## Consistent Perturbative Fixed Point Calculations in QCD and SQCD

Preprint number: CP3-Origins-2016-16 DNRF90 and DIAS-2016-16
Author:
We suggest how to consistently calculate the anomalous dimension $$\gamma_*$$ of the $$\bar{\psi}\psi$$ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the $n+1$ loop beta function and $n$ loop anomalous dimension are known then $$\gamma_*$$ can be calculated exactly and fully scheme independently through $$O(\Delta_f^n )$$ where $$\Delta_f = \bar{N_f} – N_f$$ and $$N_f$$ is the number of flavors and $$\bar{N}_f$$ is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory the calculation preserves supersymmetry order by order in $$\Delta_f$$. We then compute $$\gamma_*$$ through $$O(\Delta_f^2)$$ for supersymmetric QCD in the $$\overline{\text{DR}}$$ scheme and find that it matches the exact known result. We find that $$\gamma_*$$ is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute $$\gamma_*$$ through $$O(\Delta_f^3)$$ for QCD and a variety of other non-supersymmetric fermionic gauge theories. Small values of $$\gamma_*$$ are observed for a large range of flavors.