The off-shell axial anomaly via the transition

Frank, Michael R.; Mitchell, K.L.; Roberts, Craig D.; Tandy, P. C.

doi:10.1016/0370-2693(95)01065-x

Cited by 43 publications

(58 citation statements)

References 27 publications

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“…Such a small m cannot jeopardize the relevance of (7) for the computation of π 0 → γγ, as shown also by Ref. [15], which found (in an approach closely related to ours) that the amplitude decreased with respect to the analytic, chiral-limit axial anomaly result only by less than 1% when they introduced the non-vanishing but small u, d-quark mass m = 6.7 MeV.…”

mentioning

confidence: 73%

“…using the framework advocated by (for example) [12,7,15,8,19] in the context of electromagnetic interactions of BS bound states, and often called the generalized impulse approximation (GIA) -e.g., by [15,8]. To evaluate the triangle graph, we therefore use the dressed quark propagator S f (q), Eq.…”

Section: η-η ′ Complex and Its Axial-current Decay Constantsmentioning

confidence: 99%

“…Since solving the pertinent SD equation for the dressed quark-photon vertex Γ µ f is a difficult problem that has only recently begun to be addressed [20], it is customary to use realistic Ansätze. Following, e.g., [15,8,7,19], we choose the Ball-Chiu [21] vertex:…”

Section: η-η ′ Complex and Its Axial-current Decay Constantsmentioning

confidence: 99%

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ηandη′in a coupled Schwinger-Dyson and Bethe-Salpeter approach

1998

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Extending our earlier treatments of π 0 , η c and η b , we study the η-η ′ system and its γγ decays using a model which is a leading version of the consistently coupled Schwinger-Dyson (SD) and Bethe-Salpeter (BS) approach. The electromagnetic interactions are incorporated through a (generalized) impulse approximation consistent with this bound-state approach, so that the Ward-Takahashi identities of QED are preserved when quarks are dynamically dressed. To overcome some of the limitations due to the ladder approximation, we introduce a minimal extension to the bound-state approach employed, so that the U A (1) problem is avoided. Pointing out which of our predictions hold in the coupled SD-BS approach in general, and which are the consequences of the specific, chosen model, we present the results for the axial-current decay constants of η 8 , η 0 , and of their physical combinations η and η ′ , the results for the γγ-decay constants of η 0 and η 8 , for the two-photon decay widths of η and η ′ , and for the mixing-independent R-ratio constructed from them.

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mentioning

confidence: 73%

Section: η-η ′ Complex and Its Axial-current Decay Constantsmentioning

confidence: 99%

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ηandη′in a coupled Schwinger-Dyson and Bethe-Salpeter approach

1998

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“…They are all dressed mutually consistently, so that the pertinent Ward-Takahashi identities are respected (e.g., see Refs. [36,37,56]). This is necessary for reproducing exactly and analytically anomalous γγ (on-shell) amplitudes 3 in the chiral limit, and requires the usage of a dressed quark-photon vertex satisfying the vector Ward-Takahashi identity.…”

Section: Bmentioning

confidence: 99%

ηandη′mesons and dimension 2 gluon condensate⟨A2⟩

Kekez

Klabučar

2006

Phys. Rev. D

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The study of light pseudoscalar quark-antiquark bound states in the Dyson-Schwinger approach with the effective QCD coupling enhanced by the interplay of the dimension 2 gluon condensate A 2 and dimension 4 gluon condensate F 2 , is extended to the η-η ′ complex. We include the effects of the gluon axial anomaly into the Dyson-Schwinger approach to mesons. The calculated masses, mixing and two-photon decay widths of η and η ′ mesons are in agreement with experiment. Also, in a model-independent way, we give the modification of the Gell-Mann-Okubo and Schwinger nonet relations due to the interplay of the gluon anomaly and SU(3) flavor symmetry breaking.

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“…[1] and has recently been applied to the study of π-π scattering [2], the electromagnetic pion form factor [3], ρ-ω mixing [4] and the anomalous γ * π 0 → γ-transition form factor. [5] It is possible to obtain information about such Schwinger functions via a numerical simulation of a lattice-QCD action. [6][7][8] However, in addition to the usual problems associated with identifying and establishing the existence of the continuum limit, and recovering the global symmetries of QCD, this also requires gauge fixing on the spacetime lattice.…”

Section: Introductionmentioning

confidence: 99%

Model gluon propagator and pion and ρ-meson observables

1996

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A one parameter, model confined-gluon propagator is employed in a phenomenological application of the Dyson-Schwinger and Bethe-Salpeter equations to the calculation of a range of π-and ρ-meson observables. Good agreement is obtained with the data. The calculated quark propagator does not have a singularity on the real-p 2 axis. A mass formula for the pion, involving only the vacuum, dressed quark propagator, is presented and shown to provide an accurate estimate of the mass obtained via a direct solution of the Bethe-Salpeter equation.

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The off-shell axial anomaly via the transition

Cited by 43 publications

References 27 publications

ηandη′in a coupled Schwinger-Dyson and Bethe-Salpeter approach

ηandη′in a coupled Schwinger-Dyson and Bethe-Salpeter approach

ηandη′mesons and dimension 2 gluon condensate⟨A2⟩

Model gluon propagator and pion and ρ-meson observables

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