  General flavor changing interactions for a Goldstone boson (GB) to fermions
due to a spontaneous global $U(1)_G$ symmetry breaking are discussed. This GB
may be the Axion, solving the strong QCD CP problem, if there is a QCD anomaly
for the $U(1)_G$ charge assignments for quarks. Or it may be the Majoron in
models from lepton number violation in producing seesaw Majorana neutrino
masses if the symmetry breaking scale is much higher than the electroweak
scale. It may also, in principle, play the roles of Axion and Majoron
simultaneously as far as providing solution for the strong CP problem and
generating a small Majorana neutrino masses are concerned. Great attentions
have been focused on flavor conserving GB interactions. Recently flavor
changing Axion and Majoron models have been studied in the hope to find new
physics from rare decays in the intensity frontier. In this work, we will
provide a systematic model building aspect study for a GB having flavor
changing neutral current (FCNC) interactions in both the quark and lepton
sectors, or separately in the quark, charged lepton and neutrino sectors with
sources of FCNC interactions identified in detail. We provide a general proof
of the equivalence of using physical GB components and GB broken generators for
calculating GB couplings to two gluons and two photons, and some issues related
to models having spontaneous CP violation are discussed. We will also provide
some details for obtaining FCNC GB interactions in several popular models, such
as the Type-I, -II, -III seesaw and Left-Right symmetric models, and point out
some special features in these models.
