Abstract
We derive a factorization theorem for the Higgs-boson production amplitude in gluon-gluon fusion induced by a light-quark loop, working at next-to-leading power in soft-collinear effective theory. The factorization is structurally similar to that obtained for the h → γγ decay amplitude induced by a light-quark loop, but additional complications arise because of external color charges. We show how the refactorization-based subtraction scheme developed in previous work leads to a factorization theorem free of endpoint divergences. We use renormalization-group techniques to predict the logarithmically enhanced terms in the three-loop gg → h form factor of order \( {\alpha}_s^3{\ln}^k\left(-{M}_h^2/{m}_b^2\right) \) with k = 6, 5, 4, 3. We also resum the first three towers of leading logarithms, \( {\alpha}_s^n{\ln}^{2n-k}\left(-{M}_h^2/{m}_b^2\right) \) with k = 0, 1, 2, to all orders of perturbation theory.
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Acknowledgments
We would like to thank the Mainz Institute for Theoretical Physics (MITP) for hospitality and support during the workshop Elliptic Integrals in Fundamental Physics (September 12–16, 2022). Furthermore, we thank M. Niggetiedt for his help on the fixed-order expansion. The work of M.N., M.S. and X.W. has been supported by the Cluster of Excellence Precision Physics, Fundamental Interactions, and Structure of Matter (PRISMA+ EXC 2118/1) funded by the German Research Foundation (DFG) within the German Excellence Strategy (Project ID 39083149). X.W has also been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy — EXC 2094-390783311. Z.L.L. is funded by the European Union (ERC, grant agreement No. 101044599, JANUS). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.
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Liu, Z.L., Neubert, M., Schnubel, M. et al. Factorization at next-to-leading power and endpoint divergences in gg → h production. J. High Energ. Phys. 2023, 183 (2023). https://doi.org/10.1007/JHEP06(2023)183
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DOI: https://doi.org/10.1007/JHEP06(2023)183