Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD

摘要

We suggest how to consistently calculate the anomalous dimension gamma* of the (psi) over bar 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(n)(f)), where Delta(f) = (N) over bar (f) - N-f, N-f is the number of flavors, and (N) over barf 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(2)(f)) for supersymmetric QCD in the dimensional reduction 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(3)(f)) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of gamma* are observed for a large range of flavors.