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Janus-Facedness of the Pion: Analytic Instantaneous Bethe-Salpeter Models
High Energy Physics - Phenomenology · Submitted 8 Jul 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Inversion enables the construction of interaction potentials underlying - under fortunate circumstances even analytic - instantaneous Bethe-Salpeter descriptions of all lightest pseudoscalar mesons as quark-antiquark bound states of Goldstone-boson nature.
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Inversion enables the construction of interaction potentials underlying - under fortunate circumstances even analytic - instantaneous Bethe-Salpeter descriptions of all lightest pseudoscalar mesons as quark-antiquark bound states of Goldstone-boson nature.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Inversion enables the construction of interaction potentials underlying - under fortunate circumstances even analytic - instantaneous Bethe-Salpeter descriptions of all lightest pseudoscalar mesons as quark-antiquark bound states of Goldstone-boson nature. | contribution 0.67 | 0.55 | 0.72 | hedged possibility 0.72 |
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Original abstract
Inversion enables the construction of interaction potentials underlying - under fortunate circumstances even analytic - instantaneous Bethe-Salpeter descriptions of all lightest pseudoscalar mesons as quark-antiquark bound states of Goldstone-boson nature.
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How the literature uses it
4 arXiv papers cite this in 8 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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Describing the lightest pseudoscalar mesons as bound states of quark and antiquark within the framework of an instantaneous Bethe-Salpeter formalism constructed such as to retain (in contrast to Salpeter's equation) as much information on the relativistic effects provided by the full quark propagator as conceivable allows for a surprisingly simple implementation of their near masslessness mandatory for their interpretability as pseudo-Goldstone bosons related to the spontaneous breaking of the chiral symmetries of quantum chromodynamics.
Instantaneous Bethe-Salpeter View of Goldstone-Type Pseudoscalar Mesons · 0.80
Papers citing it · 4 sentences without a confident label
Uses its method or tool 3 papers
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As a proof of concept, we study the treatment of such pseudo-Goldstone bosons by a simple approximation [ref] to the Bethe–Salpeter equation [ref] .
Bethe-Salpeter-Motivated Modelling of Pseudo-Goldstone Pseudoscalar Mesons · Interpretation of the Lightest Pseudoscalar Mesons as (Pseudo) Goldstone Bosons · 0.90
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In Euclidean-space representation, indicated by underlining the corresponding variables, this relation between Bethe–Salpeter amplitude and the quark propagator functions $M(k^2)$ and $Z(k^2)$ can be reformulated as [ref] [equation] This relation can be capitalized to convert, by inversion [ref] , knowledge about the behaviour of the fermion propagator into information about the underlying effective quark–antiquark interactions [ref] .
Goldstonic pseudoscalar mesons in Bethe-Salpeter-inspired setting · Inversion of Dyson–Schwinger Propagator Solution · 0.85
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In order to scrutinize pseudoscalar quark–antiquark bound states for physical (i.e., non-chiral) quark masses, we ought to find the corresponding solutions to our set ([ref]) of coupled equations for the two independent radial Salpeter components $φ_1,2(p).$ Our task is greatly facilitated by a definitely obvious move enabled by the purely algebraic nature of one of the two relations ([ref]): inserting any of the two relations (1) into the other leads to single explicit eigenvalue problems for either $φ_1(p)$ or $φ_2(p)$ with mass-squared eigenvalue $M^2$ [ref] ; conversion to equivalent matrix eigenvalue problems by expansion over a convenient function-space basis is among the standard solution procedures [ref] .
Simplified Bethe-Salpeter Description of Basic Pseudoscalar-Meson Features · Pseudoscalar-Meson Properties Revisited · 0.86
What it cites · 12 sentences without a confident label
Uses the method or tool of 2 papers
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The application of suitably adapted inversion techniques [ref] allows us to retrieve all the underlying interactions — rooted, of course, in QCD — analytically in the form of a (configuration-space) central potential $V(r),$ $r≡|x|,$ from presumed solutions to the Bethe–Salpeter equation [ref] .
Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions · Introduction: quark–antiquark bound states of Goldstone-boson identity · 0.94
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The application of suitably adapted inversion techniques [ref] allows us to retrieve all the underlying interactions — rooted, of course, in QCD — analytically in the form of a (configuration-space) central potential $V(r),$ $r≡|x|,$ from presumed solutions to the Bethe–Salpeter equation [ref] .
Instantaneous Bethe-Salpeter Approach to Pseudoscalar Mesons · Introduction: quark–antiquark bound states of Goldstone-boson identity · 0.94
Uses data or values from 1 paper
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Our findings may be scrutinized by use of the chiral-limit quark mass function's pointwise form $M(k^2),$ provided graphically in Ref. [ref] and shown in Fig. [ref] as $M(k)$ with $k≡(k^2)^1/2,$ which we parametrize by [equation] Note that the product of the two exponents in the second term above yields $1.48×0.752≈1.1,$ which is pretty close to unity, as demanded by the large-$k$ constraint.
pi- and K-meson Bethe-Salpeter Amplitudes · Reliability check of findings: numerical determination of the potential CITEMARK14Z · 0.98
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