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

TL;DR

This paper studies the electromagnetic form factors of pions and kaons using the instanton vacuum model, successfully reproducing experimental charge radii and providing insights into flavor symmetry breaking effects.

Contribution

It introduces a calculation of meson electromagnetic form factors within the instanton vacuum framework, incorporating flavor SU(3) symmetry breaking and nonlocal effects.

Findings

Pion form factor agrees well with experimental data.

Kaon form factor is slightly underestimated.

Calculated charge radii are consistent with experiments.

Abstract

We investigate the pion and kaon (pi^+, K^+, K^0) electromagnetic form factors in the space-like region: Q^2 ~< 1 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>_{pi^+}=0.455 fm^2, <r^2>_{K^+}=0.486 fm^2 and <r^2>_{K^0}=-0.055 fm^2 without any adjustable free parameter except for the average instanton size and inter-instanton 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*10^{-3} from the pion charge radius.