ANL-Osaka Partial-Wave Amplitudes (PWA)

This web page presents the partial-wave amplitudes of meson-baryon reactions determined from the Argonne National Laboratory-Osaka University (ANL-Osaka) dynamical coupled-channel analysis of the data of pion-nucleon and photon-nucleon reactions in the invariant mass W ≤ 2.0 GeV region.

Channels included in the model are γN, πN, ηN, KΛ, KΣ, ππN ( π∆, ρN, σN). About 30,000 data points are included in the fits with about 350 model parameters which define phenomenologically the meson-exchange interactions between the considered meson-baryon channels and the quark-gluon excitations of the nucleon to about 20 excited states. The resulting partial-wave amplitudes can be used to:

(1) Extract nucleon resonance parameters,

(2) investigate meson production reactions on nuclei in the nucleon resonance region,

(3) predict the medium effects on the propagation of mesons and nucleon resonances in hadron matter.

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The results presented here are from the analysis reported in

H. Kamano, N. Nakamura, T.-S. H. Lee, T. Sato, Phys. Rev. C 88, 035209(2013);
H. Kamano, N. Nakamura, T.-S. H. Lee, T. Sato, Phys. Rev. C 94, 015201 (2016);

The quality of the fit to the data can be seen from comparing the the predicted total cross sections with the available data

Total cross sections : πp -> MB-1

Total cross sections : πp -> MB-2

Total cross sections : γp -> MB

Total cross sections : πp, γp -> X

Total cross sections : p(e,e') X

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The PWA presented on this webpage are for :

1. Meson-baryon reactions : MB → M′B′; where MB,M′B′ = πN, ηN, KΛ, KΣ

2. Meson photo-production reactions : γN → πN, ηN, KΛ, KΣ

3. Pion electroproduction reactions : p(e,e'π)N : γ* p → πN

4. Two-pion production reactions : πN -> ππN ( π∆, ρN, σN)

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PWA for MB->M'B'

Note: the PWA (T) is unitless and is related to the S-matrix by S = 1 + 2 i T in each partial-wave.

The predicted PWA for each process are given in tables. Selected fits to the data are shown in the listed figures.

[ πN → πN ]
Fit: dσ/dΩ
Fit: P
Table

[ πN → ηN ]
Fit: dσ/dΩ
---
Table

[ πN → KΛ ]
Fit: dσ/dΩ
Fit: P
Table

[ πN → KΣ ]
Fit: dσ/dΩ
Fit: P
Table

[ ηN → ηN ]
Table

[ ηN → KΛ ]
Table

[ ηN → KΣ ]
Table

[ KΛ → KΛ ]
Table

[ KΛ → KΣ ]
Table

[ KΣ → KΣ ]
Table

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PWA for γp → MB, γn → πN

Note: Unit of multipole amplitudes is (Fermi/1000), The standard definition of multipole amplitudes is used, and can be found here: multipoles

The predicted multipole amplitudes for each process are given in tables. Selected fits to the data are shown in the listed figures.

[ γp → π0p ]
Fit: dσ/dΩ
Fit: Σ
Table

[ γp → π+n ]
Fit: dσ/dΩ
Fit: Σ
Table

[ γp → ηp ]
Fit: dσ/dΩ
Fit: Σ, T
Table

[ γp → K+Λ ]
Fit: dσ/dΩ
Fit: P, Σ, T
Table

[ γp → K+Σ0 ]
Fit: dσ/dΩ
Fit: P, Σ
Table

[ γp → K0Σ+ ]
Fit: dσ/dΩ
Fit: P, Σ
Table

[ γn → π−p ]
Fit: dσ/dΩ
Fit: dσ/dΩ
Fit: Σ
Table

[ γn → π0n ]
Fit: dσ/dΩ
--
Fit: Σ
Table

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PWA for γ*p → π N

Note: Unit of multipole amplitudes is (Fermi/1000), The standard definition of multipole amplitudes is used, and can be found here: multipoles

The predicted multipole amplitudes for each process are given in tables. Selected fits to the data are shown in the listed figures.

[ γ*p → π0 p ]
Fit: dσ/dΩ, Q2=0.4 (GeV/c)**2
Fit: dσ/dΩ, Q2=1.76 (GeV/c)**2
Fit: dσ/dΩ, Q2=3.00 (GeV/c)**2
Table

[ γ*p → π+ n ]
Fit: dσ/dΩ, Q2=0.4 (GeV/c)**2
Fit: dσ/dΩ, Q2=1.76 (GeV/c)**2
Fit: dσ/dΩ, Q2=2.91 (GeV/c)**2
Table

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PWA of πN -> π∆, ρN, σN

Note:These amplitudes are only parts of the full amplitudes for calculating πN -> ππN cross sections. See Ref. H. Kamano et al ,Phys. Rev. C 79, 025206 (2009);

[ πN -> σN ]
Fit: σ(total)
Table

[ πN -> ρN ]
Fit: σ(total)
Table

[ πN -> π∆ ]
Fit: σ(total)
Table

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The development of the ANL-Osaka dynamical coupled-channel model analysis can be found in the following references:

T. Sato , T.-S. H. Lee, Phys. Rev. C 54, 2660(1996);
T. Sato, T.-S. H. Lee, Phys. Rev. C 63, 055201 (2001);
A. Matsuyama , T.-S. H. Lee, T. Sato, Phys. Rept. 439, 193(2007);
B. Julia-Diaz, T.-S. H. Lee, T. Sato, L.C. Smith, Phys. Rev. C 75, 015205 (2007);
B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato Phys. Rev. C 76, 065201 (2007);
B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato, L.C. Smith, Phys. Rev. C 77, 025205 (2008);
J.Durand, B. Julia-Diaz, T.-S. H. Lee, B. Saghai, T. Sato Phys. Rev. C 78, 025204 (2008);
H. Kamano, B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato Phys. Rev. C 79, 025206 (2009);
B. Julia-Diaz, H. Kamano, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki, Phys. Rev. C 80, 025207 (2009);
H. Kamano, B. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato Phys. Rev. C 80, 065203 (2009);
N. Suzuki, B. Julia-Diaz, H. Kamano, T.-S. H. Lee, A. Matsuyama, T. Sato Phys. Rev. Lett. 104, 042302 (2010);
H. Kamano, S.X. Nakamura, T.-S. H. Lee, T. Sato Phys. Rev. C 81, 065207 (2010);
H. Kamano, N. Nakamura, T.-S. H. Lee, T. Sato, Phys. Rev. C 88, 035209(2013);
H. Kamano, N. Nakamura, T.-S. H. Lee, T. Sato, Phys. Rev. C 94, 015201 (2016);

T.-S. Harry Lee
Last update August 15, 2018