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We study two versions of lightcone sum rules to calculate the$\gamma^*\gamma\rightarrow\pi^0$ transition form factor (TFF) within QCD. Whilethe standard version is based on fixed-order perturbation theory by means of apower-series expansion in the strong coupling, the new method incorporatesradiative corrections by renormalization-group summation and generates anexpansion within a generalized fractional analytic perturbation theoryinvolving only analytic couplings. Using this scheme, we determine the relativenonperturbative parameters and the first two Gegenbauer coefficients of thepion distribution amplitude (DA) to obtain TFF predictions in good agreementwith the preliminary BESIII data, while the best-fit pion DA satisfies the mostrecent lattice constraints on the second moment of the pion DA at thethree-loop level.

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