Scaling relations for the entire spectrum in mass-deformed conformal gauge theories

We consider mass-deformed conformal gauge theories (mCGT) and investigate the scaling behaviour of hadronic observables as a function of the fermion mass. Applying renormalization group arguments directly to matrix elements, we find mH∼m1/(1+γ⁎) and F∼mηF(γ⁎) for given ηF(γ⁎), for the hadronic masses and the decay constants respectively, thereby generalizing our results from a previous paper to the entire spectrum. Applying the Hellmann-Feynman theorem to the trace anomaly we obtain the hadron mass scaling independent of renormalization group arguments. From the trace anomaly we obtain a relation reminiscent of the Gell-Mann-Oakes-Renner relation in QCD. Using the new results we discuss the scaling of the S-parameter inside the conformal window. Finally, we discuss how spectral representations can be used to relate the mass and decay constant trajectories.