Dispersive analysis of glueball masses

Abstract

We develop an inverse matrix method to solve for resonance masses from a dispersion relation obeyed by a correlation function. Given the operator product expansion (OPE) of a correlation function in the deep Euclidean region, we obtain the nonperturbative spectral density, which exhibits resonance structures naturally. The value of the gluon condensate in the OPE is fixed by producing the $\rho$ meson mass in the formalism, and then input into the dispersion relations for the scalar, pseudoscalar and tensor glueballs. It is shown that the low-energy limit of the correlation function for the scalar glueball, derived from the spectral density, discriminates the lattice estimate for the triple-gluon condensate from the single-instanton estimate. The spectral densities for the scalar and pseudoscalar glueballs reveal a double-peak structure: the peak located at lower mass implies that the $f_0(500)$ and $f_0(980)$ ($\eta$ ad ${\eta }^{\prime }$) mesons contain small amount of gluonium components, and should be included into scalar (pseudoscalar) mixing frameworks. Another peak determines the scalar (pseudoscalar) glueball mass around 1.50 (1.75) GeV with a broad width about 200 MeV, suggesting that the $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$ ($\eta (1760)$) mesons are the glue-rich states. We also predict the topological susceptability ${\chi }_t^{1/4}=75$-78 MeV, deduced from the correlation function for the pseudoscalar glueball at zero momentum. Our analysis gives no resonance solution for the tensor glueball, which may be attributed to the insufficient nonperturbative condensate information in the currently available OPE.

arXiv comment21 pages, journal version, more references included

References in corpus (84)

