Hyperfine structure interval of the $2s$ state of hydrogenlike atoms and a constraint on a pseudovector boson with mass below 1 keV$/c^2$

A constraint on a spin-dependent interaction, induced by a pseudovector light boson, is presented. The interaction includes a Yukawa-type contribution $\alpha {}^{″}({\mathbf{s}}_1·{\mathbf{s}}_2)e^{-\lambda r}/r$ and a contact spin-spin term. To disentangle the long-range and contact terms we utilize experimental data on the $1s$ and $2s$ hyperfine intervals for light two-body atoms and construct a specific difference $8\times E_{\mathrm{hfs}}(2s)-E_{\mathrm{hfs}}(1s)$. That allows one to constrain the spin-dependent coupling constant $\alpha {}^{″}$ of an electron-nucleus Yukawa-type interaction in hydrogen, deuterium, and the helium-3 ion at the level below a part in ${10}^{16}$. The derived constraint is related to the range of masses below $4\hspace{0.5em}\mathrm{keV}/c^2$. The combined constraint including the contact terms is also presented.

Figure 1

Constraints on a pseudovector intermediate boson from $D_{21}$ in hydrogen, deuterium, and helium-3 ion. The lines present an upper bound for $\left|\alpha {}^{″}\right|$. The confidence level corresponds to one standard deviation.

Figure 2

Constraints on a pseudovector intermediate boson from the hfs study. The lines present the upper bound for $\left|\alpha {}^{″}\right|$ from data on $D_{21}$ (solid lines; see Fig. 1 for details) and the $1s$ hfs interval (dashed lines) in various two-body atoms. The $1s$ results are from [5]. The confidence level corresponds to one standard deviation.

Figure 3

The profile functions giving the upper bound for $\left|\alpha {}^{″}\right|$ from data on $D_{21}$ and the $1s$ hfs interval (in various two-body atoms. The $1s$ results are from [5].

Figure 4

Constraints on a pseudovector intermediate boson. The lines present the upper bound for the coupling constant $|{\alpha }_A(\mathit{xy})|$ for $\mathit{xy}=\mathit{pe},\mathit{ne},\mu e$ from data on the hfs intervals in various two-body atoms. The confidence level corresponds to one standard deviation.

Figure 5

Constraints on a pseudovector intermediate boson from data on the hfs structure of muonium and hydrogen. The solid lines represent the upper bound for the coupling constant $|{\alpha }_A(\mathit{xy})|$ for $\mathit{xy}=\mathit{pe}$ and $\mu e$ ignoring the longitudinal term, while the dashed lines are for the constraints taking those terms into account. The confidence level corresponds to one standard deviation.