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Various theories beyond the Standard Model predict new particles with massesin the sub-eV range with very weak couplings to ordinary matter which canpossess spin-dependent couplings to electrons and nucleons. Present laboratoryconstraints on exotic spin-dependent interactions with pseudoscalar and axialcouplings for exchange boson masses between meV and eV are very poor comparedto constraints on spin-independent interactions in the same mass range arisingfrom spin-0 and spin-1 boson exchange. It is therefore interesting to analyzein a general way how one can use the strong experimental bounds onspin-independent interactions to also constrain spin-dependent interactions byconsidering higher-order exchange processes. The exchange of a pair of bosonsbetween two fermions with spin-dependent couplings will possess contributionswhich flip spins twice and thereby generate a polarization-independentinteraction energy which can add coherently between two unpolarized objects. Inthis paper we derive the dominant long-range contributions to the interactionenergy between two nonrelativistic spin-1/2 Dirac fermions from double exchangeof spin-0 and spin-1 bosons proportional to couplings of the form $g_P^{4}$,$g_S^{2}g_P^{2}$, and $g_V^{2}g_A^{2}$. Our results for $g_P^{4}$ are inagreement with previous calculations that have appeared in the literature. Wedemonstrate the usefulness of this analysis to constrain spin-dependentcouplings by presenting the results of a reanalysis of data from a short-rangegravity experiment to derive an improved constraint on $(g^N_{P})^2$, thepseudoscalar coupling for nucleons, in the range between $40$ and $200~\mu$m ofabout a factor of 5 compared to previous limits. The spin-independentcontribution from 2-boson exchange with axial-vector couplings requires specialtreatment and will be explored in another paper.

physical review. d/physical review. d.

Calculations of the dominant long-range, spin-independent contributions  to the interaction energy between two nonrelativistic Dirac fermions from  double-boson exchange of spin-0 and spin-1 bosons with spin-dependent  couplings