Abstract
We study a set of two-loop non-planar master integrals needed for the NNLO QCD corrections to diphoton and dijet production at hadron colliders. The top-sector topology contains an internal massive fermion loop and is known to contain elliptic curves. Leveraging the method of differential equations, we provide a comprehensive discussion for deriving an ϵ-factorized differential equation related to the most intricate sector within the Feynman integral family. Despite the dependence on multiple scales and the presence of two elliptic sectors, we demonstrate how to leverage the properties of their maximal cuts and the factorization of the Picard-Fuchs operator to deal with the complexity of the analytic computation. In particular, we construct a transformation matrix that brings the differential equations into a format enabling the convenient expression of analytic results in terms of Chen’s iterated integrals.
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Acknowledgments
We would like to thank Claude Duhr and Vasily Sotnikov for comments on the manuscript. EC would also like to thank Christoph Dlapa for interesting discussions at the workshop ‘MathemAmplitudes 2023: QFT at the Computational Frontier’. SM would like to thank Yu Jiao Zhu for insightful discussions. The work of EC and SM is funded by the ERC grant 101043686 ‘LoCoMotive’. The work of TA is supported by Deutsche Forschungsgemeinschaft (DFG) through the Research Unit FOR 2926, Next Generation perturbative QCD for Hadron Structure: preparing for the Electron-ion collider, project number 409651613. MK would like to acknowledge financial support from IISER Mohali for this work. This work was co-funded by the European Union through the ERC Consolidator Grant LoCoMotive 101043686. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.
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Ahmed, T., Chaubey, E., Kaur, M. et al. Two-loop non-planar four-point topology with massive internal loop. J. High Energ. Phys. 2024, 64 (2024). https://doi.org/10.1007/JHEP05(2024)064
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DOI: https://doi.org/10.1007/JHEP05(2024)064