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We calculated next-to-leading-order (NLO) QCD perturbative contributions to a$J^{PC}=0^{+-}$, $d u\bar d\bar u$ tetraquark (diquark-antidiquark) correlatorin the chiral limit of massless $u$ and $d$ quarks. At NLO, there are fourquark self-energy diagrams and six gluon-exchange diagrams. Nonlocaldivergences were cancelled using diagrammatic renormalization. Dimensionallyregularized integrals were numerically computed using pySecDec. The combinationof pySecDec with diagrammatic renormalization establishes a valuable newmethodology for NLO calculations of QCD correlation functions. Compared toleading-order (LO) perturbation theory, we found that NLO perturbation theoryis significant. To quantify the impact of NLO perturbation theory on physicalpredictions, we computed NLO perturbative contributions to QCD Laplace,Gaussian, and finite-energy sum rules. Using QCD sum rules, we determined upperand lower bounds on the $0^{+-}$, $d u\bar d\bar u$ tetraquark ground-statemass, $M$: at NLO in perturbation theory, we found $2.2~\text{GeV}\lesssimM\leq 4.2~\text{GeV}$ whereas, at LO, we found $2.4~\text{GeV}\lesssim M\leq4.6~\text{GeV}$. This mass range suggests the possibility of mixing between$0^{+-}$, light-quark (i.e., $u$ and $d$ quarks) hybrid and $d u\bar d\bar u$tetraquark states. Taking into account uncertainties in QCD parameters, wefound no evidence for a $0^{+-}$, $d u\bar d\bar u$ tetraquark under 1.9 GeV.

A Sum-Rules Analysis of Next-to-Leading-Order (NLO) QCD Perturbative Contributions to a $J^{PC}=0^{+-}$, $du\bar{d}\bar{u}$ Tetraquark Correlator