Bethe-Salpeter studies of mesons beyond rainbow-ladder

Richard Williams

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Bethe-Salpeter studies of mesons beyond rainbow-ladder

Richard Williams

High Energy Physics - Phenomenology · Submitted 17 Dec 2009

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

The authors' main claim We find that sub-leading Abelian corrections are further suppressed dynamically, and that our results supersede early qualitative predictions with significantly simpler truncation schemes.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.24 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.89 · mentions code or data availability 0.02.

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We investigate the masses of light mesons from a coupled system of Dyson-Schwinger and Bethe-Salpeter equations. The dominant non-Abelian and sub-leading Abelian contributions to the dressed quark-gluon vertex are explicitly taken into account. We also include unquenching effects in the form of hadronic resonance contributions via the back-reaction of pions. We construct the corresponding Bethe--Salpeter kernel that satisfies the axial-vector Ward-Takahashi identity. Our numerical treatment fully includes all momentum dependencies with all equations solved completely in the complex plane. This approach goes well beyond the rainbow-ladder approximation and permits us to investigate the relative impact of different corrections beyond rainbow-ladder on the properties of mesons. We find that sub-leading Abelian corrections are further suppressed dynamically, and that our results supersede early qualitative predictions with significantly simpler truncation schemes.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the masses of light mesons from a coupled system of Dyson-Schwinger and Bethe-Salpeter equations.	contribution 0.95	0.94	0.03	asserted 0.94
s1	The dominant non-Abelian and sub-leading Abelian contributions to the dressed quark-gluon vertex are explicitly taken into account.	method 0.88	0.87	0.04	asserted 0.99
s2	We also include unquenching effects in the form of hadronic resonance contributions via the back-reaction of pions.	method 0.80	0.91	0.03	asserted 1.00
s3	We construct the corresponding Bethe--Salpeter kernel that satisfies the axial-vector Ward-Takahashi identity.	method 0.90	0.95	0.03	asserted 1.00
s4	Our numerical treatment fully includes all momentum dependencies with all equations solved completely in the complex plane.	method 0.99	0.94	0.03	asserted 1.00
s5	This approach goes well beyond the rainbow-ladder approximation and permits us to investigate the relative impact of different corrections beyond rainbow-ladder on the properties of mesons.	contribution 0.71	0.70	0.12	asserted 0.91
s6	We find that sub-leading Abelian corrections are further suppressed dynamically, and that our results supersede early qualitative predictions with significantly simpler truncation schemes.	result 0.91	0.95	0.83	asserted 1.00

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Original abstract

We investigate the masses of light mesons from a coupled system of Dyson-Schwinger and Bethe-Salpeter equations. The dominant non-Abelian and sub-leading Abelian contributions to the dressed quark-gluon vertex are explicitly taken into account. We also include unquenching effects in the form of hadronic resonance contributions via the back-reaction of pions. We construct the corresponding Bethe--Salpeter kernel that satisfies the axial-vector Ward-Takahashi identity. Our numerical treatment fully includes all momentum dependencies with all equations solved completely in the complex plane. This approach goes well beyond the rainbow-ladder approximation and permits us to investigate the relative impact of different corrections beyond rainbow-ladder on the properties of mesons. We find that sub-leading Abelian corrections are further suppressed dynamically, and that our results supersede early qualitative predictions with significantly simpler truncation schemes.

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14 arXiv papers cite this in 24 sentences

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Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We find that sub-leading Abelian corrections are further dynamically suppressed, and that our results supersede early qualitative predictions from simple truncation schemes.

Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation · 0.99

Papers citing it · 18 sentences without a confident label

Builds on it 1 paper

Here we include the sub-leading Abelian corrections together with the pion back-reaction [ref] .

Bethe-Salpeter equations: mesons beyond the rainbow-ladder truncation · Introduction · 0.85

Uses its method or tool 1 paper

The normalization of the pseudoscalar BSA is therefore determined from [ref]

Pion Electromagnetic Form Factor from Bethe-Salpeter Amplitudes with Appropriate Kinematics · BSA Normalization in Minkowski space · 0.87

Compares with it 1 paper

Covariant gauge studies of the effect of non-Abelian corrections to the equation as applied to the light quark sector indicate that they are dominant compared to the Abelian corrections [ref] .

