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We study the conformal window of QCD using perturbation theory, starting fromthe perturbative upper edge and going down as much as we can towards thestrongly coupled regime. We do so by exploiting the available five-loopcomputation of the $\overline{{\rm MS}}$ $\beta$-function and employing Borelresummation techniques both for the ordinary perturbative series and for theBanks-Zaks conformal expansion. Large-$n_f$ results are also used. We arguethat the perturbative series for the $\overline{{\rm MS}}$ $\beta$-function ismost likely asymptotic and non-Borel resummable, yet Borel resummationtechniques allow to improve on ordinary perturbation theory. We findsubstantial evidence that QCD with $n_f=12$ flavours flows in the IR to aconformal field theory. Though the evidence is weaker, we find indications thatalso $n_f=11$ might sit within the conformal window. We also compute the valueof the mass anomalous dimension $\gamma$ at the fixed point and compare it withthe available lattice results. The conformal window might extend for lowervalues of $n_f$, but our methods break down for $n_f<11$, where we expect thatnon-perturbative effects become important. A similar analysis is performed inthe Veneziano limit.

Looking through the QCD Conformal Window with Perturbation Theory