Eur. Phys. J. Plus (2026) 141: 328
https://doi.org/10.1140/epjp/s13360-026-07560-5

Regular Article

Probing short-distance modifications of gravity via spin-independent and spin-dependent effects in muonic atoms

¹ Department of Physics, Federal University of Paraiba, 58051-900, João Pessoa, PB, Brazil
² Departamento de Ciências Exatas e Tecnologia da Informação, Universidade Federal Rural do Semi-Árido, 59515-000, Angicos, Rio Grande do Norte, Brazil

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Received: 5 January 2026
Accepted: 10 March 2026
Published online: 24 March 2026

Abstract

Spectroscopy of muonic atoms provides a powerful probe for new short-range interactions predicted by theories beyond the Standard Model (SM). In this work, we derive new constraints on both spin-independent and spin-dependent non-Newtonian gravity by leveraging the outstanding sensitivity of these systems. For spin-independent Yukawa-type forces, we analyze two complementary approaches: the $2S-2P$ Lamb shift in the muonic helium-4 ion and the deuteron–proton squared charge radii difference obtained from the muonic hydrogen–deuterium isotope shift. The found constraints have reached a competitive level at sub-picometer scales, with the isotope shift method yielding the most stringent bounds for the entire sub-nanometer range and significantly surpassing limits derived exclusively from electronic atom spectroscopy for $\lambda \lesssim {10}^{-12}\text{m}$. For spin-dependent effects, we analyze the influence of the gravitational spin–orbit coupling on the $2P_{3/2}-2P_{1/2}$ fine-structure splitting in muonic helium, establishing new limits on post-Newtonian parameters. These bounds are shown to be more restrictive than those from other leading experimental techniques for ranges $\lambda \lesssim {10}^{-11}\text{m}$. Our findings highlight the widespread usefulness of muonic atoms in exploring new fundamental physics at short-distance scales.