Consistent Perturbative Fixed Point Calculations in QCD and SQCD
TA Ryttov - arXiv preprint arXiv:1604.00687, 2016 - arxiv.org
TA Ryttov
arXiv preprint arXiv:1604.00687, 2016•arxiv.orgWe 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 …
$\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 …
We suggest how to consistently calculate the anomalous dimension of the operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the loop beta function and loop anomalous dimension are known then can be calculated exactly and fully scheme independently through where and is the number of flavors and is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory the calculation preserves supersymmetry order by order in . We then compute through for supersymmetric QCD in the scheme and find that it matches the exact known result. We find that is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute through for QCD and a variety of other non-supersymmetric fermionic gauge theories. Small values of are observed for a large range of flavors.
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