Complete next-to-leading order perturbative QCD prediction for the pion electromagnetic form factor

Abstract

We present the results of a complete leading-twist next-to-leading order (NLO) QCD analysis of the spacelike pion electromagnetic form factor at large momentum transfer Q. We have studied their dependence on the form of the pion distribution amplitude. For a given distribution amplitude, we have examined the sensitivity of the predictions to the choice of the renormalization and factorization scales. Compared to the renormalization scale, the factorization scale turns out to be of secondary importance. The renormalization scale dependence of the leading-order (LO) results has been significantly reduced by including the NLO corrections. Adopting the criteria according to which a NLO prediction is considered reliable if both the ratio of the NLO to LO contributions and the strong coupling constant are reasonably small, we find that reliable perturbative predictions for the pion electromagnetic form factor with all distribution amplitudes considered can already be made at a momentum transfer Q of the order $5\ensuremath{-}10$ GeV, with corrections to the LO results being up to $\ensuremath{\sim}30%.$ The theoretical uncertainty related to the renormalization scale ambiguity has been estimated to be less than $10%.$ To check our predictions and to discriminate between the distribution amplitudes, it is necessary to obtain experimental data extending to higher values of Q.