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

Abstract

We consider the quadratic scalar radius of the pion, $ $, and the mixed $K-π$ scalar radius, $ $. With respect to the second, we point out that the more recent (post-1974) experimental results in $K_{l3}$ decays imply a value, $ =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 $ $ suggests the existence of a low mass S$\tfrac{1}{2}$ $Kπ$ resonance. With respect to $ $, we contest the central value and accuracy of current evaluations, that give $ =0.61\pm0.04 {\rm fm}^2$. Based on experiment, we find a robust lower bound of $ \geq0.70\pm0.06 {\rm fm}^2$ and a reliable estimate, $ =0.75\pm0.07 {\rm fm}^2$, where the error bars are attainable. This implies, in particular, that the chiral result for $ $ 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.