Comment on “Confirmation of the Sigma Meson”

Isgur, Nathan; Speth, J.

doi:10.1103/physrevlett.77.2332

Cited by 39 publications

(49 citation statements)

References 6 publications

(26 reference statements)

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“…Their fit to ππ data in terms of the amplitude A gives quite different parameters than using the full amplitude T of Eq. (18). That there is more to dynamics than s-channel resonances has been noted by Isgur and Speth in this same context [18].…”

Section: Scattering Amplitudesmentioning

confidence: 74%

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Dynamical generation of scalar mesons

2002

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractStarting with just one bare seed for each member of a scalar nonet, we investigate when it is possible to generate more than one hadronic state for each set of quantum numbers.In the framework of a simple model, we find that in the I = 1 sector it is possible to generate two physical states with the right features to be identified with the a 0 (980) and the a 0 (1450). In the I = 1/2 sector, we can generate a number of physical states with masses higher than 1 GeV, including one with the right features to be associated with the K * 0 (1470), but none which can be identified with the light κ scalar meson. The I = 0 sector is the most complicated and elusive: since all outcomes are very strongly model dependent, we cannot draw any robust conclusion. Nevertheless, we find that in that case too, depending on the coupling scheme adopted, the occurrence of numerous states can be achieved. This shows that dynamical generation of physical states is a possible solution to the problem of accounting for more scalar mesons than can fit in a single nonet, as experiments clearly deliver.

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Section: Scattering Amplitudesmentioning

confidence: 74%

“…(18). That there is more to dynamics than s-channel resonances has been noted by Isgur and Speth in this same context [18].…”

Section: Scattering Amplitudesmentioning

confidence: 74%

Dynamical generation of scalar mesons

2002

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“…Even if the first pion excitation state is identified with the Π(1300) resonance, whose mass pole is still likely to be below the continuum threshold, the width of this resonance may be as large as 600 MeV [5]. Moreover, the lowest isoscalar 0 + meson, if it exists at all [6], may have a width even larger than its mass [7], though arguments for a σ(550)-resonance with a somewhat more moderate width have also been recently advanced [8].…”

Section: Laplace Sum-rule Width Corrections To the Lowest-lying Resonmentioning

confidence: 99%

Broad sub-continuum resonances and the case for finite-energy sum-rules

et al. 1998

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There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We first discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We then show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension > 6 condensates containing at least one q q pair. We extract the direct single-instanton contribution to the F 1 sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass-resonance contributions within the pseudoscalar channel.

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“…The radial dimensions and potential strenghts are quite comparable. It is obvious to ask if the implied great width resonance supported by this potential can be identified with the isoscalar σ meson which OBE potential require and which is of general interest [23,24,25,26]. It is intended to study this resonance in more details by our OSBEP approach and use also other experimental information.…”

Section: B πN Scattering Lengths and πN N Coupling Constantsmentioning

confidence: 99%

Inversion potentials for meson-nucleon and meson-meson interactions

Sander

Geramb

1997

Inverse and Algebraic Quantum Scattering Theory

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Two-body interactions of elementary particles are useful in particle and nuclear physics to describe qualitatively and quantitatively few-and many-body systems. We are extending for this purpose the quantum inversion approach for systems consisting of nucleons and mesons. From the wide range of experimentally studied two-body systems we concentrate here on πN , ππ, K + N , Kπ and KK. As input we require results of phase shift analyses. Quantum inversion Gelfand-Levitan and Marchenko single and coupled channel algorithms are used for Schrödinger type wave equations in partial wave decomposition. The motivation of this study comes from our two approaches: to generate and investigate potentials directly from data by means of inversion and alternatively use linear and nonlinear boson exchange models. The interesting results of inversion are coordinate space informations about radial ranges, strengths, long distance behaviors, resonance characteristics, threshold effects, scattering lengths and bound state properties.

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Comment on “Confirmation of the Sigma Meson”

Cited by 39 publications

References 6 publications

Dynamical generation of scalar mesons

Dynamical generation of scalar mesons

Broad sub-continuum resonances and the case for finite-energy sum-rules

Inversion potentials for meson-nucleon and meson-meson interactions

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