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

Understand

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 m_H ~ m^{1/(1+gamma*)} and F ~ m^{\eta_F(gamma*)} for the decay constants, thereby generalizing our results from a previous paper to the entire spectrum.
• We derive the scaling law m_H \~m^{1/(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.