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

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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+gamma*) and F mηF(gamma*) for the decay constants, thereby generalizing our results from a previous paper to the entire spectrum. We derive the scaling law mₕ m1/(1+gamma*) using the Hellmann-Feynman theorem, and thus provide a derivation which does not rely on renormalization group arguments. Using the new results we reiterate, on the phenomenologically important, S-parameter. Finally, we discuss how spectral representations can be used to relate the mass and decay constant trajectories.