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

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

2003-09-04

arxiv.org/abs/hep-ph/0309039v3

Phys.Lett.B578:99-108,2004; Erratum-ibid.B586:439-440,2004

Physics

High Energy Physics

High Energy Physics - Phenomenology

PlainTeX file. Corrected asymptotic phase; numerical results unaffected

Scientific paper

10.1016/j.physletb.2003.10.037

We consider the quadratic scalar radius of the pion, $$, and the mixed $K-\pi$ scalar radius, $$. 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 $2 \sigma$ above estimates based on chiral perturbation theory. On the other hand, we show that this value of $$ suggests the existence of a low mass S$\tfrac{1}{2}$ $K\pi$ resonance. With respect to $$, 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 $1.4 \sigma$ 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.

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