  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.
