Effective Field Theory Perspective On King Non-linearity

[2512.03157] Effective Field Theory Perspective On King Non-linearity Skip to main content Search Submit Donate Log in High Energy Physics - Phenomenology arXiv:2512.03157 (hep-ph) [Submitted on 2 Dec 2025 ( v1 ), last revised 24 Aug 2026 (this version, v2)] Title: Effective Field Theory Perspective On King Non-linearity Authors: Benoît Assi , Sam Carey , Sebastian Jäger , Gabriel Lee , Gil Paz , Gilad Perez , Jure Zupan View PDF HTML (experimental) Abstract: Precision spectroscopic measurements of isotope shifts have recently reached a high level of accuracy. Tests of King non-linearity (NL) along isotope chains have been proposed as a tool to search for fifth-force mediators. At the same time, these tests can potentially teach us about the structure of heavy nuclei at unprecedented precision, where King NL has already been observed in several systems. A robust interpretation of the existing data, however, is hampered by incomplete control over the Standard Model (SM) contributions. We develop a systematic effective field theory framework, matching the SM onto scalar non-relativistic QED in the infinite nuclear mass limit and then onto quantum-mechanical potentials. This approach organizes all nuclear effects into a small set of Wilson coefficients and cleanly separates short- and long-distance physics. We show that the commonly used treatment of the $\langle r^2\rangle^2$ term needs to be reconsidered, as it arises only at second-order in perturbation theory, and we derive the long-range $1/r^4$ potential from nuclear polarizability. Applying the framework to hydrogen-like systems, we provide a transparent classification of SM sources of King NL relevant for current and future isotope-shift experiments. The formalism can be applied to learn about the shape of the heavy scalar nuclei at a higher level of precision and detail than what was previously attainable. Comments: 44 pages, 7 figures, v2: Typos corrected Subjects: High Energy Physics - Phenomenology (hep-ph) ; Nuclear Theory (nucl-th); Atomic Physics (physics.atom-ph) Report number: WSU-HEP-2503 Cite as: arXiv:2512.03157 [hep-ph] (or arXiv:2512.03157v2 [hep-ph] for this version) https://doi.org/10.48550/arXiv.2512.03157 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Gil Paz [ view email ] [v1] Tue, 2 Dec 2025 19:03:20 UTC (365 KB) [v2] Mon, 24 Aug 2026 18:06:50 UTC (364 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: hep-ph < prev | next > new | recent | 2025-12 Change to browse by: nucl-th physics physics.atom-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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