Pion decay constant, electromagnetic form factor, and quark electromagnetic self-energy in quantum chromodynamics

Abstract

We examine dynamical chiral symmetry breaking in quantum chromodynamics (QCD). To lowest order in a double perturbation expansion in $g$, the gauge coupling, and $\ensuremath{\lambda}=\mathrm{exp}(\ensuremath{-}\frac{1}{b{g}^{2}})$ we obtain exact representations for the pion decay constant ${f}_{\ensuremath{\pi}}$ and electromagnetic form factor ${F}_{\ensuremath{\pi}}({q}^{2})$. Using the experimental values for ${f}_{\ensuremath{\pi}}$ and ${F}_{\ensuremath{\pi}}({q}^{2})$, we estimate the dynamically generated quark mass to be 270-300 MeV, in good agreement with a value obtained from ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data. We also calculate the finite electromagnetic self-energy of a quark in QCD and discuss the implications.