Pion-photon transition form factor in LCSR and tests of asymptotics

TL;DR

This paper uses advanced light cone sum rules with high-order QCD corrections to analyze the pion-photon transition form factor, testing theoretical models against experimental and lattice data to refine understanding of pion distribution amplitudes.

Contribution

It presents a comprehensive NNLO QCD analysis of the pion-photon TFF using LCSR, including detailed uncertainty quantification and comparison with experimental and lattice constraints.

Findings

Stringent bounds on pion distribution amplitudes.

Insights into the asymptotic behavior of the TFF.

Compatibility of various DAs with experimental data.

Abstract

We study the pion-photon transition form factor (TFF) $F^{\gamma*\gamma\pi^0}(Q^2)$ 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 $1\sigma$ and $2\sigma$ 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.