Sergey Mikhailov

We obtain the electromagnetic pion form factor (emFF) F π for spacelike midrange of momentum transfer in quantum chromodynamics (QCD). We use renormalization group (RG) summation within the light cone sum rules (LCSRs) to obtain the QCD radiative corrections to the F π and involve contributions of the leading twist 2 and, twists 4, 6. The additional conditions to apply here this RG summation are discussed in details. The strong coupling constants in this approach are free of Landau singularities, which allows one to go down to the lower transferred momentum Q 2 . The prediction of the calculations performed reproduces the experimental data below/around Q 2 = 1 GeV 2 significantly better than analogous predictions based on a fixed-order power-series expansion in the standard QCD.

Different ways exist to obtain the elements of the {β}-expansion for renormgroup invariant quantities. Here we consider independent confirmation within the standard QCD of a number of our results [1] for the values of elements of this expansion for the nonsinglet Adler D _A -function, Bjorken polarized sum rules S ^Bjp up to the order N⁴LO. We suggest an approach to estimate the results of high order QCD calculations using a smaller number of diagrams of the specific type. This type is based on a proposed generalization of Naive NonAbelianization.

We derive explicit expressions for the elements of the {β}-expansion for the nonsinglet Adler D_A-function and Bjorken polarized sum rules S^Bjp in the N⁴LO using recent results by Chetyrkin for these quantities computed within extended QCD including any number of fermion representations. We discuss the properties of the {β}-expansion for D_A and S^Bjp at higher orders which follow from the Crewther [1] and the Broadhurst-Kataev [2] relation.

We study two versions of lightcone sum rules to calculate the γ*γ → π⁰ 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.