Abstract
Field redefinitions are commonly used to reduce the number of operators in the Lagrangian by removing redundant operators and transforming to a minimal operator basis. We give a general argument that such field redefinitions, while leaving the S-matrix invariant and consequently finite, lead not only to infinite Green’s functions, but also to infinite field anomalous dimensions γϕ. These divergences cannot be removed by counterterms without reintroducing redundant operators.
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References
J.S.R. Chisholm, Change of variables in quantum field theories, Nucl. Phys. 26 (1961) 469 [INSPIRE].
H.D. Politzer, Power Corrections at Short Distances, Nucl. Phys. B 172 (1980) 349 [INSPIRE].
C. Arzt, Reduced effective Lagrangians, Phys. Lett. B 342 (1995) 189 [hep-ph/9304230] [INSPIRE].
A.V. Manohar, Introduction to Effective Field Theories, in the proocedings of the Les Houches summer school: EFT in Particle Physics and Cosmology Les Houches (Chamonix Valley), France, July 3–28, 2017 [https://doi.org/10.1093/oso/9780198855743.003.0002] [arXiv:1804.05863] [INSPIRE].
J.C. Criado and M. Pérez-Victoria, Field redefinitions in effective theories at higher orders, JHEP 03 (2019) 038 [arXiv:1811.09413] [INSPIRE].
E.E. Jenkins, A.V. Manohar, L. Naterop and J. Pagès, Two loop renormalization of scalar theories using a geometric approach, JHEP 02 (2024) 131 [arXiv:2310.19883] [INSPIRE].
A.V. Bednyakov, A.F. Pikelner and V.N. Velizhanin, Three-loop SM beta-functions for matrix Yukawa couplings, Phys. Lett. B 737 (2014) 129 [arXiv:1406.7171] [INSPIRE].
F. Herren, L. Mihaila and M. Steinhauser, Gauge and Yukawa coupling beta functions of two-Higgs-doublet models to three-loop order, Phys. Rev. D 97 (2018) 015016 [Erratum ibid. 101 (2020) 079903] [arXiv:1712.06614] [INSPIRE].
F. Herren and A.E. Thomsen, On ambiguities and divergences in perturbative renormalization group functions, JHEP 06 (2021) 116 [arXiv:2104.07037] [INSPIRE].
G. ’t Hooft, Dimensional regularization and the renormalization group, Nucl. Phys. B 61 (1973) 455 [INSPIRE].
E.E. Jenkins, A.V. Manohar, L. Naterop and J. Pagès, An algebraic formula for two loop renormalization of scalar quantum field theory, JHEP 12 (2023) 165 [arXiv:2308.06315] [INSPIRE].
F. Herzog and B. Ruijl, The R*-operation for Feynman graphs with generic numerators, JHEP 05 (2017) 037 [arXiv:1703.03776] [INSPIRE].
W. Cao, F. Herzog, T. Melia and J.R. Nepveu, Renormalization and non-renormalization of scalar EFTs at higher orders, JHEP 09 (2021) 014 [arXiv:2105.12742] [INSPIRE].
Acknowledgments
We thank Xiaochuan Lu for helpful discussions. JRN thanks Franz Herzog for collaboration on related topics and for providing access to his implementation of the R* operation [12, 13] to calculate the counterterms. This work is supported in part by the U.S. Department of Energy (DOE) under award numbers DE-SC0009919. JRN is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — Projektnummer 417533893/GRK2575 “Rethinking Quantum Field Theory.” This project has received funding from the European Union’s Horizon Europe research and innovation programme under the Marie Skłodowska-Curie Staff Exchange grant agreement No 101086085 — ASYMMETRY.
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Manohar, A.V., Pagès, J. & Nepveu, J.R. Field redefinitions and infinite field anomalous dimensions. J. High Energ. Phys. 2024, 18 (2024). https://doi.org/10.1007/JHEP05(2024)018
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DOI: https://doi.org/10.1007/JHEP05(2024)018