Pion Form Factor

Abstract

We give the normalized leading asymptotic $Q^2$ dependence of the pion form factor in quantum chromodynamics: $F_{\pi }\left(Q^2\right)\underset{Q^2\to \pm \infty }{\to }-\frac{2{f_{\pi }}^2}{b}{Q}^2\ln \left|Q^2\right|$, where $f_{\pi }$ is the pion decay constant and $b=\frac{(11-\frac{2}{3}{N}_f)}{16{\pi }^2}$. Up to non-leading-logarithmic corrections, this is equivalent to $F_{\pi }\left(Q^2\right)\underset{Q^2\to \pm \infty }{\to }8\pi {\alpha }_s\left(Q^2\right)\frac{{f_{\pi }}^2}{(-Q^2)}$. These results are obtained by solving the light-cone pion Bethe-Salpeter equation in quantum chromodynamics to leading-logarithmic accuracy.