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

TL;DR

This paper estimates the theoretical uncertainties in calculating the pion-photon transition form factor using light-cone sum rules, focusing on low to mid momentum transfer regions, and compares predictions with experimental data.

Contribution

It systematically quantifies various sources of theoretical uncertainties in the light-cone sum rule calculation of the form factor.

Findings

Predictions agree with experimental data within errors for 1-5 GeV^2

Uncertainty estimates include higher-order corrections and resonance modeling

Results support the reliability of the light-cone sum rule approach

Abstract

We consider the calculation of the pion-photon transition form factor $F^{\gamma^*\gamma\pi^0}(Q^2)$ 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 $F^{\gamma^*\gamma\pi^0}(Q^2)$ 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.