Probing Short-Distance Modifications of Gravity via Spin-Independent and Spin-Dependent Effects in Muonic Atoms

Abstract

High-precision 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 interaction ranges $\lambda \lesssim10^{-13}\text{m}$. 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 $\lambda \lesssim10^{-10}\text{m}$. Our findings highlight the widespread usefulness of muonic atoms in exploring new fundamental physics at short-distance scales.