论文标题
对$ j^{pc} = 0^{+ - } $，$ du \ bar {d} \ bar {u} $ tetraquark corelator的临近订单（NLO）QCD QCD扰动贡献的总和分析
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
论文作者
论文摘要
我们计算了对$ j^{pc} = 0^{+ - } $，$ d u \ bar d \ bar d \ bar u $ tetraquark（diquark-antidiquark）相关器的近代领域（NLO）QCD扰动贡献。在NLO，有四个夸克自能图和六个Gluon-Extchange图。使用图解的重态化取消了非局部差异。使用PYSECDEC对尺寸正则化积分进行数值计算。 PYSECDEC与示意性重新归化的组合为NLO计算QCD相关函数的计算建立了有价值的新方法。与领先（LO）扰动理论相比，我们发现NLO扰动理论很重要。为了量化NLO扰动理论对物理预测的影响，我们计算了NLO对QCD拉普拉斯，高斯和有限能源总和规则的扰动贡献。使用QCD总规则，我们确定了$ 0^{+ - } $，$ d u \ bar d \ bar d \ bar u $ tetraquark地基质量，$ M $：在扰动理论中的上限和下限$ 2.4〜 \ text {gev} \ sillsim m \ leq 4.6〜 \ text {gev} $。该质量范围表明，可以在$ 0^{+ - } $，Light-Quark（即$ u $和$ u $和$ d $ Quarks）混合中混合混合和$ d u \ bar d \ bar d \ bar u $ tetraquark States。考虑到QCD参数中的不确定性，我们没有发现$ 0^{+ - } $，$ d u \ bar d \ bar u $ tetraquark以下1.9 GEV下的证据。
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.
