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Microscopic quark study of the eta and eta' masses

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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O. Lakhina, P. Bicudo

High Energy Physics - Phenomenology · Submitted 7 Aug 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that it is necessary to go beyond the BCS (rainbow-ladder) approximation to split the $\eta$ and $\eta'$ masses from the $\pi$ and K masses.

how it is stated · asserted 1.00 read the record →

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arXiv ID0708.0984 (version 1)
Pith IDJ3J3UMCC, Pith's permanent record of this paper and its review
CitationO. Lakhina, P. Bicudo. "Microscopic quark study of the eta and eta' masses." arXiv:0708.0984 (2007). https://pith.science/paper/J3J3UMCC
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,861 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.22 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.63 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We show that it is necessary to go beyond the BCS (rainbow-ladder) approximation to split the $\eta$ and $\eta'$ masses from the $\pi$ and K masses. We determine the self-consistent set of one-quark-loop diagrams both for the Schwinger-Dyson quark mass gap equation and for the Bethe-Salpeter quark-antiquark boundstate equation. We identify the dominant diagrams, and we focus on the boundstate equation. We detail the Bethe-Salpeter equation, adding the dominant new diagram to the BCS kernel. The relevant numerical techniques are also discussed. The ideal cases of one, two and three light flavors, relevant to lattice QCD are also explored, together with the case of realistic current quark masses.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that it is necessary to go beyond the BCS (rainbow-ladder) approximation to split the $\eta$ and $\eta'$ masses from the $\pi$ and K masses. result 0.80 0.71 0.84 asserted 1.00
s1 We determine the self-consistent set of one-quark-loop diagrams both for the Schwinger-Dyson quark mass gap equation and for the Bethe-Salpeter quark-antiquark boundstate equation. method 0.75 0.95 0.07 asserted 1.00
s2 We identify the dominant diagrams, and we focus on the boundstate equation. method 0.59 0.93 0.04 asserted 0.98
s3 We detail the Bethe-Salpeter equation, adding the dominant new diagram to the BCS kernel. method 0.88 0.90 0.08 asserted 0.83
s4 The relevant numerical techniques are also discussed. method 1.00 0.53 0.02 asserted 0.68
s5 The ideal cases of one, two and three light flavors, relevant to lattice QCD are also explored, together with the case of realistic current quark masses. contribution 0.84 0.84 0.04 asserted 0.91

What kind of paper the classifier reports this is: theoretical result 0.67 · evidence from simulation or computation 0.95.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We show that it is necessary to go beyond the BCS (rainbow-ladder) approximation to split the $\eta$ and $\eta'$ masses from the $\pi$ and K masses. We determine the self-consistent set of one-quark-loop diagrams both for the Schwinger-Dyson quark mass gap equation and for the Bethe-Salpeter quark-antiquark boundstate equation. We identify the dominant diagrams, and we focus on the boundstate equation. We detail the Bethe-Salpeter equation, adding the dominant new diagram to the BCS kernel. The relevant numerical techniques are also discussed. The ideal cases of one, two and three light flavors, relevant to lattice QCD are also explored, together with the case of realistic current quark masses.

Human review

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How the literature uses it

3 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Cites it as background 1 paper

What it cites · 18 sentences without a confident label

Builds on 6 papers
  • 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] .

    eta and eta' in a coupled Schwinger-Dyson and Bethe-Salpeter approach · A calculable Bethe Salpeter Kernel · 1.00

  • Together with the isovector ground state pseudoscalars [ref] , first excited pseudoscalar states [ref] and ground state vectors [ref] , this is a new case among the few where the Euclidian Bethe Salpeter equation has been solved so far.

    The $\pi$, $K^+$, and $K^0$ electromagnetic form factors · Conclusion · 0.89

  • Together with the isovector ground state pseudoscalars [ref] , first excited pseudoscalar states [ref] and ground state vectors [ref] , this is a new case among the few where the Euclidian Bethe Salpeter equation has been solved so far.

    Pseudoscalar Meson Radial Excitations · Conclusion · 0.89

Uses the method or tool of 2 papers
  • We used the Maris-Tandy model [ref] in our calculations, G(k^2)/k^2 = 4π^2 D/w^6k^2 e^-k^2/w^2 + 4π^2γ_m F(k^2)/1/2ln[τ+(1+k^2/Λ^2_QCD)^2], where $F(k^2)=(1-exp-k^2/4m_t^2)/k^2$, $γ_m=12/(33-2N_f)$ an where the parameters are $m_t=0.5$ GeV, $N_f=4$, $Λ_QCD=0.234$ GeV, $τ=e^2-1$, $D=0.93$ GeV$^2$ and $w=0.4$ GeV.

    pi- and K-meson Bethe-Salpeter Amplitudes · A calculable Bethe Salpeter Kernel · 0.98

  • We used the Maris-Tandy model [ref] in our calculations, G(k^2)/k^2 = 4π^2 D/w^6k^2 e^-k^2/w^2 + 4π^2γ_m F(k^2)/1/2ln[τ+(1+k^2/Λ^2_QCD)^2], where $F(k^2)=(1-exp-k^2/4m_t^2)/k^2$, $γ_m=12/(33-2N_f)$ an where the parameters are $m_t=0.5$ GeV, $N_f=4$, $Λ_QCD=0.234$ GeV, $τ=e^2-1$, $D=0.93$ GeV$^2$ and $w=0.4$ GeV.

    Bethe-Salpeter Study of Vector Meson Masses and Decay Constants · A calculable Bethe Salpeter Kernel · 0.98

Cites as support 2 papers
Cites as background 2 papers

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