Constraints on Light Pseudoscalars Implied by Tests of the Gravitational Inverse-Square Law

The exchange of light pseudoscalars between fermions leads to a spinindependent potential in order g4, where g is the Yukawa pseudoscalar-fermion coupling constant. This potential gives rise to detectable violations of both the weak equivalence principle (WEP) and the gravitational inverse-square law (ISL), even if g is quite small. We show that when previously derived WEP constraints are combined with those arising from ISL tests, a direct experimental limit on the Yukawa coupling of light pseudoscalars to neutrons can be inferred for the first time (g2 n/4π ∼ 1.6×10−7), along with a new (and significantly improved) limit on the coupling of light pseudoscalars to protons. 04.80.Ce, 14.80.-j Typeset using REVTEX