Abstract
We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending ’t Hooft’s one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizable topologies do not contribute to the renormalization group equations. The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order.
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Acknowledgments
We thank Tim Engel, Javier Fuentes-Martín, Xiaochuan Lu, Chia-Hsien Shen, Peter Stoffer and Anders Thomsen for helpful discussions. This work is supported in part by the U.S. Department of Energy (DOE) under award numbers DE-SC0009919. LN gratefully acknowledges financial support from the Swiss National Science Foundation (Project No. PCEFP2_194272 and mobility grant PCEFP2_194272/2).
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Jenkins, E.E., Manohar, A.V., Naterop, L. et al. An algebraic formula for two loop renormalization of scalar quantum field theory. J. High Energ. Phys. 2023, 165 (2023). https://doi.org/10.1007/JHEP12(2023)165
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DOI: https://doi.org/10.1007/JHEP12(2023)165