Duality and the reaction πN to πΔ

Froggatt, C.D.; Parsons, Nigel H.

doi:10.1088/0305-4616/3/2/008

Cited by 54 publications

(126 citation statements)

References 33 publications

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“…3a). Omitting from its definition the 6) with the definitions and expressions of the functions R, R and F given in Appendix D.…”

Section: Electromagnetic Radiative Correctionsmentioning

confidence: 99%

“…Unfortunately, the lack of direct low energy data forces one to reconstruct the low energy scattering amplitude from extrapolations [5,6,7] from high energy data [8,9,10] and from indirect information coming from K l4 decay [11], at the price of increasing error bars on numerical values. The 20% uncertainty of the "experimental" value of the isospin zero S-wave scattering length, a 0 0 = 0.26 ± 0.05 [6,12,13,14], does not allow one to draw a clear-cut conclusion when the latter is compared with the theoretical prediction of standard chiral perturbation theory, which is 0.20 to the one-loop order [3] and 0.217 to the two-loop order [15].…”

Section: Introductionmentioning

confidence: 99%

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Erratum: Relativistic effects in the pionium lifetime [Phys. Rev. D 58, 014011 (1998)]

Jallouli¹,

Sazdjian²

1998

Phys. Rev. D

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The pionium decay width is evaluated in the framework of chiral perturbation theory and the relativistic bound state formalism of constraint theory. Corrections of order O(α) are calculated with respect to the conventional lowest-order formula, in which the strong interaction amplitude has been calculated to two-loop order with charged pion masses.Strong interaction corrections from second-order perturbation theory of the bound state wave equation are found to be of the order of 0.4%. Electromagnetic radiative corrections, due to pion-photon interactions, are estimated to be of the order of −0.1%. Electromagnetic mass shift insertions in internal propagators produce a correction of the order of 0.3%. The correction due to the passage from the strong interaction scattering amplitude evaluated with the mass parameter fixed at the charged pion mass to the amplitude evaluated with the mass parameter fixed at the neutral pion mass is found to be of the order of 6.4%.

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“…3a). Omitting from its definition the 6) with the definitions and expressions of the functions R, R and F given in Appendix D.…”

Section: Electromagnetic Radiative Correctionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Erratum: Relativistic effects in the pionium lifetime [Phys. Rev. D 58, 014011 (1998)]

Jallouli¹,

Sazdjian²

1998

Phys. Rev. D

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“…Here we use results of the CERN-Munich experiment [7] π − p → π + π − n for all channels with ℓ ≤ 3. The scattering is purely elastic up to M ππ = 987.3 MeV where a coupling π + π − ↔ KK becomes dominant.…”

Section: B πN Scattering Lengths and πN N Coupling Constantsmentioning

confidence: 99%

“…The scattering is purely elastic up to M ππ = 987.3 MeV where a coupling π + π − ↔ KK becomes dominant. In addition to the experimental data of Froggatt et al [7] we use data from meson exchange models [18] and chiral perturbation theory χPT [19]. Notation for the isospin and angular momentum channels uses δ T ℓ or V T ℓ .…”

Section: B πN Scattering Lengths and πN N Coupling Constantsmentioning

confidence: 99%

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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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Dispersion theory of nucleon Compton scattering and polarizabilities

Schumacher

Scadron

2013

Fortschritte der Physik

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A status report on the topic Compton scattering and polarizabilities is presented with emphasis on the scalar t-channel as entering into dispersion theory. Precise values for the polarizabilities are obtained leading to $\alpha_p = 12.0\pm 0.6$ $(12.0)$, $\beta_p=1.9\mp 0.6$ $(1.9)$, $\alpha_n= 12.5\pm 1.7$ $(13.4)$, $\beta_n= 2.7 \mp 1.8$ $(1.8)$ in units of $10^{-4}$ fm$^3$ and $\gamma^{(p)}_\pi = -36.4 \pm 1.5$ $(-36.6)$, $\gamma^{(n)}_\pi = 58.6 \pm 4.0$ $(58.3)$, $(\gamma^{(p)}_0= -0.58\pm 0.20)$, $(\gamma^{(n)}_0 = +0.38\pm 0.22)$ in units of $10^{-4}$ fm$^4$, for the proton (p) and neutron (n), respectively. The data given with an error are {\it recommended} experimental values with updates compared to [1] where necessary, the data in parentheses are predicted values. These predicted values are not contained in [1], but are the result of a newly developed analysis which is the main topic of the present paper. The most important recent discovery is that the largest part of the electric polarizability and the total diamagnetic polarizability of the nucleon are properties of the $\sigma$ meson as part of the constituent-quark structure, as expected from the mechanism of chiral symmetry breaking. This view is supported by an experiment on Compton scattering by the proton carried out in the second resonance region, where a large contribution from the $\sigma$ meson enters into the scattering amplitudes. This experiment led to a determination of the mass of the $\sigma$ meson of $m_\sigma = 600 \pm 70$ MeV. From the experimental $\alpha_p$ and predicted differences $(\alpha_n - \alpha_p)$ neutron polarizabilities in the range $\alpha_n= 12.0 - 13.4$ are predicted, where the uncertainties are related to the $f_0(980)$ and $a_0(980)$ scalar mesons

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Duality and the reaction πN to πΔ

Cited by 54 publications

References 33 publications

Erratum: Relativistic effects in the pionium lifetime [Phys. Rev. D 58, 014011 (1998)]

Erratum: Relativistic effects in the pionium lifetime [Phys. Rev. D 58, 014011 (1998)]

Inversion potentials for meson-nucleon and meson-meson interactions

Dispersion theory of nucleon Compton scattering and polarizabilities

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