Coulomb gauge confinement in the heavy quark limit · Summary, discussion and conclusions · 0.81

Cites it as background 3 papers

In the context of BSE studies, it has been investigated in Refs. [ref] .

The quark-gluon vertex in Landau gauge bound-state studies · Abelian diagram · 0.88
Beyond this approximation, models with dressed vertex contributions [ref] and unquenching effects [ref] have been considered, and more sophisticated numerical methods to solve both the homogeneous and the inhomogeneous equation have been recently developed [ref] .

Higher order heavy quark Green's functions in Coulomb gauge · Introduction · 0.80
Beyond this approximation, models with dressed vertex contributions [ref] and unquenching effects [ref] have been considered, and more sophisticated numerical methods to solve both the homogeneous and the inhomogeneous equation have been recently developed [ref] .

Quark sector of Coulomb gauge Quantum Chromodynamics · Faddeev equation for baryons · 0.86

What it cites · 49 sentences without a confident label

Builds on 4 papers

We improved upon previous beyond-the-rainbow investigations, which focused upon pion unquenching corrections [ref] and the dominant non-Abelian corrections to the quark-gluon vertex [ref] by including the sub-leading Abelian corrections to the quark-gluon vertex.

Hadronic unquenching effects in the quark propagator · Discussion and Outlook · 0.95
We improved upon previous beyond-the-rainbow investigations, which focused upon pion unquenching corrections [ref] and the dominant non-Abelian corrections to the quark-gluon vertex [ref] by including the sub-leading Abelian corrections to the quark-gluon vertex.

Probing the gluon self-interaction in light mesons · Discussion and Outlook · 0.95
We improved upon previous beyond-the-rainbow investigations, which focused upon pion unquenching corrections [ref] and the dominant non-Abelian corrections to the quark-gluon vertex [ref] by including the sub-leading Abelian corrections to the quark-gluon vertex.

On Gribov's supercriticality picture of quark confinement · Discussion and Outlook · 0.95

Uses the method or tool of 7 papers

To obtain solutions, we employ the `shell-method' described in the appendix of Ref. [ref] .

Hadronic unquenching effects in the quark propagator · Solution · 1.00
Thus, we approximate the DSE following the detailed investigation of Refs. [ref] .

The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement · Quark-Gluon vertex · 0.95
The contribution is further approximated according to [ref] such that a symmetry preserving Bethe–Salpeter kernel is constructable.

On Gribov's supercriticality picture of quark confinement · Unquenching Effects · 0.97

Uses data or values from 1 paper

Their results, taken from the figure contained in Ref. [ref] , are shown in Table [ref].

Sketching the Bethe-Salpeter kernel · Results · 0.96

Compares with 10 papers

The result of our Abelian correction can be directly compared with the study of [ref] .

Bethe-Salpeter Meson Masses Beyond Ladder Approximation · Results · 1.00
For comparative purposes, we tested this truncation against the non-trivial kernel's present in Refs. [ref] .

Beyond the rainbow: effects from pion back-coupling · Decay constants and normalisation · 0.97
An further advantage of using the gluon propagator of Eq. ([ref]) is that it allows us to make a direct comparison with other truncations in the literature that have employed the same form of the interaction [ref] .

Probing the gluon self-interaction in light mesons · Results · 0.89

Cites as background 18 papers

The calculation of observables from the Bethe–Salpter amplitudes, such as leptonic decay constants for the pseudoscalar and vector mesons [ref] , requires that they are properly normalised.

Bethe-Salpeter Study of Vector Meson Masses and Decay Constants · Decay constants and normalisation · 0.83
The calculation of observables from the Bethe–Salpter amplitudes, such as leptonic decay constants for the pseudoscalar and vector mesons [ref] , requires that they are properly normalised.

Vector meson form factors and their quark-mass dependence · Decay constants and normalisation · 0.83
The calculation of observables from the Bethe–Salpter amplitudes, such as leptonic decay constants for the pseudoscalar and vector mesons [ref] , requires that they are properly normalised.

pi- and K-meson Bethe-Salpeter Amplitudes · Decay constants and normalisation · 0.83

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