Instantaneous Bethe-Salpeter View of Goldstone-Type Pseudoscalar Mesons

Franz F. Sch\"oberl; Wolfgang Lucha

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Instantaneous Bethe-Salpeter View of Goldstone-Type Pseudoscalar Mesons

Wolfgang Lucha, Franz F. Schöberl

High Energy Physics - Phenomenology · Submitted 15 Jun 2016

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

The authors' main claim 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.

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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.

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s0	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.	contribution 0.68	0.74	0.81	asserted 0.95

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Original abstract

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.

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7 arXiv papers cite this in 20 sentences

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Papers whose main result relates to this one's

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States the same result 2 papers

A nontrivial instantaneous variant of the Bethe-Salpeter formalism allows us to discuss massless pseudoscalar mesons from a configuration-space-potential point of view.

Goldstone-Type Pseudoscalar Mesons: Instantaneous Bethe-Salpeter Models · 0.91
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.

Janus-Facedness of the Pion: Analytic Instantaneous Bethe-Salpeter Models · 0.80

Papers citing it · 14 sentences without a confident label

Uses its method or tool 3 papers

There is no need to announce in detail the expectable outline of this paper: By applying the “Bethe–Salpeter-inspired” bound-state formalism constructed in Ref. [ref] (Sec. [ref]) to the lowest pseudoscalar mesons (Sec. [ref]), some of their thus predicted basic features (Sec. [ref]) are examined, for the Goldstone-friendly interquark potential derived in Ref. [ref] (Sec. [ref]), with regard to their compatibility with relationships of Gell-Mann–Oakes–Renner type (Sec. [ref]).

Goldstonic pseudoscalar mesons in Bethe-Salpeter-inspired setting · Stimulus: Janiform Nature of Pseudoscalar Mesons · 0.92
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
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 · 24 sentences without a confident label

Builds on 1 paper

Here, we generalize these Goldstone-boson analyses to the bound-state equation of Ref. [ref] .

Instantaneous Bethe-Salpeter Equation with Exact Propagators · Introduction · 0.98

Uses the method or tool of 1 paper

For our present analysis, we rely on the model proposed in Ref. [ref] , where the intended infrared enhancement of the effective strong coupling strength is accomplished without the introduction of a singular but integrable $δ$ function in momentum space.

Bethe-Salpeter Study of Vector Meson Masses and Decay Constants · Quark-Propagator-Defined Bethe–Salpeter Vertex · 0.98

Uses data or values from 1 paper

Accordingly, we have to extract pointwise the behaviour of both propagator functions $M(k^2)$ and $Z(k^2)$ from their graphs available in the literature: Figure [ref] shows the outcome of our simple interpolation of the results published in Ref. [ref] .

Continuum QCD and light mesons · Quark-Propagator-Defined Bethe–Salpeter Vertex · 1.00

Compares with 3 papers

In contrast to that, in our previous analyses of similar applications of the Salpeter equation we encountered parameter-dependent occurrences of singularities or nonconfinement [ref] .

Light Pseudoscalar Mesons in Bethe-Salpeter Equation with Instantaneous Interaction · Summary, Findings, Conclusions, and Perspectives · 0.95
In contrast to that, in our previous analyses of similar applications of the Salpeter equation we encountered parameter-dependent occurrences of singularities or nonconfinement [ref] .

Analytic Bethe-Salpeter Description of the Lightest Pseudoscalar Mesons · Summary, Findings, Conclusions, and Perspectives · 0.95
In contrast to that, in our previous analyses of similar applications of the Salpeter equation we encountered parameter-dependent occurrences of singularities or nonconfinement [ref] .

Instantaneous Bethe-Salpeter Kernel for the Lightest Pseudoscalar Mesons · Summary, Findings, Conclusions, and Perspectives · 0.95

Cites as background 1 paper

Bearing in mind the fact that the actual targets of the present study, the pseudo-Goldstone bosons of QCD, are pseudoscalar mesons, let us recall[The appropriate reasoning resembles the one used in, e.g., Refs. [ref] for the case of Salpeter's equation.] the general Lorentz structure of the Salpeter amplitude for bound states of fermion and antifermion whose spins add up to zero.

On the instantaneous Bethe-Salpeter equation · Spin-singlet fermion–antifermion states: Salpeter amplitude · 0.82

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