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We suggest how to consistently calculate the anomalous dimension $\gamma_*$of the $\bar{\psi}\psi$ operator in finite order perturbation theory at aninfrared fixed point for asymptotically free theories. If the $n+1$ loop betafunction and $n$ loop anomalous dimension are known then $\gamma_*$ can becalculated 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 byorder in $\Delta_f$. We then compute $\gamma_*$ through $O(\Delta_f^2)$ forsupersymmetric QCD in the $\overline{\text{DR}}$ scheme and find that itmatches the exact known result. We find that $\gamma_*$ is astonishingly welldescribed in perturbation theory already at the few loops level throughout theentire 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.

Consistent Perturbative Fixed Point Calculations in QCD and SQCD