Non-Abelian axial anomaly, axial-vector duality, and the pseudoscalar glueball

Abstract

We generalize the dispersive approach to axial anomaly by A.D. Dolgov and V.I. Zakharov to a non-Abelian case with arbitrary photon virtualites. We derive the anomaly sum rule for the singlet current and obtain the ${\pi }^0,\eta ,{\eta }^{\prime }\to \gamma {\gamma }^{\ast }$ transition form factors. Using them, we established the behavior of a nonperturbative gluon matrix element $⟨0|G\tilde{G}|\gamma {\gamma }^{\ast }(q^2)⟩$ in both spacelike and timelike regions. We found a significant contribution of the non-Abelian axial anomaly to the processes with one virtual photon, comparable to that of the electromagnetic anomaly. The duality between the axial and the vector channels was observed: the values of duality intervals and mixing parameters in the axial channel were related to vector resonances' masses and residues. The possibility of a light pseudoscalar glueball-like state is conjectured.

arXiv comment22 pages, 15 figures. Revised version. Accepted for publication in PRD

References in corpus (60)

• Mixing and Decay Constants of Pseudoscalar Mesons
• Measurements of the Meson-Photon Transition Form Factors of Light Pseudoscalar Mesons at Large Momentum Transfer
• Measurement of the gamma gamma* --> pi0 transition form factor
• Measurement of gamma gamma* --> pi0 transition form factor at Belle
• Rho-omega mixing, vector meson dominance and the pion form-factor
• Phenomenological Evidence for the Gluon Content of $\eta$ and ${\eta }^{\prime }$
• Study of the eta-eta' system in the two mixing angle scheme
• Meson Transition Form Factors in Light-Front Holographic QCD
• Measurement of the gamma gamma* --> eta and gamma gamma* --> eta' transition form factors
• Perturbative and nonperturbative renormalization of anomalous quark triangles
• Dispersive analysis for $\eta \to \gamma {\gamma }^{\ast }$
• Transition Form Factor gamma gamma* -> pi0 and QCD sum rules
• γ*γ\rightarrow π^0 transition form factor at low-energies from a model-independent approach
• Measurement of the eta and etaprime transition form factors at q^2=112 GeV^2
• Decay of the pseudoscalar glueball into scalar and pseudoscalar mesons
• Pseudoscalar glueball mass from $\eta$-${\eta }^{\prime }$-$G$ mixing
• The VV'P form factors in resonance chiral theory and the pi-eta-eta' light-by-light contribution to the muon g-2
• The ${\eta }^{\prime }$ transition form factor from space- and time-like experimental data
• ηand η' transition form factors from rational approximants
• Precision study of the $\eta \to {\mu }^{+}{\mu }^{-}\gamma$ and $\omega \to {\mu }^{+}{\mu }^{-}{\pi }^0$ electromagnetic transition form-factors and of the $\rho \to {\mu }^{+}{\mu }^{-}$ line shape in NA60
• Glueballs, closed fluxtubes and eta(1440)
• Transition form factors ${\gamma }^{\ast }\gamma \to \eta$ and ${\gamma }^{\ast }\gamma \to {\eta }^{\prime }$ in QCD
• The eta transition form factor from space- and time-like experimental data
• Study of the Processes e+ e- --> eta gamma, e+ e- --> pi0 gamma --> 3 gamma in the c.m. Energy Range 600--1380 MeV at CMD-2
• Observation of the Dalitz Decay ${\eta }^{\prime }\to \gamma e^{+}{e}^{-}$
• Measurement of the omega -> pi^0 e^+e^- and eta -> e^+e^-g Dalitz decays with the A2 setup at MAMI
• Can we understand an auxetic pion-photon transition form factor within QCD? BaBar faces Belle
• Study of the reaction $e^{+}{e}^{-}\to {\pi }^0\gamma$ with the SND detector at the VEPP-2M collider
• Axial anomaly and the precise value of the ${\pi }^0\to 2\gamma$ decay width
• Axial anomaly as a collective effect of meson spectrum
• On the possibility to measure the (pi0 to gamma gamma) decay width and the (gamma* gamma to pi0) transition form factor with the KLOE-2 experiment
• Systematic estimation of theoretical uncertainties in the calculation of the pion-photon transition form factor using light-cone sum rules
• Modeling interactions of photons with pseudoscalar and vector mesons
• Transition Form Factors and Mixing of Pseudoscalar Mesons from Anomaly Sum Rule
• Axial anomaly: the modern status
• Measurement of the pi^0 -> e^+e^-gamma Dalitz decay at the Mainz Microtron
• eta(1405) in a chiral approach based on mixing of the pseudoscalar glueball with the first radial excitations of eta and eta'
• Reanalysis of the $e^{+}{e}^{-}\to \eta \gamma$ reaction cross section
• Axial anomaly and mixing: from real to highly virtual photons
• Spacelike and timelike form factors for the $({\pi }^0,\eta ,{\eta }^{\prime })\to {\gamma }^{\ast }\gamma$ transitions in the light-front quark model
• Interpolation Formulas for the Eta-Gamma and Eta'-Gamma Transition Form Factors
• Study of the process $e^{+}{e}^{-}\to \eta \gamma$ in the center-of-mass energy range 1.07--2.00 GeV
• ${\pi }^0$-$\eta$-${\eta }^{\prime }$ mixing from $V\to P\gamma$ and $P\to V\gamma$ decays
• Universal behaviour of the ${\gamma }^{\ast }\gamma \to ({\pi }^0,\eta ,{\eta }^{\prime })$ transition form factors
• Fate of the ${\eta }^{\prime }$ in the Quark Gluon Plasma
• Holography and Anomaly Matching for Resonances
• Axial anomaly and vector meson dominance model
• Pion transition form factor in the constituent quark model
• Influence of confining gluon configurations on the $P\to {\gamma }^{\ast }\gamma$ transition form factors
• Matching lightcone- and anomaly-sum-rule predictions for the pion-photon transition form factor
• Measurement of the $e^{+}{e}^{-}\to {\pi }^0\gamma$ cross section in the energy range 1.075--2 GeV at SND
• MesonNet 2013 International Workshop. Mini-proceedings
• Dispersive approach to the axial anomaly and nonrenormalization theorem
• The ${\pi }^0-\eta -{\eta }^{\prime }$ mixing in a generalized multi-quark interaction scheme
• Quark-hadron duality, axial anomaly and mixing
• Decay of the pseudoscalar glueball and its first excited state into scalar and pseudoscalar mesons and their first excited states
• Finite-width Gaussian sum rules for $0^{-+}$ pseudoscalar glueball based on correction from instanton-gluon interference to correlation function
• $\eta$-$\gamma$ and ${\eta }^{\prime }$-$\gamma$ transition form factors in a nonlocal NJL model
• Analysis of the $e^{+}{e}^{-}\to {\pi }^0\gamma$ process using anomaly sum rules approach
• Dispersive approach to non-Abelian axial anomaly

Cited by in corpus (2)

• Nonlocal gluon condensates in QCD sum rules
• Nature of $X(2370)$