Consistent Perturbative Fixed Point Calculations in QCD and SQCD

Understand

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.