Improved calculation of the $\gamma^*\gamma \rightarrow \pi$ process at low $Q^2$ using LCSR's and renormalization-group summation

TL;DR

This paper introduces an improved method for calculating the $ ightarrow$ transition form factor at low $Q^2$ using lightcone sum rules with renormalization-group summation, aligning well with experimental and lattice data.

Contribution

The paper develops a novel approach incorporating renormalization-group summation into lightcone sum rules for better TFF predictions.

Findings

Good agreement with BESIII data

Pion distribution amplitude consistent with lattice constraints

Enhanced theoretical precision at low $Q^2$

Abstract

We study two versions of lightcone sum rules to calculate the $\gamma^*\gamma\rightarrow\pi^0$ transition form factor (TFF) within QCD. While the standard version is based on fixed-order perturbation theory by means of a power-series expansion in the strong coupling, the new method incorporates radiative corrections by renormalization-group summation and generates an expansion within a generalized fractional analytic perturbation theory involving only analytic couplings. Using this scheme, we determine the relative nonperturbative parameters and the first two Gegenbauer coefficients of the pion distribution amplitude (DA) to obtain TFF predictions in good agreement with the preliminary BESIII data, while the best-fit pion DA satisfies the most recent lattice constraints on the second moment of the pion DA at the three-loop level.