Transition form factors of the pion in light-cone QCD sum rules with next-to-next-to-leading order contributions

TL;DR

This paper calculates the pion-photon transition form factor using Light-Cone QCD Sum Rules, including next-to-next-to-leading order corrections, and analyzes their impact on theoretical predictions and experimental data.

Contribution

It introduces NNLO radiative corrections to the form factor within Light-Cone QCD Sum Rules and assesses their significance using BLM scale-setting.

Findings

NNLO corrections are relatively small but significant for precision.

Predictions are sensitive to the pion distribution amplitude's endpoint behavior.

High-Q^2 BaBar data cannot be explained by NNLO perturbative corrections.

Abstract

The transition pion-photon form factor is studied within the framework of Light-Cone QCD Sum Rules. The spectral density for the next-to-leading order corrections is calculated for any Gegenbauer harmonic. At the level of the next-to-next-to-leading (NNLO) radiative corrections, only that part of the hard-scattering amplitude is included that is proportional to the $\beta$-function, taking into account the leading zeroth-order harmonic. The relative size of the NNLO contribution in the prediction for the form factor $F^{\gamma^{*}\gamma\pi}(Q^2)$ has been analyzed, making use of the BLM scale-setting procedure. In addition, predictions for the form factor $F^{\gamma^{*}\rho\pi}$ are obtained that turn out to be sensitive to the endpoint behavior of the pion distribution amplitude, thus providing in connection with experimental data an additional adjudicator for the pion distribution amplitude. In a note added, we comment on the preliminary high-$Q^2$ BaBar data on $F^{\gamma^{*}\gamma\pi}$ arguing that the significant growth of the form factor between 10 and 40 GeV$^2$ cannot be explained in terms of higher-order perturbative corrections at the NNLO.