QFT In the literature: open

Does QCD perturbation theory plus condensates resum to the exact answer

In plain words

QCD predictions combine a divergent power series with small corrections from vacuum condensates. Whether this combination, properly resummed, is complete and unambiguous is unknown.

Precise statement

For the Adler function $D(Q^2)$ of massless QCD, determine whether the perturbative series in $\alpha_s(Q^2)$ together with OPE power corrections (condensates such as $\langle \alpha_s G^2\rangle/Q^4$) forms a resurgent transseries whose median resummation equals the exact function, with each condensate uniquely defined once the summation prescription is fixed.

What would settle it

A proof in QCD or a controlled large-$N_{f}$ or lattice comparison showing the resummed transseries equals $D(Q^{2})$, or a counterexample term not captured by the OPE.

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