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Dynamical generation of hadronic resonances in effective models with derivative interactions
High Energy Physics - Phenomenology · Submitted 23 Aug 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Light scalar mesons can be understood as dynamically generated resonances.
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The abstract, sentence by sentence
Light scalar mesons can be understood as dynamically generated resonances. They arise as 'companion poles' in the propagators of quark-antiquark seed states when accounting for hadronic loop contributions to the self-energies of the latter. Such a mechanism may explain the overpopulation in the scalar sector - there exist more resonances with total spin $J=0$ than can be described within a quark model. Along this line, we study an effective Lagrangian approach where the isovector state $a_{0}(1450)$ couples via both non-derivative and derivative interactions to pseudoscalar mesons. It is demonstrated that the propagator has two poles: a companion pole corresponding to $a_{0}(980)$ and a pole of the seed state $a_{0}(1450)$. The positions of these poles are in quantitative agreement with experimental data. Besides that, we investigate similar models for the isodoublet state $K_{0}^{\ast}(1430)$ by performing a fit to $\pi K$ phase shift data in the $I=1/2,$ $J=0$ channel. We show that, in order to fit the data accurately, a companion pole for the $K_{0}^{\ast}(800)$, that is, the light $\kappa$, is required. A large-$N_{c}$ study confirms that both resonances below $1$ GeV are predominantly four-quark states, while the heavy states are quarkonia.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Light scalar mesons can be understood as dynamically generated resonances. | background 0.98 | 0.14 | 0.31 | asserted 0.88 |
| s1 | They arise as 'companion poles' in the propagators of quark-antiquark seed states when accounting for hadronic loop contributions to the self-energies of the latter. | background 0.90 | 0.14 | 0.15 | asserted 1.00 |
| s2 | Such a mechanism may explain the overpopulation in the scalar sector - there exist more resonances with total spin $J=0$ than can be described within a quark model. | background 0.68 | 0.10 | 0.10 | hedged possibility 0.99 |
| s3 | Along this line, we study an effective Lagrangian approach where the isovector state $a_{0}(1450)$ couples via both non-derivative and derivative interactions to pseudoscalar mesons. | contribution 0.62 | 0.83 | 0.05 | asserted 0.92 |
| s4 | It is demonstrated that the propagator has two poles: a companion pole corresponding to $a_{0}(980)$ and a pole of the seed state $a_{0}(1450)$. | result 1.00 | 0.92 | 0.28 | asserted 1.00 |
| s5 | The positions of these poles are in quantitative agreement with experimental data. | result 1.00 | 0.87 | 0.17 | asserted 1.00 |
| s6 | Besides that, we investigate similar models for the isodoublet state $K_{0}^{\ast}(1430)$ by performing a fit to $\pi K$ phase shift data in the $I=1/2,$ $J=0$ channel. | contribution 0.59 | 0.94 | 0.04 | asserted 0.88 |
| s7 | We show that, in order to fit the data accurately, a companion pole for the $K_{0}^{\ast}(800)$, that is, the light $\kappa$, is required. | result 1.00 | 0.93 | 0.18 | asserted 1.00 |
| s8 | A large-$N_{c}$ study confirms that both resonances below $1$ GeV are predominantly four-quark states, while the heavy states are quarkonia. | result 0.63 | 0.84 | 0.30 | asserted 1.00 |
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The paper
Original abstract
Light scalar mesons can be understood as dynamically generated resonances. They arise as 'companion poles' in the propagators of quark-antiquark seed states when accounting for hadronic loop contributions to the self-energies of the latter. Such a mechanism may explain the overpopulation in the scalar sector - there exist more resonances with total spin $J=0$ than can be described within a quark model. Along this line, we study an effective Lagrangian approach where the isovector state $a_{0}(1450)$ couples via both non-derivative and derivative interactions to pseudoscalar mesons. It is demonstrated that the propagator has two poles: a companion pole corresponding to $a_{0}(980)$ and a pole of the seed state $a_{0}(1450)$. The positions of these poles are in quantitative agreement with experimental data. Besides that, we investigate similar models for the isodoublet state $K_{0}^{\ast}(1430)$ by performing a fit to $\pi K$ phase shift data in the $I=1/2,$ $J=0$ channel. We show that, in order to fit the data accurately, a companion pole for the $K_{0}^{\ast}(800)$, that is, the light $\kappa$, is required. A large-$N_{c}$ study confirms that both resonances below $1$ GeV are predominantly four-quark states, while the heavy states are quarkonia.
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How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it
Cites it as support 1 paper
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Recent work [ref] supports this phenomenon of generating extra resonances in the light scalar sector (also see Ref. [ref] and references therein).
Why static bound-state calculations of tetraquarks should be met with scepticism · Unquenching the quark model · 0.97
Cites it as background 1 paper
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In this context, scenarios such as tetraquark states [ref] , molecular states [ref] and dynamically generated states from meson-meson interactions [ref] or a quark-antiquark seed [ref] have been adopted to describe the mysterious properties of the $a_0(980)$; see Refs. [ref] for reviews in this matter.
Low-mass enhancement of kaon pairs in $B^+\to\bar{D}^{(*)0}K^+\bar{K}^0$ and $B^0\to D^{(*)-}K^+\bar{K}^0$ decays · Introduction · 0.90
What it cites · 218 sentences without a confident label
Builds on 5 papers
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In Chapter [ref], we then have repeated and extended previous calculations of Törnqvist and Roos [ref] and Boglione and Pennington [ref] in order to clarify some open issues concerning the dynamical generation in the isovector sector ($I=1$).
