Chiral symmetry and the near threshold pion-induced 2π production on the nucleon

Jäkel, Oliver; Ortner, H.; Dillig, M.; Vasconcellos, C. A. Z.

doi:10.1016/0375-9474(90)90120-b

Cited by 23 publications

(8 citation statements)

References 35 publications

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“…This allows one to understand why resonance models like in refs. [11,12] work fairly well even in the threshold region (although these are not as precise as the calculation presented here). The effect of the terms proportional to the dimension three LECs is somewhat more pronounced.…”

Section: Discussioncontrasting

confidence: 56%

One-loop analysis of the reaction πN→ππN

2000

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Single pion production off nucleons is studied in the framework of heavy baryon chiral perturbation theory to third order in the chiral expansion. Using total and some older differential cross section data to pin down the low-energy constants, most of the recent differential cross sections and angular correlation functions can be described as well as total cross sections at higher energies. We show that the contributions from the one loop graphs are essentially negligible and that the dominant terms at second and third order are related to pion-nucleon scattering graphs with one pion added. We also discuss the possibility of extracting the pion-pion S-wave scattering lengths from the unpolarized data.

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Section: Discussioncontrasting

confidence: 56%

One-loop analysis of the reaction πN→ππN

2000

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“…1c. These last two diagrams are the basic element in the description of πN → ππN reaction near the threshold [35][36][37][38]. The appearance of the pole terms and contact 3πN N interactions at the same order of the chiral expansion is crucial for the in-medium calculations where due to the partial cancellations the physical amplitudes become independent of the parameterization of U matrix even in the presence of the nuclear background in accord with the equivalence theorem [39].…”

Section: Effective Lagrangianmentioning

confidence: 98%

Two pion mediated scalar isoscalarNNinteraction in the nuclear medium

2006

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We study the modification of the nucleon nucleon interaction in a nuclear medium in the scalar isoscalar channel, mediated by the exchange of two correlated (σ channel) or uncorrelated pions. For this purpose we use a standard approach for the renormalization of pions in nuclei. The corrections obtained for the N N interaction in the medium in this channel are of the order of 20% of the free one in average, and the consideration of short range correlations plays an important role in providing these moderate changes. Yet, the corrections are sizable enough to suggest further studies of the stability and properties of nuclear matter.

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“…and is more tuned to the resonance than to the threshold region. Similarly, the work of the Erlangen group [5] shows the importance of the non-linear pion couplings at tree level but does not include higher derivative operators as done here. Our appraoch lends more credit to the conclusions of these papers that the intricate dynamics of the reaction πN → ππN reveals itself best in double differential cross sections and angular correlation functions but not in the total cross sections.…”

Section: Comparison To Other Calculationsmentioning

confidence: 99%

“…In particular, it will tell to which extent loop effects are necessary (and thus testing the sensitivity to the pion-pion interaction beyond tree level) and to which extent one has to incorporate resonance degrees of freedom like the Roper and the ∆-isobar as well as heavier mesons (σ, ρ, ω) as dynamical degrees of freedom (as it is done in many models, see e.g. [4] [5]). Our calculation is in spirit closest to the one of ref.…”

Section: Introductionmentioning

confidence: 99%

The reaction πN → ππN above threshold in chiral perturbation theory

1997

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Single pion production off nucleons is studied in the framework of relativistic baryon chiral perturbation theory at tree level with the inclusion of the terms from the dimension two effective pion-nucleon Lagrangian. The five appearing low-energy constants are fixed from pion-nucleon scattering data. Despite the simplicity of the approach, most of the existing data for total and differential cross sections as well as for the angular correlation functions for incoming pion kinetic energies up to 400 MeV can be satisfactorily described.

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Chiral symmetry and the near threshold pion-induced 2π production on the nucleon

Cited by 23 publications

References 35 publications

One-loop analysis of the reaction πN→ππN

One-loop analysis of the reaction πN→ππN

Two pion mediated scalar isoscalarNNinteraction in the nuclear medium

The reaction πN → ππN above threshold in chiral perturbation theory

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