Extending the application of the LCSR method to low momenta using QCD renormalization-group summation. Theory and phenomenology

We show that using renormalization-group summation to generate the QCD radiative corrections to the $\pi -\gamma$ transition form factor, calculated with lightcone sum rules (LCSR), renders the strong coupling free of Landau singularities while preserving the QCD form-factor asymptotics. This enables a reliable applicability of the LCSR method to momenta well below 1 GeV${}^2$. This way, one can use the new preliminary BESIII data with unprecedented accuracy below 1.5 GeV${}^2$ to fine tune the prefactor of the twist-six contribution. Using a combined fit to all available data below 3.1 GeV${}^2$, we are able to determine all nonperturbative scale parameters and a few Gegenbauer coefficients entering the calculation of the form factor. Employing these ingredients, we determine a pion distribution amplitude with conformal coefficients $(b_2,b_4)$ that agree at the $1\sigma$ level with the data for $Q^2⩽3.1$ GeV${}^2$ and fulfill at the same time the lattice constraints on $b_2$ at N${}^3$LO together with the constraints from QCD sum rules with nonlocal condensates.The form-factor prediction calculated herewith reproduces the data below 1 GeV${}^2$ significantly better than analogous predictions based on a fixed-order power-series expansion in the strong coupling constant.