Abstract
We compute the two-loop master integrals for leading-color QCD scattering amplitudes including a closed light-quark loop in \( t\overline{t}H \) production at hadron colliders. Exploiting numerical evaluations in modular arithmetic, we construct a basis of master integrals satisfying a system of differential equations in ϵ-factorized form. We present the analytic form of the differential equations in terms of a minimal set of differential one-forms. We explore properties of the function space of analytic solutions to the differential equations in terms of iterative integrals which can be exploited for studying the analytic form of related scattering amplitudes. Finally, we solve the differential equations using generalized series expansions to numerically evaluate the master integrals in physical phase space. As the first computation of a set of two-loop seven-scale master integrals, our results provide valuable input for analytic studies of scattering amplitudes in processes involving massive particles and a large number of kinematic scales.
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Acknowledgments
We thank Samuel Abreu and Vasily Sotnikov for helpful conversations. The work of F.F.C., G.F. and L.R. is supported in part by the U.S. Department of Energy under grant DESC0010102. This work has been made possible in part through the support of the FSU Council on Research and Creativity (“Black Holes Under the Microscope”; SEED Grant, 2023). M.K. is supported by the DGAPA-PAPIIT grant IA102224 and the PIIF grant at UNAM. L.R. acknowledges the Aspen Center for Physics, supported by National Science Foundation grant PHY-2210452, and its kind hospitality while she was working on this project. The authors acknowledge the Instituto de Física (UNAM) for providing computing infrastructure and Carlos Ernesto López Natarén for his HPC support. The computing for this project was partly performed on the HPC cluster at the Research Computing Center at the Florida State University (FSU).
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Cordero, F.F., Figueiredo, G., Kraus, M. et al. Two-loop master integrals for leading-color \( pp\to t\overline{t}H \) amplitudes with a light-quark loop. J. High Energ. Phys. 2024, 84 (2024). https://doi.org/10.1007/JHEP07(2024)084
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DOI: https://doi.org/10.1007/JHEP07(2024)084