• The glueball spectrum from an anisotropic lattice study
• The QCD axion, precisely
• Glueball Spectrum and Matrix Elements on Anisotropic Lattices
• A comprehensive lattice study of SU(3) glueballs
• Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme
• The Physics of Glueballs
• Masses, decays and mixings of gluonia in QCD
• Glueballs and k-strings in SU(N) gauge theories : calculations with improved operators
• EVIDENCE FOR A SCALAR GLUEBALL
• Scalar Quarkonium Masses and Mixing with the Lightest Scalar Glueball
• QCD Sum Rules for Skeptics
• Axion phenomenology and $\theta$-dependence from $N_f=2+1$ lattice QCD
• Gluon Condensates and m_{c,b} from QCD-Moments and their ratios to Order alpha_s^3 and <G^4>
• The puzzle of anomalously large isospin violations in $\eta (1405/1475)\to 3\pi$
• QCD tests from $e^+e^- \rar I=1~$ hadrons data and implication on the value of ${\alpha }_s$ from $\tau$-decays
• Scalar nonet quarkonia and the scalar glueball: mixing and decays in an effective chiral approach
• Production of $f_0(1710)$, $f_0(1500)$, and $f_0(1370)$ in $J/\psi$ hadronic decays
• Topological Susceptibility and QCD Axion Mass: QED and NNLO corrections
• Power corrections to alpha_s(M_τ),|V_{us}| and m_s
• Gluon Condensates and m_b(m_b) from QCD-Exponential Moments at Higher Orders
• The glueball spectrum of SU(3) gauge theory in 3+1 dimension
• The mixing of the f0(1370), f0(1500) and f0(1710) and the search for the scalar glueball
• Weinberg-Type Sum Rules at Zero and Finite Temperature
• Gluon condensates and c, b quark masses from quarkonia ratios of moments
• Understanding the property of $\eta (1405/1475)$ in the $J/\psi$ radiative decay
• Direct instantons, topological charge screening and QCD glueball sum rules
• The $\rho$-meson and related meson wave functions in QCD sum rules with nonlocal condensates
• Pseudoscalar glueball mass from $\eta$-${\eta }^{\prime }$-$G$ mixing
• Isosinglet Scalar Mesons Below 2 GeV and the Scalar Glueball Mass
• Scalar isoscalar mesons and the scalar glueball from radiative $J/\psi$ decays
• QCD Parameters Correlations from Heavy Quarkonia
• Glueballs, closed fluxtubes and eta(1440)
• Mass Uncertainties of f0(600) and f0(1370) and their Effects on Determination of the Quark and Glueball Admixtures of the I=0 Scalar Mesons
• Spectral function and excited states in lattice QCD with maximum entropy method
• A Bayesian approach to QCD sum rules
• Chiral Sum Rules and Their Phenomenology
• Spectrum of scalar and pseudoscalar glueballs from functional methods
• Revisiting Scalar Glueballs
• Pinched weights and Duality Violation in QCD Sum Rules: a critical analysis
• Scalar Gluonium and Instantons
• Violation of Quark-Hadron Duality and Spectral Chiral Moments in QCD
• Color dependence of tensor and scalar glueball masses in Yang-Mills theories
• $D$ meson mixing as an inverse problem
• Glueball spectrum from $N_f=2$ lattice QCD study on anisotropic lattices
• Determination of the scalar glueball mass in QCD sum rules
• Pseudoscalar production at omega omega threshold in J/psi -> gamma omega omega
• Contribution of the QCD $\Theta$-term to nucleon electric dipole moment
• Parity projection of QCD sum rules for the nucleon
• Internal particle width effects on the the triangle singularity mechanism in the study of the $\eta (1405)$ and $\eta (1475)$ puzzle
• A Gaussian Sum-Rules Analysis of Scalar Glueballs
• Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow
• QCD sum rules for rho mesons in vacuum and in-medium, re-examined
• eta(1405) in a chiral approach based on mixing of the pseudoscalar glueball with the first radial excitations of eta and eta'
• Two-loop calculations for the propagators of gluonic currents. Erratum
• Exclusive Processes at Intermediate Energy, Quark-Hadron Duality and the Transition to Perturbative QCD
• Low-energy constants and condensates from the tau hadronic spectral functions
• A Study of J/psi-->gamma gamma V(rho,phi) Decays with the BESII Detector
• The scalar glueball spectrum
• Evidence of the four-quark nature of $f_0(980)$ and $f_0(500)$
• ${\eta }_c$ mixing effects on charmonium and $B$ meson decays
• Instanton and Higher-Loop Perturbative Contributions to the QCD Sum-Rule Analysis of Pseudoscalar Gluonium
• Topological susceptibility and ${\eta }^{\prime }$ meson mass from $N_f=2$ lattice QCD at the physical point
• Chiral sum rules and vacuum condensates from tau-lepton decay data
• QCD sum rules with spectral densities solved in inverse problems
• Di-Gluonium Sum Rules, I = 0 Scalar Mesons and Conformal Anomaly
• Study of $\eta (1475)$ and $X(1835)$ in radiative $J/\psi$ decays to $\gamma \varphi$
• The pseudoscalar glueball in a chiral Lagrangian model with instanton effect
• Mass spectrum of pseudo-scalar glueballs from a Bethe-Salpeter approach with the rainbow-ladder truncation
• The $\rho (1S,2S)$, $\psi (1S,2S)$, ${\rm Y}(1S,2S)$ and ${\psi }_t(1S,2S)$ mesons in a double pole QCD Sum Rule
• Rho meson distribution amplitudes from QCD sum rules with nonlocal condensates
• Revisiting the pseudoscalar meson and glueball mixing and key issues in the search for pseudscalar glueball state
• Gluonic Mesons in J/Psi Radiative Decay
• Parton-Hadron duality in QCD sum rules: quantum mechanical examples
• Mass of Pseudoscalar Gluonium: A Higher-Loop QCD Sum-Rule Estimate
• $0^{++}$ scalar glueball in finite-width Gaussian sum rules
• Study of the theta dependence of the vacuum energy density in chiral effective Lagrangian models at zero temperature
• Vacuum polarization contribution to muon $g-2$ as an inverse problem
• A comprehensive revisit of the $\rho$ meson with improved Monte-Carlo based QCD sum rules
• New meson mass relation and lowest pseudoscalar glueball mass
• Mixing among lowest-lying scalar mesons and scalar glueball
• Stability Analysis of Sum Rules for Compton Scattering
• The finite-width Laplace sum rules for $0^{++}$ scalar glueball in instanton liquid model
• Finite-width Gaussian sum rules for $0^{-+}$ pseudoscalar glueball based on correction from instanton-gluon interference to correlation function
• Fermion correction to the mass of the scalar glueball in QCD sum rule

Cited by in corpus (5)

• An updated review of the new hadron states
• Dispersive analysis of neutral meson mixing
• Dispersive derivation of the pion distribution amplitude
• Perturbative QCD analysis of neutral $B$-meson decays into $\sigma \sigma ,\sigma f_0$ and $f_0{f}_0$
• Constraint of $\xi$-moments calculated with QCD sum rules on the pion distribution amplitude models