Abstract
We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for pp → \( t\overline{t}j \). We derive differential equations for the master integrals by solving the integration-by-parts identities over finite fields. Of the two systems of differential equations, one is presented in canonical ‘d log’ form, while the other is found to have an elliptic sector. For the elliptic topology we identify the relevant elliptic curve, and present the differential equations in a more general form which depends quadratically on ε and contains non-logarithmic one-forms in addition to the canonical d log’s. We solve the systems of differential equations numerically using generalised series expansions with the boundary terms obtained using the auxiliary mass flow method. A summary of all one-loop and two-loop planar topologies is presented including the list of alphabet letters for the ‘d log’ form systems and high-precision boundary values.
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Acknowledgments
We are grateful to Heribertus Bayu Hartanto, Colomba Brancaccio, Ekta Chaubey and Christoph Dlapa for many enlightening discussions. We also thank Colomba Brancaccio and Xuhang Jiang for helpful comments on this paper. This project has received funding from the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101105486, and ERC Starting Grant No. 101040760 FFHiggsTop. This work has received funding from the Italian Ministry of Universities and Research through FARE grant R207777C4R. This research was supported in part by the Swiss National Science Foundation (SNF) under contract 200021_212729. SB has been partially supported by the Italian Ministry of Universities and Research (MUR) through grant PRIN 2022BCXSW9.
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Badger, S., Becchetti, M., Giraudo, N. et al. Two-loop integrals for \( t\overline{t} \)+jet production at hadron colliders in the leading colour approximation. J. High Energ. Phys. 2024, 73 (2024). https://doi.org/10.1007/JHEP07(2024)073
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DOI: https://doi.org/10.1007/JHEP07(2024)073