Pion form factor in QCD at intermediate momentum transfers

Abstract

We present a quantitative analysis of the electromagnetic pion form factor in the light-cone sum rule approach, including radiative corrections and higher-twist effects. The comparison to the existing data favors the asymptotic profile of the pion distribution amplitude and allows us to estimate the deviation: $[\ensuremath{\int}du/u{\ensuremath{\varphi}}_{\ensuremath{\pi}}(u)]/[\ensuremath{\int}du/u{\ensuremath{\varphi}}_{\ensuremath{\pi}}^{\mathrm{as}}(u)]=1.1\ifmmode\pm\else\textpm\fi{}0.1$ at the scale of 1 GeV. Special attention is paid to the precise definition and interplay of soft and hard contributions at intermediate momentum transfer, and to the matching of the sum rule to the perturbative QCD prediction. We observe a strong numerical cancellation between the soft (end-point) contribution and power-suppressed hard contributions of higher twist, so that the total nonperturbative correction to the usual $\mathrm{PQCD}$ result turns out to be of the order of $30%$ for ${Q}^{2}\ensuremath{\sim}1 {\mathrm{GeV}}^{2}.$