Three-body QED test and fifth-force constraint from vibrations and rotations of ${\mathrm{HD}}^{+}$

We present a parts-per-million test of quantum electrodynamics (QED) in the ${\text{HD}}^{+}$ molecular hydrogen ion, improving on previous tests based on vibrational and rotational transitions by factors of 76 and 1.4, respectively. The test is performed following a unified statistical approach that also produces improved constraints on physics beyond the standard model. We furthermore show how individual constraints derived from the various degrees of freedom in ${\text{HD}}^{+}$ and antiprotonic helium can be combined to enhance the sensitivity, thus ruling out “fifth forces” on the Ångstrom scale that are ${10}^{11}$ times weaker than the electromagnetic interaction.

Figure 1

Sizes and signs of contributions of order $R_{\infty }{\alpha }^n$ to the SM prediction of the $(v,L)$: $(0,3)\to (9,3)$ transition frequency ${\nu }_{\text{theo}}$. Light blue, pure relativistic terms; dark blue, QED corrections. Contributions from muonic and hadronic vacuum polarization are also shown. The combined uncertainty (dashed horizontal line) is comparable to the $R_{\infty }{\alpha }^6$-order QED correction. Inset: Frequency uncertainties, $u$, of the contributions of orders $R_{\infty }{\alpha }^4$ through $R_{\infty }{\alpha }^6$ (the lower-order and NR terms are essentially exact). The experimental uncertainty, $u\left({\nu }_{\text{expt}}\right)$, is small enough to test state-of-the-art three-body QED theory at its very limit. The quadratic sum of all uncertainties shown here, including the contribution from the physical constants, $u\left({\nu }_{\text{constants}}\right)$, equals ${\sigma }_{c,\mathrm{vib}}$.

Figure 2

90%-CL constraints on scalar hadron-hadron interactions inferred from a hypothesis test with significance level 0.0027. Individual constraints are obtained from rotational and vibrational spectroscopy of ${\text{HD}}^{+}$ and from studies of ${\overline{\text{p}}}^3\text{He}$ and ${\overline{\text{p}}}^4\text{He}$ [8, 9, 15, 16, 24]. Black curve: Combined constraint obtained from a least-squares adjustment involving seven transitions. The upper yellow region indicates $(\lambda ,{\alpha }_5)$ values excluded by the ${\mathrm{H}}_2$ dissociation limit (solid yellow curve [39]) and the previous best constraint from vibrational spectroscopy of ${\text{HD}}^{+}$ (dashed yellow curve [19]). Below, the orange area represents the parameter space excluded by the work of Alighanbari et al. [8]. Our combined constraint expands the excluded area further into the light blue region. The solid gray curve illustrates the constraint on a hypothetical electron-neutron coupling based on the three recent ${\text{HD}}^{+}$ measurements [8, 9, 24].