Form factor $\pi^0 \gamma^* \gamma$ in lightcone sum rules combined with renormalization-group summation vs experimental data

TL;DR

This paper develops an advanced lightcone sum-rule approach combined with renormalization-group techniques to accurately predict the pion-photon transition form factor, achieving excellent agreement with recent experimental data at low and intermediate momentum transfers.

Contribution

It introduces a novel scheme merging lightcone sum rules with renormalization-group summation, extending perturbation theory's validity to lower momenta in QCD.

Findings

Predictions match BESIII data at low $Q^2$ with small errors.

The approach extends perturbation theory applicability to $Q^2 \\lesssim 1$ GeV$^2$.

Results are consistent with previous fixed-order perturbation theory at higher $Q^2$.

Abstract

We consider the lightcone sum-rule (LCSR) description of the pion-photon transition form factor in combination with the renormalization group of QCD. The emerging scheme represents a certain version of Fractional Analytic Perturbation Theory and significantly extends the applicability domain of perturbation theory towards lower momenta $Q^2\lesssim 1$ GeV$^2$. We show that the predictions calculated herewith agree very well with the released preliminary data of the BESIII experiment, which have very small errors just in this region, while the agreement with other data at higher $Q^2$ is compatible with the LCSR predictions obtained recently by one of us using fixed-order perturbation theory.