Consistent calculations of physical quantities in Physical Review Letters

August 18, 2016

The article Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD by CP3-Scientist Thomas Ryttov has just been been published in the prestigious journal Physical Review Letters.

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.