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 $\lambda =\exp (-\frac{1}{b{g}^2})$ we obtain exact representations for the pion decay constant $f_{\pi }$ and electromagnetic form factor $F_{\pi }\left(q^2\right)$. Using the experimental values for $f_{\pi }$ and $F_{\pi }\left(q^2\right)$, we estimate the dynamically generated quark mass to be 270-300 MeV, in good agreement with a value obtained from $e^{+}{e}^{-}$ annihilation data. We also calculate the finite electromagnetic self-energy of a quark in QCD and discuss the implications.