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We develop a new technique, based on a low-energy theorem (LET) of NSVZ typederived in arXiv:1701.07833, for the nonperturbative investigation of SU(N) QCDwith N${}_f$ massless quarks - or, more generally, of massless QCD-liketheories - in phases where the beta function, $\beta(g)$, with $g=g(\mu)$ therenormalized gauge coupling, admits an isolated zero, $g_*$, in the infrared(IR) or ultraviolet (UV). We point out that the LET sets constraints on 3-pointcorrelators involving the insertion of $Tr\, F^2$, its anomalous dimension$\gamma_{F^2}$, and the anomalous dimensions of multiplicatively renormalizableoperators at $g_*$. These constraints intertwine with the exact conformalscaling for $g(\mu)\rightarrow g_*$ with $\mu\neq 0,+\infty$ fixed and theIR/UV asymptotics - which may or may not coincide with the IR/UV limit of theaforementioned conformal scaling - for $\Lambda_{\scriptscriptstyle{IR/UV}}$fixed. In the conformal case we also discuss how the LET for bare correlatorsis the rationale for the existence in massless QCD of the mysterious divergentcontact term in the OPE of $Tr\,F^2$ with itself discovered in perturbationtheory in arXiv:1209.1516, arXiv:1407.6921 and computed to all orders inarXiv:1601.08094. Specifically, if $\gamma_{F^2}$ does not vanish, thedivergent contact term in the rhs of the LET for the 2-point correlator of$Tr\,F^2$ has to match - and we verify by direct computation that it actuallydoes - the divergence in the lhs due to the nontrivial anomalous dimension of$Tr\,F^2$. Hence, remarkably, the additive renormalization due to the divergentcontact term in the rhs is related by the LET to the multiplicativerenormalization in the lhs, in such a way that a suitably renormalized versionof the LET has no ambiguity for additive renormalization.

Low-energy theorem and OPE in the conformal window of massless QCD