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eta and eta' in a coupled Schwinger-Dyson and Bethe-Salpeter approach
High Energy Physics - Phenomenology · Submitted 1 Oct 1997
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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 eta_8, eta_0, and of their physical combinations eta and eta', the results for the gamma-gamma decay constants of eta_0 and eta_8, for the two-photon decay widths of eta and eta', and for the mixing-independent R-ratio constructed from them.
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Extending our earlier treatments of pi0, eta_c and eta_b, we study the eta-eta' system and its gamma-gamma 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 eta_8, eta_0, and of their physical combinations eta and eta', the results for the gamma-gamma decay constants of eta_0 and eta_8, for the two-photon decay widths of eta and eta', and for the mixing-independent R-ratio constructed from them.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Extending our earlier treatments of pi0, eta_c and eta_b, we study the eta-eta' system and its gamma-gamma decays using a model which is a leading version of the consistently coupled Schwinger-Dyson (SD) and Bethe-Salpeter (BS) approach. | contribution 1.00 | 0.89 | 0.08 | asserted 0.97 |
| s1 | 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. | method 0.99 | 0.77 | 0.04 | asserted 0.88 |
| s2 | 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. | method 0.76 | 0.89 | 0.08 | asserted 0.96 |
| s3 | 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 eta_8, eta_0, and of their physical combinations eta and eta', the results for the gamma-gamma decay constants of eta_0 and eta_8, for the two-photon decay widths of eta and eta', and for the mixing-independent R-ratio constructed from them. | result 0.77 | 0.93 | 0.20 | asserted 0.98 |
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Original abstract
Extending our earlier treatments of pi0, eta_c and eta_b, we study the eta-eta' system and its gamma-gamma 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 eta_8, eta_0, and of their physical combinations eta and eta', the results for the gamma-gamma decay constants of eta_0 and eta_8, for the two-photon decay widths of eta and eta', and for the mixing-independent R-ratio constructed from them.
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2 arXiv papers cite this in 3 sentences
Papers citing it · 1 sentence without a confident label
Builds on it 1 paper
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Thus the masses of the $η$ and $η'$ mesons are computable in the SDE and BSE formalism, extending the Klabucar and Kekez parametrization of the $U_a(1)$ breaking [ref] .
Microscopic quark study of the eta and eta' masses · A calculable Bethe Salpeter Kernel · 1.00
Cites it as background 1 paper
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The latter is exemplified by Functional Renormalization Group (see, e.g., Refs. [ref] and references therein) and Schwinger–Dyson equations (see, e.g., Refs. [ref] for reviews and Refs. [ref] for examples of calculations of some observables addressed also in the present paper).
Pion observables calculated in Minkowski and Euclidean spaces with Ans\"atze for quark propagators · Introduction · 0.83
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