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. Theoretical uncertainty of the LO results related to the renormalization scale ambiguity 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 <

Abstract. Using the Feynman parameter method, we have calculated in an elegant manner a set of one−loop box scalar integrals with massless internal lines, but containing 0, 1, 2, or 3 external massive lines. To treat IR divergences (both soft and collinear), the dimensional regularization method has been employed. The results for these integrals, which appear in the process of evaluating one−loop (N ≥ 5)−point integrals and in subdiagrams in QCD loop calculations, have been obtained for arbitrary values of the relevant kinematic variables and presented in a simple and compact form.

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The next-to-leading order ͑NLO͒ Brodsky-Lepage-Mackenzie ͑BLM͒ scale for the pion transition form factor is determined. To achieve that, a consistent calculation up to n f -proportional next-to-next-to-leading order contributions to both the hard-scattering amplitude and the perturbatively calculable part of the pion distribution amplitude is performed. By combining and matching the results obtained for these two amplitudes, a proper cancellation of collinear singularities is established and the ␥ 5 ambiguity problem ͑related to the use of the dimensional regularization method͒ is resolved by using the naive-␥ 5 as well as the 't Hooft-Veltman ͑HV͒ schemes. It is demonstrated that the prediction for the pion transition form factor is independent of the factorization scale F 2 at every order in the strong coupling constant, making it possible to use the simplest choice F 2 ϭQ 2 at the intermediate steps of the calculation. Assuming the pion asymptotic distribution amplitude and working in the MS scheme, we find the BLM scale to be R 2 ϭ BLM 2 ϷQ 2 /9. Based on the same distribution, the complete NLO prediction for the pion transition form factor is calculated in the ␣ V definition of the QCD coupling renormalized at R 2 ϭ V 2 ϭe 5/3 BLM 2 ϷQ 2 /2. It is in good agreement with the presently available experimental data.

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