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

TL;DR

The paper tackles the problem of testing short-distance modifications to gravity by leveraging high-precision muonic-atom spectroscopy. It deploys three complementary methods: spin-independent Yukawa-type corrections from the $2S-2P$ Lamb shift in $(\mu^{4}\mathrm{He})^{+}$ and from the muonic H–D isotope shift via $r_d^2-r_p^2$, and spin-dependent effects through gravitational spin-orbit coupling on the $2P_{3/2}-2P_{1/2}$ fine structure in muonic helium, within a Post-Newtonian framework. The analysis yields exclusion regions in the Yukawa parameter space $(\lambda,\alpha)$ with isotope shifts providing the strongest constraints for $\lambda \lesssim 10^{-13}$ m, and bounds on the Post-Newtonian combination $(\alpha/2+\tilde{\alpha})$ for $\lambda \lesssim 10^{-10}$ m that outperform several competing techniques. Overall, the results demonstrate that muonic atoms offer a powerful and competitive avenue to probe gravity at sub-nanometer scales, potentially uncovering new physics beyond the Standard Model.

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

Figures (2)

• Figure 1: Exclusion limits for the spin-independent Yukawa strength parameter $\alpha$ as a function of the interaction range $\lambda$. The new constraints derived in this work, obtained from the $\mu^{4}\text{He}^{+}$$2S-2P$ Lamb shift (Sec. II) and the $r_{d}^{2}-r_{p}^{2}$ isotope shift (Sec. III), are shown as dashed lines. These are compared with the existing $90\%$ C.L. spectroscopic bounds from atomic transitions (such as H(1S-3S) and p$^{4}$He$^{+}$) lemos4 and molecular HD$^{+}$ transitions Germann:2021koc. The shaded area denotes the excluded region.
• Figure 2: Constraints on the PPN parameter combination $(\alpha/2+\tilde{\alpha})$ at $68\%$ C.L.. The new bound derived in this work from the muonic helium-4 fine-structure splitting is depicted by the dashed blue line. This result is compared with existing limits from neutron interferometry Rocha:2021zgw (green line), MTV-G experiment data murataTanaka:2014jfaTanaka:2013ika (purple line), and from the analysis of the fine-structure of the hydrogen $2P$-level lemos4 (red line). The parameter space within the shaded region is excluded.