Pion Form Factor

Abstract

We give the normalized leading asymptotic ${Q}^{2}$ dependence of the pion form factor in quantum chromodynamics: ${F}_{\ensuremath{\pi}}({Q}^{2})\underset{{Q}^{2}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}}{\ensuremath{\rightarrow}}\ensuremath{-}\frac{2{{f}_{\ensuremath{\pi}}}^{2}}{b}{Q}^{2}\mathrm{ln}|{Q}^{2}|$, where ${f}_{\ensuremath{\pi}}$ is the pion decay constant and $b=\frac{(11\ensuremath{-}\frac{2}{3}{N}_{f})}{16{\ensuremath{\pi}}^{2}}$. Up to non-leading-logarithmic corrections, this is equivalent to ${F}_{\ensuremath{\pi}}({Q}^{2})\underset{{Q}^{2}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}}{\ensuremath{\rightarrow}}8\ensuremath{\pi}{\ensuremath{\alpha}}_{s}({Q}^{2})\frac{{{f}_{\ensuremath{\pi}}}^{2}}{(\ensuremath{-}{Q}^{2})}$. These results are obtained by solving the light-cone pion Bethe-Salpeter equation in quantum chromodynamics to leading-logarithmic accuracy.