Dynamical coupled-channels study of pi N --&gt; pi pi N reactions

Kamano, H.; Julia-Diaz, B.; Lee, T. -S. H.; Matsuyama, A.; Sato, T.

doi:10.48550/arxiv.0807.2273

Cited by 3 publications

(6 citation statements)

References 31 publications

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“…These results are far more successful than all of the previous investigations, as discussed in Ref. [13]. When only the term with M ′ B ′ = M B in the Eq.…”

Section: 32supporting

confidence: 64%

“…This has been done in Ref. [13] in the study of πN → ππN reactions which are known to be dominated by these unstable particle channels. Before we present the predicted πN → ππN cross sections, we note here that the main feature of our approach is a dynamical coupled-channels treatment of the unstable π∆, ρN, σN channels.…”

Section: 32mentioning

confidence: 99%

“…In this article, we give a review of the dynamical reaction models developed in Refs. [4,5,6,7,8,9,10,11,12,13,14]. Other approaches for investigating N * states have been reviewed in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Such a model has been developed by using the unitary transformation method in Ref. [8] and applied to investigate πN elastic scattering [10], γN → πN reactions [11] πN → ηN reactions [12], and πN → ππN reactions [13]. In this article, we will also review these results.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical models of the excitations of nucleon resonances

Satô

Lee

2009

J. Phys. G: Nucl. Part. Phys.

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The development of a dynamical model for investigating the nucleon resonances using the reactions of meson production from πN , γN , N (e, e ′ ), and N (ν, l ) reactions is reviewed. The results for the ∆ (1232) state are summarized and discussed. The progress in investigating higher mass nucleon resonances is reported.N (ν, l π)N reactions.The main challenge of developing dynamical reaction models of meson production reactions in the higher mass N * region can be seen in Fig.1. We see that two-pion photo-production cross sections shown in the left-hand-side become larger than the one-pion photo-production as the γp invariant mass exceeds W ∼ 1.4 GeV. In the right-hand-side, KY ( K + Λ, K + Σ 0 , K 0 Σ + ), ηp, and ωp production cross sections are a factor of about 10 weaker than the dominant π + π − p production. From the unitarity condition, we have for any single meson production processwhere ρ α denotes an appropriate phase space factor for the channel α. The large two-pion production cross sections seen in Fig.1 indicate that the second term in the right-hand-side of Eq.(1) is significant and hence the single meson production reactions above the ∆ region must be influenced strongly by the coupling with the two-pion channels. Similarly, the two-pion production γN → ππN is also influenced by the transition to two-body M B channelClearly, a sound dynamical reaction model must be able to describe the two pion production and to account for the above unitarity conditions. Such a model has been developed by using the unitary transformation method in Ref.[8] and applied to investigate πN elastic scattering[10], γN → πN reactions[11] πN → ηN reactions[12], and πN → ππN reactions[13]. In this article, we will also review these results. This article is organized as follows. In section 2, we explain the unitary transformation method developed in Ref.[31] using a simple model. The constructed model Hamiltonian for investigating N * states is given in section 3. The multi-channel multi-resonance reaction model developed in Refs.[4,8] for calculating the mesonbaryon reaction amplitudes is presented in section 4. In section 5, we give formula for defining the N -N * transition form factors and calculating the cross sections of pion production from πN , γN , N (e, e ′ ), and N (ν, l ) reactions. The results in the ∆ (1232) region and in the higher mass N * region are reviewed in section 6. A summary and discussions of future developments are given in section 7. Unitary Transformation MethodThe unitary transformation method was essentially based on the same idea of the Foldy-Wouthuysenth transformation developed in the study of electromagnetic interactions. It was first developed in 1950's by Fukuda, Sawada and Taketani [32], and independently by Okubo[33]. This approach, called the FST-Okubo method, has been very useful in investigating nuclear electromagnetic currents [34,35] and relativistic descriptions of nuclear interactions [36,37,38]. The advantage of this approach is that the resulting effective Hamiltonian is energy...

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“…These results are far more successful than all of the previous investigations, as discussed in Ref. [13]. When only the term with M ′ B ′ = M B in the Eq.…”

Section: 32supporting

confidence: 64%

Section: 32mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamical models of the excitations of nucleon resonances

Satô

Lee

2009

J. Phys. G: Nucl. Part. Phys.

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“…[22] is currently being improved by also fitting other data of πN and γN reactions. For example, some progress has been made to also fit the data of πN → ππN [36], γN → πN [37], and πN → ηN [38]. We thus do not include the results for other partial waves in Table I.…”

Section: Resonance Model With Non-resonant Interactionsmentioning

confidence: 99%

Extraction of resonances from meson-nucleon reactions

2009

Self Cite

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We present a pedagogical study of the commonly employed Speed-Plot (SP) and Time-delay (TD) methods for extracting the resonance parameters from the data of two particle coupled-channels reactions. Within several exactly solvable models, it is found that these two methods find poles on different Riemann sheets and are not always valid. We then develop an analytic continuation method for extracting nucleon resonances within a dynamical coupled-channel formulation of πN and γN reactions. The main focus of this paper is on resolving the complications due to the coupling with the unstable π∆, ρN, σN channels which decay into ππN states. By using the results from the considered exactly solvable models, explicit numerical procedures are presented and verified. As a first application of the developed analytic continuation method, we present the nucleon resonances in some partial waves extracted within a recently developed coupled-channels model of πN reactions. The results from this realistic πN model, which includes πN , ηN , π∆, ρN , and σN channels, also show that the simple pole parametrization of the resonant propagator using the poles extracted from SP and TD methods works poorly.

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Chiral perturbation theory calculation for pn $ \rightarrow$ d $ \pi$ $ \pi$ at threshold

et al. 2011

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We investigate the reaction pn → dππ in the framework of Chiral Perturbation Theory. For the first time a complete calculation of the leading order contributions is presented. We identify various diagrams that are of equal importance as compared to those recognized in earlier works.The diagrams at leading order behave as expected by the power counting. Also for the first time the nucleon-nucleon interaction in the initial, intermediate and final state is included consistently and found to be very important. This study provides a theoretical basis for a controlled evaluation of the non-resonant contributions in two-pion production reactions in nucleon-nucleon collisions.

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Dynamical coupled-channels study of pi N --> pi pi N reactions

Cited by 3 publications

References 31 publications

Dynamical models of the excitations of nucleon resonances

Dynamical models of the excitations of nucleon resonances

Extraction of resonances from meson-nucleon reactions

Chiral perturbation theory calculation for pn $ \rightarrow$ d $ \pi$ $ \pi$ at threshold

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