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

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 $$2S-2P$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>S</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> <mml:mi>P</mml:mi> </mml:mrow> </mml:math> 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 $$\lambda \lesssim 10^{-12}\text { m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>≲</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:mtext>m</mml:mtext> </mml:mrow> </mml:math> . For spin-dependent effects, we analyze the influence of the gravitational spin–orbit coupling on the $$2P_{3/2}-2P_{1/2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>P</mml:mi> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>P</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> 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 $$\lambda \lesssim 10^{-11}\text { m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>≲</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>11</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:mtext>m</mml:mtext> </mml:mrow> </mml:math> . Our findings highlight the widespread usefulness of muonic atoms in exploring new fundamental physics at short-distance scales.