Stringent Constraints on New Pseudoscalar & Vector Bosons from Precision Hyperfine Splitting Measurements

Abstract

Axion-like particles and similar new pseudoscalar as well as vector bosons coupled to nucleons and electrons are predicted to lead to spin-dependent forces in atoms and ions. We argue that hyperfine structure measurements in hydrogen- and lithium-like charge states are a sensitive probe to this effect. Employing specific differences of these splittings reduces uncertainties due to nuclear effects in hyperfine structure calculations and measurements. Using this, we show that existing measurements on Be provide competitive limits in the region $m_φ\gtrsim 100\,{\rm keV}$, confirming, or improving by up to a factor of 2, existing constraints for pseudoscalar couplings, depending on the nuclear model. We also find that future measurements on Cs have a further factor of $2-2.5$ improved discovery potential for pseudoscalars and an order of magnitude for new vector bosons when compared with the corresponding current constraints.

Figures (2)

• Figure 1: Bounds on the pseudoscalar (top) and vector (bottom) parameter space. The left plots $(a)$ and $(c)$ show bounds on the product of the electron & proton couplings, whereas the right, $(b)$ and $(d)$, show the bounds on the product of electron & neutron couplings. Red lines (projections) and orange regions (current constraints) are derived in this work. The gray area on the left denotes bounds from the hydrogen specific difference $D_{21}^{\rm H}$Cong:2024nat and $1s$ HFS PhysRevA.108.052804. The gray area on the right-hand side denotes bounds from the helium-$3$ specific difference $D_{21}^{\rm He}$ and $1s$ HFS. In the vector electron–neutron case, isotope-shift constraints are shown in purple Cong:2024qlyPhysRevD.96.115002. Green shows TEXONO Chang_2007 and Borexino BOREXINO:2025dbp constraints; blue denotes astrophysical constraints Cong:2024qly. Solid lines show conservative bounds accounting for estimated uncertainties (see Appendix) and possible Schmidt-model errors Kimball_2015. Dashed lines indicate Schmidt model results. The bismuth constraint is a projection assuming that a direct measurement of the magnetic moment will agree with the NMR result.
• Figure 2: Version of our results that includes the error bands (shaded regions) on our constraints/sensitivity projections (solid lines) from our comparison with Ref. PhysRevResearch.2.013364, as well as the errors arising from our choice of nuclear model for the coupling to the nucleus Kimball_2015. Dashed lines indicate bounds derived within the one particle Schmidt model.