Pion-photon transition---the new QCD frontier

TL;DR

This paper analyzes pion-photon transition form factor data using light-cone sum rules with higher-order QCD corrections, finding consistency with some models but highlighting challenges posed by high-Q^2 BaBar data.

Contribution

It provides a comprehensive NLO analysis of existing data, incorporating higher-twist effects and comparing results with nonlocal QCD sum rule predictions, clarifying the compatibility of data with theoretical models.

Findings

Data up to 9 GeV$^2$ overlaps with nonlocal QCD sum rule predictions.

High-Q^2 BaBar data cannot be accurately fitted with current models.

The analysis constrains pion distribution amplitudes using multiple theoretical inputs.

Abstract

We perform a detailed analysis of all existing data (CELLO, CLEO, BaBar) on the pion-photon transition form factor by means of light-cone sum rules in which we include the NLO QCD radiative corrections and the twist-four contributions. The NNLO radiative correction together with the twist-six contribution are also taken into account in terms of theoretical uncertainties. Keeping only the first two Gegenbauer coefficients $a_2$ and $a_4$, we show that the $1\sigma$ error ellipse of all data up to 9 GeV$^2$ greatly overlaps with the set of pion distribution amplitudes obtained from nonlocal QCD sum rules---within the range of uncertainties due to twist-four. This remains valid also for the projection of the $1\sigma$ error ellipsoid on the $(a_2,a_4)$ plane when including $a_6$. We argue that it is not possible to accommodate the high-$Q^2$ tail of the BaBar data with the same accuracy, despite opposite claims by other authors, and conclude that the BaBar data still pose a challenge to QCD.