Preprint number: CP3-Origins-2016-16 DNRF90 and DIAS-2016-16

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External link: arXiv.org

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. 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.