On axion-mediated macroscopic forces again
  In a supersymmetric unified theory or in a generic model where a large neutron electric dipole moment $d_N$ is expected, close to the present bound, we estimate the relation g_aNN = 10^{-21\pm1}(d_N/10^{-25} e cm)(10^10 GeV/f_a) between d_N itself, the scalar coupling g_{aNN} to nucleons of the axion, assumed to exist, and the breaking scale, f_a, of the Peccei-Quinn symmetry. Newly developing techniques to search for sub-cm macroscopic forces might reveal a signal due to axion exchange at least in a favorable range of f_a. 
R. Barbieri, A. Romanino and A. Strumia