https://doi.org/10.1140/epja/s10050-026-01836-1
Regular Article - Theoretical Physics
Auxiliary counterterms and their role in effective field theory
School of Physics, Beihang University, 100191, Beijing, China
a
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Received:
5
December
2025
Accepted:
9
March
2026
Published online:
5
April
2026
Abstract
Effective field theories include contact-range interactions (or counterterms) for two reasons: representing the unknown short-range physics in a model independent manner and ensuring the cutoff independence of observables. Both are intertwined: cutoff independence alone (modulo truncation errors) already generates counterterms encoding physical information not present in the known long-range physics. Yet, there is also residual cutoff dependence, which is smaller than the uncertainties that are achievable within the effective field theory description and thus can be safely neglected in most settings. If one insists on exact cutoff independence though, new counterterms will be required, but they encode no new physical information and are thus what one could call redundant, or auxiliary, counterterms. It happens that auxiliary counterterms are still useful for solving certain inconsistencies that appear during renormalization or for improving the convergence of the effective field theory expansion. Examples of these use cases are discussed, including the interpretation of the improved actions or the relation between perturbative and non-perturbative renormalization.
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Communicated by Vittorio Somá.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
