Abstract
We propose a novel method to determine the structure of symbols for any family of polylogarithmic Feynman integrals. Using the d log-bases and simple formulas for the leading order and next-to-leading contributions to the intersection numbers, we give a streamlined procedure to compute the entries in the coefficient matrices of canonical differential equations, including the symbol letters and the rational coefficients. We also provide a selection rule to decide whether a given matrix element must be zero. The symbol letters are deeply related to the poles of the integrands and also have interesting connections to the geometry of Newton polytopes. Our method can be applied to many cutting-edge multi-loop calculations. The simplicity of our results also hints at the possible underlying structure in perturbative quantum field theories.
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We thank Xuhang Jiang for valuable discussions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11935013, 11947301, 12047502 (Peng Huanwu Center), 12247120, 12247103, 11975030, 12147103, and U2230402), the China Postdoctoral Science Foundation (Grant No. 2022M720386), and the Fundamental Research Funds for the Central Universities.
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Chen, J., Feng, B. & Yang, L. Intersection theory rules symbology. Sci. China Phys. Mech. Astron. 67, 221011 (2024). https://doi.org/10.1007/s11433-023-2239-8
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DOI: https://doi.org/10.1007/s11433-023-2239-8