Dynamical Generation of Scalar Mesons · Summary and conclusions · 0.99
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In Chapter [ref], we then have repeated and extended previous calculations of Törnqvist and Roos [ref] and Boglione and Pennington [ref] in order to clarify some open issues concerning the dynamical generation in the isovector sector ($I=1$).
UNDERSTANDING THE SCALAR MESON $q\bar q$ NONET · Summary and conclusions · 0.99
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In Chapter [ref], we then have repeated and extended previous calculations of Törnqvist and Roos [ref] and Boglione and Pennington [ref] in order to clarify some open issues concerning the dynamical generation in the isovector sector ($I=1$).
Resurrection of the Sigma Meson · Summary and conclusions · 0.99
Uses the method or tool of 11 papers
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Hierzu wurden durch das sogenannte “erweiterte Lineare Sigma Modell” (eLSM) [ref] inspirierte effektive Theorien mit derivativen Kopplungen eingesetzt, um den eingangs erwähnten Isovektor $a_0(980)$ und das Isodoublet $K_0^∗(800)$ (auch $κ$ genannt) zu beschreiben.
Quarkonium Phenomenology in Vacuum · Deutsche Zusammenfassung · 0.81
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Hierzu wurden durch das sogenannte “erweiterte Lineare Sigma Modell” (eLSM) [ref] inspirierte effektive Theorien mit derivativen Kopplungen eingesetzt, um den eingangs erwähnten Isovektor $a_0(980)$ und das Isodoublet $K_0^∗(800)$ (auch $κ$ genannt) zu beschreiben.
Vacuum Properties of Mesons in a Linear Sigma Model with Vector Mesons and Global Chiral Invariance · Deutsche Zusammenfassung · 0.81
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Hierzu wurden durch das sogenannte “erweiterte Lineare Sigma Modell” (eLSM) [ref] inspirierte effektive Theorien mit derivativen Kopplungen eingesetzt, um den eingangs erwähnten Isovektor $a_0(980)$ und das Isodoublet $K_0^∗(800)$ (auch $κ$ genannt) zu beschreiben.
Meson vacuum phenomenology in a three-flavor linear sigma model with (axial-)vector mesons · Deutsche Zusammenfassung · 0.81
Uses data or values from 2 papers
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The final values for the resonance above $1$ GeV have been given as $m_K_0^∗=1.450±0.001$ GeV and $Γ=0.285±0.012$ GeV [ref] .
Quarkonium Phenomenology in Vacuum · Some words on the scalar isodoublet resonances · 0.99
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The final values for the resonance above $1$ GeV have been given as $m_K_0^∗=1.450±0.001$ GeV and $Γ=0.285±0.012$ GeV [ref] .
Meson vacuum phenomenology in a three-flavor linear sigma model with (axial-)vector mesons · Some words on the scalar isodoublet resonances · 0.99
Compares with 10 papers
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The results are shown in Figure [ref] and are in agreement with previous works on the subject [ref] : $(i)$ We observe a rapidly falling inelasticity when the $KK̅$ threshold is reached.
Form factors of the isovector scalar current and the $\eta\pi$ scattering phase shifts · Phase shifts and inelasticity · 0.99
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The results are shown in Figure [ref] and are in agreement with previous works on the subject [ref] : $(i)$ We observe a rapidly falling inelasticity when the $KK̅$ threshold is reached.
Meson-Meson interaction in a non-perturbative chiral approach · Phase shifts and inelasticity · 0.99
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We have repeated previous calculations of Törnqvist and Roos [ref] and Boglione and Pennington [ref] concerning the scalar isotriplet channel.
Dynamical Generation of Scalar Mesons · Summary and conclusions · 0.81
Cites as support 8 papers
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This is in agreement with various other works on this topic [ref] : virtual kaon-kaon pairs near the corresponding threshold are important for the dynamical generation of the resonance $a_0(980)$.
Radiative $\phi$ decays with derivative interactions · Branching ratios and coupling constants for $a_0(980)$ · 0.98
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This is in agreement with various other works on this topic [ref] : virtual kaon-kaon pairs near the corresponding threshold are important for the dynamical generation of the resonance $a_0(980)$.
Strong and radiative decays of the scalars f0(980) and a0(980) in a hadronic molecule approach · Branching ratios and coupling constants for $a_0(980)$ · 0.98
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This is in agreement with various other works on this topic [ref] : virtual kaon-kaon pairs near the corresponding threshold are important for the dynamical generation of the resonance $a_0(980)$.
Decay of light scalar mesons into vector-photon and into pseudoscalar mesons · Branching ratios and coupling constants for $a_0(980)$ · 0.98
Cites as background 43 papers
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The eLSM was formulated for $N_f=3$ quark flavors, vanishing temperatures and densities, and includes vector and axial-vector mesons, in some versions also candidates for the lowest lying scalar and pseudoscalar glueballs [ref] .
Is f0(1710) a glueball? · The extended Linear Sigma Model in a nutshell · 0.85
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The eLSM was formulated for $N_f=3$ quark flavors, vanishing temperatures and densities, and includes vector and axial-vector mesons, in some versions also candidates for the lowest lying scalar and pseudoscalar glueballs [ref] .
The Glueball in a Chiral Linear Sigma Model with Vector Mesons · The extended Linear Sigma Model in a nutshell · 0.85
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We now recapitulate the seminal works TR [ref] and BP [ref] , where the latter uses the same model as the former but with a slightly different set of parameters.
Dynamical Generation of Scalar Mesons · Approach of TR and BP · 0.87
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