Can we understand an auxetic pion-photon transition form factor within QCD? BaBar faces Belle

Abstract

A state-of-the-art analysis of the pion-photon transition form factor is presented based on an improved theoretical calculation that includes the effect of a finite virtuality of the quasi-real photon in the method of light-cone sum rules. We carry out a detailed statistical analysis of the existing experimental data using this method and by employing pion distribution amplitudes with up to three Gegenbauer coefficients $a_2,a_4,a_6$. Allowing for an error range in the coefficient $a_6\approx 0$, the theoretical predictions for ${\gamma }^{\ast }\gamma \to {\pi }^0$ obtained with nonlocal QCD sum rules are found to be in good agreement with all data that support a scaling behavior of the transition form factor at higher $Q^2$, like those of the Belle Collaboration. The data on ${\gamma }^{\ast }\gamma \to \eta /{\eta }^{\prime }$ from CLEO and \babar are also reproduced, while there is a strong conflict with the auxetic trend of the \babar data above 10 GeV${}^2$. The broader implications of these findings are discussed.

Comments: v4: 13 pages, 1 table, 8 figures. Paper body radically redesigned and extended to include Belle data. Contains statistical data analysis and photon small virtuality. Conclusions and references updated. V5 matches version to appear in Physical Review D