Toward the Effective Light and Heavy QCD Axion Scenarios

In this work, we investigate the effective parameter space associated with the axion mass and the axion decay constant in both the light and heavy QCD axion scenarios. We initiate our discussion by considering the simplest case of two axions, quantitatively analyzing the parameter space in these two distinct scenarios. We find that the axion mass ratios exhibit a high degree of similarity in these two situations. In contrast, the ratios of axion decay constants display a complete opposition. Furthermore, we generalize our conclusions to encompass the case of multiple axions.