Extending the application of the light-cone sum rules 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 light-cone 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 GeV2. This way, one can use the new preliminary BESIII data with unprecedented accuracy below 1.5 GeV2 to fine tune the prefactor of the twist-six contribution. Using a combined fit to all available data below 3.1 GeV2, 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 1s level with the data for Q(2) <= 3.1 GeV2 and fulfill at the same time the lattice constraints on b(2) at (NLO)-L-3 together with the constraints from QCD sum rules with nonlocal condensates. The form-factor prediction calculated herewith reproduces the data below 1 GeV2 significantly better than analogous predictions based on a fixed-order power-series expansion in the strong coupling constant.