Units and numerical values of the effective couplings in perturbative heterotic string vacua

We determine the units and numerical values for a class of couplings in the effective theory of perturbative heterotic string vacua, with the emphasis on the correct translation between the canonical gauge coupling g and Planck scale M-Planck similar to 1.2x10(19) GeV as used in the effective theory description and the string coupling g(string) and string tension alpha' as used in the S-matrix amplitude calculation. In particular, we determine the effective couplings in the superpotential and reexamine the Fayet-Iliopoulos (FI) term in a class of models with an anomalous U(1). We derive the values of the effective Yukawa couplings (at the third and fourth order) after the restabilization of vacuum along a particular F- and D-flat direction and show that they are comparable in magnitude. The result corrects results quoted in the literature, and may have implications for the string derived phenomenology, e.g., that of fermion textures. [S0556-2821(99)03510-9].