Abstract
In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the methodology developed in the context of Banana integrals can also be extended to these cases and obtain ε-factorized differential equations for all sectors. The letters are combinations of modular forms on the corresponding elliptic curves and algebraic functions arising from the sub-sectors. With uniform transcendental boundary conditions, we express our results in terms of iterated integrals order-by-order in the dimensional regulator, which can be evaluated efficiently. Our method can be straightforwardly generalized to other elliptic integral families and have important applications to precision physics at current and future high-energy colliders.
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Acknowledgments
We thank Stefan Weinzierl and Sebastian Pögel for detailed comments on the manuscript and fruitful discussions, Guo-Xing Wang for discussions about the Mellin-Barnes representations, and Roman Lee for providing LiteRed2. X.W is grateful for the inspiring and fruitful discussion with Christoph Nega and Lorenzo Tancredi during the work. This work was partly supported by the National Natural Science Foundation of China under Grant No. 11975030 and 12147103, and the Fundamental Research Funds for the Central Universities. X.W was supported by the Excellence Cluster ORIGINS funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Grant No. EXC - 2094 - 390783311.
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Jiang, X., Wang, X., Yang, L.L. et al. ε-factorized differential equations for two-loop non-planar triangle Feynman integrals with elliptic curves. J. High Energ. Phys. 2023, 187 (2023). https://doi.org/10.1007/JHEP09(2023)187
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DOI: https://doi.org/10.1007/JHEP09(2023)187