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

TL;DR

This paper investigates the scaling behavior of hadronic observables in mass-deformed conformal gauge theories, deriving new relations for masses and decay constants as functions of fermion mass using renormalization group and Hellmann-Feynman theorem.

Contribution

It generalizes previous results to the entire spectrum and introduces a derivation of scaling laws that does not depend on renormalization group arguments.

Findings

Mass scales as m^{1/(1+gamma*)}

Decay constants scale as m^{eta_F(gamma*)}

Provides insights into the S-parameter and spectral relations

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 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. Finally, we discuss how spectral representations can be used to relate the mass and decay constant trajectories.