Analytic coupling and Sudakov effects in exclusive processes: pion and $\gamma^{*}\gamma\to\pi^{0}$ form factors

We develop and discuss in technical detail an infrared-finite factorization and optimized renormalization scheme for calculating exclusive processes, which enables the inclusion of transverse degrees of freedom without entailing suppression of calculated observables, like form factors. This is achieved by employing an analytic, i.e., infrared stable, running strong coupling $\alpha _{\rm s}(Q^{2})$ which removes the Landau singularity at $Q^{2}=\Lambda_{\rm QCD}^{2}$ by a minimum power-behaved correction. The ensuing contributions to the cusp anomalous dimension - related to the Sudakov form factor - and to the quark anomalous dimension - which controls evolution - lead to an enhancement at high $Q^{2}$ of the hard part of exclusive amplitudes, calculated in perturbative QCD, while simultaneously improving its scaling behavior. The phenomenological implications of this framework are analyzed by applying it to the pion's electromagnetic form factor, including the NLO contribution to the hard-scattering amplitude, and also to the pion-photon transition at LO. For the pion wave function, an improved ansatz of the Brodsky-Huang-Lepage type is employed, which includes an effective (constituent-like) quark mass, $m_{\rm q}=0.33$ GeV. Predictions for both form factors are presented and compared to the experimental data, applying Brodsky-Lepage-Mackenzie commensurate scale setting. We find that the perturbative hart part prevails at momentum transfers above about 20 GeV ${}^{2}$, while at lower $Q^{2}$-values the pion form factor is dominated by Feynman-type contributions. The theoretical prediction for the $\gamma ^{*}\gamma \to \pi ^{0}$ form factor indicates that the true pion distribution amplitude may be somewhat broader than the asymptotic one.