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

Abstract

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.