Progress Made in Theoretical Study of Pion Electromagnetic Form Factor


Recently an important progress in accurate prediction of the pion electromagnetic form factor (EMFF) has been made by Prof. JIA Yu from the Theory Division of Institute of High Energy Physics of Chinese Academy of Sciences and his collaborators. They computed for the first time the next-to-next-to-leading-order (NNLO) QCD correction to this observable in the context of collinear factorization, and conducted a comprehensive comparison between theoretical predictions and available experimental data. This work was published in Physical Review Letter on May 13 (Phys. Rev. Lett. 132.201901(2024)).


The pion mesons have always occupied the central stage throughout the historic advancement of the strong interaction. The pion mesons 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, JIA Yu and his collaborators finally computed the next-to-next-to-leading order (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, the authors 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 (Figure 1). The phenomenological analysis provides strong constraint on the second Gegenbauer moment of the pion LCDA.


The authors of this paper are Prof. CHEN Long-Bin from Guangzhou University, Dr. CHEN Wen from South China Normal University, Prof. FENG Feng from China University of Mining and Technology, and Prof. JIA Yu from IHEP, respectively. This work is supported in part by the National Science Fund for Distinguished Young Scholars and the Collaborative Research Center CRC110 co-funded by Chinese and German Institutions.


Fig.1 Comparison between perturbative QCD predictions and experimental data for pion EMFF in space-like (left panel) and time-like (right panel) regions. In theoretical predictions, the numerical value of the second Gegenbauer moment of the pion LCDA is taken from the lattice QCD RQCD collaboration. (Credit: IHEP)




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Ms. JIA Yinghua