Constraining the couplings of massive pseudoscalars using gravity and optical experiments

The simultaneous exchange of two pseudoscalars between fermions leads to a spin-independent force between macroscopic objects. Previous work has demonstrated that one can combine this interaction with tests of the weak equivalence principle, gravitational inverse square law, and studies of laser beam propagation in magnetic fields, to set significant new constraints on the Yukawa couplings of massless pseudoscalars to nucleons. Here we extend these results to massive pseudoscalars, and derive new constraints which relate the strengths of these couplings to the pseudoscalar mass.