Pion form factor in QCD: From nonlocal condensates to next-to-leading-order analytic perturbation theory

We present an investigation of the pion’s electromagnetic form factor $F_{\pi }{(Q}^2)$ in the spacelike region utilizing two new ingredients: (i) a double-humped, end-point-suppressed pion distribution amplitude derived before via QCD sum rules with nonlocal condensates—found to comply at the $1\sigma$ level with the CLEO data on the $\pi \gamma$ transition—and (ii) analytic perturbation theory at the level of parton amplitudes for hadronic reactions. The computation of $F_{\pi }{(Q}^2)$ within this approach is performed at the next to leading order (NLO) of QCD perturbation theory (standard and analytic), including the evolution of the pion distribution amplitude at the same order. We consider the NLO corrections to the form factor in the $\overline{\mathrm{MS}}$ scheme with various renormalization scale settings and also in the ${\alpha }_V$ scheme. We find that using standard perturbation theory, the size of the NLO corrections is quite sensitive to the adopted renormalization scheme and scale setting. The main results of our analysis are the following: (i) Replacing the QCD coupling and its powers by their analytic images, both dependencies are diminished and the predictions for the pion form factor are quasi-scheme- and scale-setting independent. (ii) The magnitude of the factorized pion form factor, calculated with the aforementioned pion distribution amplitude, is only slightly larger than the result obtained with the asymptotic one in all considered schemes. (iii) Including the soft pion form factor via local duality and ensuring the Ward identity at $Q^2=0,$ we present predictions that are in remarkably good agreement with the existing experimental data both in trend and magnitude.