Electromagnetic form factors of the pion and kaon from the instanton vacuum

Abstract

We investigate the pion and kaon (${\ensuremath{\pi}}^{+}$, ${K}^{+}$, ${K}^{0}$) electromagnetic form factors in the spacelike region: ${Q}^{2}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{GeV}$, based on the gauged low-energy effective chiral action from the instanton vacuum in the large ${N}_{c}$ limit. Explicit flavor SU(3) symmetry breaking is taken into account. The nonlocal contributions turn out to be crucial to reproduce the experimental data. While the pion electromagnetic form factor is in good agreement with the data, the kaon one seems underestimated. We also calculate the electromagnetic charge radii for the pion and kaon: $⟨{r}^{2}{⟩}_{{\ensuremath{\pi}}^{+}}=0.455\text{ }\text{ }{\mathrm{fm}}^{2}$, $⟨{r}^{2}{⟩}_{{K}^{+}}=0.534\text{ }\text{ }{\mathrm{fm}}^{2}$, and $⟨{r}^{2}{⟩}_{{K}^{0}}=\ensuremath{-}0.060\text{ }\text{ }{\mathrm{fm}}^{2}$ without any adjustable free parameter except for the average instanton size and interinstanton distance, and they are compatible with the experimental data. The low-energy constant ${L}_{9}$ in the large ${N}_{c}$ limit is estimated to be $8.42\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ from the pion charge radius.