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

We present a phenomenological constraint on a long-range spin-dependent interaction ${\alpha }^{\prime \prime }({\mathbf{s}}_1·{\mathbf{s}}_2){\mathrm{e}}^{-\lambda r}/r$, which can be induced by a pseudovector light boson beyond the standard model. In the range of masses from $4\mathrm{keV}/c^2$ to those related to macroscopic distances (${\lambda }^{-1}\sim 1\mathrm{cm}$) 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 if extended to higher masses. The strongest constraint is related to the lepton-lepton interaction. Constraints on spin-dependent interactions of an electron with some other particles are also discussed. The results are obtained from data on the hyperfine splitting (HFS) interval of the ground state in muonium and a few other light hydrogenlike atoms.

Figure 1

Constraint on a long-term spin-dependent interaction from the HFS intervals of the ground state in light two-body atoms. The lines present the upper bound on $|{\alpha }^{\prime \prime }|$ from data on the $1s$ HFS interval in muonium, hydrogen, deuterium, tritium, helium-3 ion, and positronium. A mass of an intermediate particle $\lambda$ is the inverse Yukawa radius. The confidence level is related to one standard deviation.