Systematic estimation of theoretical uncertainties in the calculation of the pion-photon transition form factor using light-cone sum rules

Abstract

We consider the calculation of the pion-photon transition form factor $F^{{\gamma }^{\ast }\gamma {\pi }^0}(Q^2)$ within light-cone sum rules focusing attention to the low-mid region of momenta. The central aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale $M^2$, (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for $F^{{\gamma }^{\ast }\gamma {\pi }^0}(Q^2)$ are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the $Q^2$ range between 1 and 5 GeV${}^2$, thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical predictions with forthcoming data bearing small statistical errors.

15 pages, 4 figures. Version 3 includes complete Fig. 4 and all Eqs.(B7). Conclusions unchanged; matches version to appear in Phys. Rev. D

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