Constraints on a long-range spin-independent interaction from precision atomic physics

Constraints on a spin-independent interaction by the exchange of a neutral light boson are derived from precision data on the electron anomalous magnetic moment and from atomic spectroscopy of hydrogen and deuterium atoms. The mass range from $1\mathrm{eV}/c^2$ to $1\mathrm{MeV}/c^2$ is studied, and the effective coupling constant ${\alpha }^{\prime }$ is allowed below the level of ${10}^{-11}–{10}^{-13}$ depending on the value of the boson mass. The mass range corresponds to the Yukawa radius from 0.0002 nm to 20 nm, which covers the distances far above and far below the Bohr radius of the hydrogen atom.

Figure 1

Constraints on a long-term spin-independent interaction from hydrogen spectroscopy and $g_e-2$, including a constraint from hydrogen spectroscopy with low and Rydberg states ($a$), a comparison of low states, and $g_e-2$ ($b$). The lines are for $|{\alpha }^{\prime }|$, and the confidence level corresponds to 1 standard deviation.

Figure 2

The profile functions which determine the coverage of the constraints on a long-term spin-independent interaction from hydrogen spectroscopy and the anomalous magnetic moment of an electron. The profile function ${\mathcal{F}}_{30}(x)$ is with $n=27$ and $n=29$.

Figure 3

Determination of the fine structure constant $\alpha$ in the CODATA-2006 adjustment [1], where the references can be found. The vertical band stands for the adjusted CODATA-2006 value. The figure is reproduced from 26.