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

Abstract

We calculated next-to-leading-order (NLO) QCD perturbative contributions to a $J^{PC}=0^{+-}$, $du\bar{d}\bar{u}$ 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 $0^{+-}$, $du\bar{d}\bar{u}$ tetraquark ground-state mass, $M$: at NLO in perturbation theory, we found $2.2\text{GeV}\lesssim M\le 4.2\text{GeV}$ whereas, at LO, we found $2.4\text{GeV}\lesssim M\le 4.6\text{GeV}$. This mass range suggests the possibility of mixing between $0^{+-}$, light-quark (i.e., $u$ and $d$ quarks) hybrid and $du\bar{d}\bar{u}$ tetraquark states. Taking into account uncertainties in QCD parameters, we found no evidence for a $0^{+-}$, $du\bar{d}\bar{u}$ tetraquark under 1.9 GeV.

arXiv comment22 pages, 13 figures. Updated version contains additional discussion

References in corpus (36)

• Hadronic molecules
• The hidden-charm pentaquark and tetraquark states
• Cuba - a library for multidimensional numerical integration
• Observation of a charged charmoniumlike structure in e+e- to pi+pi-J/psi at \sqrt{s}=4.26 GeV
• The $XYZ$ states: experimental and theoretical status and perspectives
• Non-Standard Heavy Mesons and Baryons, an Experimental Review
• Pentaquark and Tetraquark states
• Heavy-Quark QCD Exotica
• Study of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ and Observation of a Charged Charmonium-like State at Belle
• Exotics: Heavy Pentaquarks and Tetraquarks
• Observation of structure in the $J/\psi$-pair mass spectrum
• A new look at scalar mesons
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• Evidence for a $B_s^0{\pi }^{\pm }$ State
• QCD tests from $e^+e^- \rar I=1~$ hadrons data and implication on the value of ${\alpha }_s$ from $\tau$-decays
• Gluon Condensates and m_b(m_b) from QCD-Exponential Moments at Higher Orders
• Recent Progress in QCD Condensate Evaluations and Sum Rules
• The I^G J^{PC}=1^- 1^{-+} Tetraquark States
• How small can the light quark masses be?
• The I^G J^{PC}=0^+ 1^{-+} Tetraquark State
• A Gaussian Sum-Rules Analysis of Scalar Glueballs
• Study of the $X^{\pm }(5568)$ state with semileptonic decays of the $B_s^0$ meson
• Gaussian Sum-Rules and Prediction of Resonance Properties
• The Possible J^{PC}=0^{--} Exotic State
• Light 1-+ exotics: molecular resonances
• Investigation of the light four-quark states with exotic $J^{PC}=0^{--}$
• Instanton Effects on the Role of the Low-Energy Theorem for the Scalar Gluonic Correlation Function
• Mass Calculations of Light Quarkonium, Exotic $J^{PC}=0^{+-}$ Hybrid Mesons from Gaussian Sum-Rules
• Possible $J^{PC}=0^{+-}$ Exotic State
• QCD Coulomb Gauge Approach to Exotic Hadrons
• Holder Inequalities and Bounds on the Masses of Light Quarks
• Exotic tetraquark states with $J^{PC}=0^{+-}$
• Perturbative $O({\alpha }_s)$ corrections to the correlation functions of light tetraquark currents
• Next-to-Leading Order (NLO) Perturbative Effects in QCD Sum-Rule Analyses of Light Tetraquark Systems: A Case Study in the Scalar-Isoscalar Channel
• Applications of Diagrammatic Renormalization Methods in QCD Sum-Rules
• Numerically Computing QCD Laplace Sum-Rules Using pySecDec

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