HFS interval of the $2s$ state of hydrogen-like atoms and a constraint on a pseudovector boson with mass below $1\;$keV$/c^2$

Abstract: A constraint on a long-range spin-dependent interaction $\alpha^{\prime\prime}({\bf s}1\cdot{\bf s}_2)\,{\rm e}^{-\lambda r}/r$, which can be induced by a pseudovector light boson, is presented. We study theoretical and experimental data on a specific difference $8\times E{\rm hfs}(2s)-E_{\rm hfs}(1s)$ for light two-body atoms. The spin-dependent coupling constant $\alpha^{\prime\prime}$ of electron-nucleus interaction in hydrogen, deuterium and helium-3 ion is constrained at the level below a part in $10^{16}$. The derived constraints are related to the range of masses below $4\;{\rm keV}/c^2$.