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.
Parent problems
- Special case of Semiclassical origin of renormalons in asymptotically free theories · open · from revision 1 The parent was revised since revision 1: it now states another question.
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