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

Various theories beyond the Standard Model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter which can possess spin-dependent couplings to electrons and nucleons. Present laboratory constraints on exotic spin-dependent interactions with pseudoscalar and axial couplings for exchange boson masses between meV and eV are very poor compared to constraints on spin-independent interactions in the same mass range arising from spin-0 and spin-1 boson exchange. It is therefore interesting to analyze in a general way how one can use the strong experimental bounds on spin-independent interactions to also constrain spin-dependent interactions by considering higher-order exchange processes. The exchange of a pair of bosons between two fermions with spin-dependent couplings will possess contributions which flip spins twice and thereby generate a polarization-independent interaction energy which can add coherently between two unpolarized objects. In this paper we derive the dominant long-range contributions to the interaction energy between two nonrelativistic spin-1/2 Dirac fermions from double exchange of spin-0 and spin-1 bosons proportional to couplings of the form gP4, gS2gP2, and gV2gA2. Our results for gP4 are in agreement with previous calculations that have appeared in the literature. We demonstrate the usefulness of this analysis to constrain spin-dependent couplings by presenting the results of a reanalysis of data from a short-range gravity experiment to derive an improved constraint on (gPN)2, the pseudoscalar coupling for nucleons, in the range between 40 and 200 μm of about a factor of 5 compared to previous limits. We hope that the expressions derived in this work will be employed by other researchers in the future to evaluate whether or not they can constrain exotic spin-dependent interactions from spin-independent measurements. The spin-independent contribution from 2-boson exchange with axial vector couplings of the form gA4 requires special treatment and will be explored in another paper.