Two researchers (Dr. Gao Jing and Prof. Wang Yuming) in the research group of Prof. Wang Yuming at the School of Physics of Nankai University, in collaboration with Dr. Tobias Huber from the University of Siegen, Germany and Dr. Ji Yao (currently a postdoctoral fellow in professor Martin Beneke's research group at the Technical University of Munich), have taken the lead to realize the dual-cyclic graph analytic calculation of shape factor in "Gold hard exclusive process" (two-photon generation of π meson), breaking the standstill deadlock of the related theoretical research since unicyclic graph result was obtained in 1981, mutually authenticating the theoretical results obtained by the joint research team of the University of Regensburg and the University of Hamburg in Germany.

In particular, it is worth pointing out that the two research groups above mentioned adopted the completely different theoretical method and technical means, and their research results were published in the preprint database (arXiv.org) on the same day. The research group of Nankai University and the University of Siegen applied the factorization scheme of perturbation quantum chromodynamics based on the hierarchy of operator and referred to the matching program calculating the corresponding perturbation short-range Wilson coefficient including evanescent light cone operator, which was built by professor Wang Yuming and associate professor Shen Yuelong from Ocean University of China in 2017 (JHEP 12 (2017) 037).

In addition, a series of modern techniques for calculating dual-cyclic Feynman diagram (FIG. 1) were used in this work to achieve the reduction of scalar integrals and the analytical calculation of principal integrals. This study shows that the comparison between the newly obtained dual-cyclic graph calculation results and future Belle II experimental data helps double the accuracy of extracting shape parameter of distribution amplitude of pi-meson light cone (FIG. 2), having important scientific significance for exploring the intrinsic structure of hadron bound state system and QCD dynamics.

Figure 1: Typical dual-cyclic Feynman diagram

Figure 2: Shape parameters of distribution amplitude of π meson

On February 8, 2022, the research work entitled "Next-to-Next-to-Leading-Order QCD prediction for the photon-pion form factor" was published in the Physical Review Letters online.

The above research work has been supported by the General Project and Key Project of the National Natural Science Foundation of China, the Outstanding Youth Project of Tianjin Natural Science Foundation, and the Research Project of Hundred Young Academic Leaders of Nankai University. (Contributed by the School of Physics)

Related links:

Physical Review Letters paper：https://link.aps.org/doi/10.1103/PhysRevLett.128.062003

JHEP paper：https://link.springer.com/content/pdf/10.1007/JHEP12(2017)037.pdf

(Edited and translated by Nankai News Team)