimate, $<r^2_{{\rm S},π}>=0.75\pm0.07 {\rm fm}^2$, where the error bars are attainable. This implies, in particular, that the chiral result for $<r^2_{{\rm S},π}>$ is $1.4 σ$ away from experiment. We also comment on implications about the chiral parameter $\bar{l}_4$, very likely substantially larger (and with larger errors) than usually assumed.