Next-to-leading-order QCD corrections to nucleon Dirac form factors

The leading-order perturbative QCD (pQCD) predictions to nucleon electromagnetic form factors were first made in late 70s. In this Letter for the first time we accomplish the calculation of the next-to-leading-order (NLO) QCD corrections to nucleon's Dirac form factors at large momentum transfer, to the leading-twist accuracy in collinear factorization approach, specifically within the Krankl and Manashov renormalization scheme. The effect of NLO perturbative corrections turns out to be positive and substantial. Taking the nucleon leading-twist light-cone-distribution amplitudes (LCDAs) determined from the recent lattice simulations as input, we find that the state-of-the-art pQCD predictions significantly underestimate the available nucleon Dirac form factors in both space-like and time-like domains. This nuisance indicates that some additional soft nonfactorizable contribution might be called for to account for the measured nucleon electromagnetic form factor data up to $Q^2\approx 30\;{\rm GeV^2}$.