In a study published in Physical Review Letter, Prof. JIA Yu from the Theory Division of Institute of High Energy Physics (IHEP) of the Chinese Academy of Sciences and his collaborators, made progress in accurate prediction of the pion electromagnetic form factor (EMFF). They computed for the first time the next-to-next-to-leading-order (NNLO) quantum chromodynamics (QCD) correction to this observable in the context of collinear factorization, and conducted a comprehensive comparison between theoretical predictions and available experimental data. 

The pion mesons have always occupied the central stage throughout the historic advancement of the strong interaction. They were originally proposed by Yukawa as the strong nuclear force carrier in 1935, subsequently discovered in the cosmic rays in 1947. As the lightest particles in the hadronic world, the pion mesons entail extremely rich QCD dynamics exemplified by color confinement and chiral symmetry breaking. Notwithstanding extensive explorations during the past seven decades, our understanding towards the internal structure of the pion mesons is still far from satisfactory.  

The pion EMFF is an important observable, which probes the charge distribution inside the pion meson. During the past half century, there has been extensive investigation on the pion EMFF from the experimental perspective. On the theoretical side, it is widely believed that at large momentum transfer, the collinear factorization approach based on perturbative QCD should give an adequate account of this observable. 

The leading order (LO) prediction to this observable was made in late 1970s. The next-to-leading order (NLO) correction was originally calculated by three groups independently in early 80s, however some discrepancies exist among these results. In 1987 Braaten and Tse presented the correct expression of the NLO hard-scattering kernel. Nearly four decades later, Prof. JIA and his collaborators finally computed the NNLO QCD correction to this basic observable, and obtained the NNLO hard-scattering kernel in closed form. The validity of collinear factorization at NNLO has been explicitly verified. 

The NNLO QCD correction turns to be positive and significant. Implementing this piece of new correction, and employing the pion meson light-cone distribution amplitude (LCDA) predicted by the recent lattice QCD simulation as the input parameter, researchers presented the state-of-the-art predictions for pion EMFFs, and made a comprehensive comparison between the finest theoretical predictions and numerous pion EMFF measurements in both space-like and time-like regimes. The phenomenological analysis provided strong constraint on the second Gegenbauer moment of the pion LCDA.