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

TL;DR

This paper computes next-to-leading-order QCD contributions to a specific exotic tetraquark correlator, introduces a new methodology combining pySecDec with diagrammatic renormalization, and refines the mass bounds for the tetraquark state.

Contribution

It provides the first NLO calculation for the $J^{PC}=0^{+-}$, $duar dar u$ tetraquark correlator and establishes a new computational approach for QCD sum rule analyses.

Findings

NLO corrections significantly affect the predicted tetraquark mass range.

The mass bounds suggest mixing with hybrid states is possible.

No evidence for a tetraquark below 1.9 GeV within uncertainties.

Abstract

We calculated next-to-leading-order (NLO) QCD perturbative contributions to a $J^{PC}=0^{+-}$, $d u\bar d\bar u$ tetraquark (diquark-antidiquark) correlator in the chiral limit of massless $u$ and $d$ quarks. At NLO, there are four quark self-energy diagrams and six gluon-exchange diagrams. Nonlocal divergences were cancelled using diagrammatic renormalization. Dimensionally regularized integrals were numerically computed using pySecDec. The combination of pySecDec with diagrammatic renormalization establishes a valuable new methodology for NLO calculations of QCD correlation functions. Compared to leading-order (LO) perturbation theory, we found that NLO perturbation theory is significant. To quantify the impact of NLO perturbation theory on physical predictions, we computed NLO perturbative contributions to QCD Laplace, Gaussian, and finite-energy sum rules. Using QCD sum rules, we determined upper and lower bounds on the $0^{+-}$, $d u\bar d\bar u$ tetraquark ground-state mass, $M$: at NLO in perturbation theory, we found $2.2~\text{GeV}\lesssim M\leq 4.2~\text{GeV}$ whereas, at LO, we found $2.4~\text{GeV}\lesssim M\leq 4.6~\text{GeV}$. 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, we found no evidence for a $0^{+-}$, $d u\bar d\bar u$ tetraquark under 1.9 GeV.