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

We present a phenomenological constraint on a pseudovector light boson beyond the Standard Model, which can induce a long-range spin-dependent interaction $\alpha^{\prime\prime}({\bf s}_1\cdot{\bf s}_2)\,{\rm e}^{-\lambda r}/r$. In the range of masses from $4\;{\rm keV}/c^2$ to those related to macroscopic distances (of $\lambda^{-1}\sim1\;$cm) the spin-dependent coupling constant $\alpha^{\prime\prime}$ of the electron-muon interaction is constrained at the level below a part in $10^{15}$. The constraint is weakened while extending to higher masses. The strongest constraint is related to the lepton-lepton interaction. Constraints on spin-dependent interactions of some other particles are also discussed. The results are obtained from data on the HFS interval of the ground state in muonium and a few other light hydrogen-like atoms.