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Pion-photon transition: The new QCD frontier

A. P. Bakulev^1,*, S. V. Mikhailov^1,†, A. V. Pimikov^1,‡, and N. G. Stefanis^2,§

¹Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia
²Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum, Germany

^*bakulev@theor.jinr.ru
^†mikhs@theor.jinr.ru
^‡pimikov@theor.jinr.ru
^§stefanis@tp2.ruhr-uni-bochum.de

Phys. Rev. D 84, 034014 – Published 8 August, 2011

DOI: https://doi.org/10.1103/PhysRevD.84.034014

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 next-to-leading order QCD radiative corrections and the twist-four contributions. The next-to-next-to-leading order 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 $1 σ$ 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 $1 σ$ 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.

Article Text

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