## Consistent calculations of physical quantities in Physical Review Letters

August 18, 2016

In the Letter it is suggested 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 in a Banks-Zaks expansion 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 $$\Delta_f$$. $$\gamma_*$$ is then computed through $$O(\Delta_f^2)$$ for supersymmetric QCD in the $$\overline{\text{DR}}$$ scheme and it is found 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.