Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD

We suggest how to consistently calculate the anomalous dimension γ∗ of the ψψ 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 γ∗ can be calculated exactly and fully scheme independently in a Banks-Zaks expansion through O(Δfn), where Δf=Nf-Nf, Nf is the number of flavors, and Nf is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory, the calculation preserves supersymmetry order by order in Δf. We then compute γ∗ through O(Δf2) for supersymmetric QCD in the dimensional reduction scheme and find that it matches the exact known result. We find that γ∗ is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute γ∗ through O(Δf3) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ∗ are observed for a large range of flavors.