Pion-photon transition form factor in light cone sum rules and tests of asymptotics
N. G. Stefanis
Abstract
We study the pion-photon transition form factor (TFF) ${F}^{\ensuremath{\gamma}*\ensuremath{\gamma}{\ensuremath{\pi}}^{0}}({Q}^{2})$ using a state-of-the art implementation of light cone sum rules (LCSRs) within fixed-order QCD perturbation theory. The spectral density in the dispersion relation includes all currently known radiative corrections up to the next-to-next-to-leading-order (NNLO) and all twist contributions up to order six. Predictions for the TFF are obtained for various pion distribution amplitudes (DAs) of twist two, including two-loop evolution which accounts for heavy-quark mass thresholds. The influence of the main theoretical uncertainties is quantified in order to enable a more realistic comparison with the data. The characteristics of various pion DAs are analyzed in terms of the conformal coefficients ${a}_{2}$ and ${a}_{4}$ in comparison with the $1\ensuremath{\sigma}$ and $2\ensuremath{\sigma}$ error regions of the data and the most recent lattice constraints on ${a}_{2}$ with NLO and NNLO accuracy. Our results provide more stringent bounds on the variation of the pion DA and illuminate the corresponding asymptotic behavior of the calculated TFF.