Two-loop QCD corrections to pion electromagnetic form factors

We calculate the next-to-next-to-leading order (NNLO) QCD radiative correction to the pion electromagnetic form factor with large momentum transfer for the first time. We explicitly verify the validity of the collinear factorization to two-loop order for this observable, and obtain the respective IR-finite two-loop hard-scattering kernel in the closed form. The NNLO QCD correction turns to be positive and significant. Incorporating this new ingredient of correction, we then make a comprehensive comparison between the finest theoretical predictions and numerous data for both space-like and time-like pion form factors. Our phenomenological analysis provides strong constraint on the second Gegenbauer moment of the pion light-cone distribution amplitude (LCDA) obtained from recent lattice QCD studies.