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.

The development of the ANL-Osaka model and the formula for using the PWA presented on this web page to calculate cross sections can be found here: ANL-Osaka Model

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The results presented here are from the analysis reported in

H. Kamano, S.X Nakamura, T.-S. H. Lee, T. Sato, Phys. Rev. C 88, 035209(2013);
S.X. Nakamura, H.Kamano, T. Sato, Phys. Rev. D 92, 074024 (2015);
H. Kamano, S.X. 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 parameters of the extracted nucleon resonances are in

Resonance Pole Positions and Residues of πN -> πN PWA

Helicity amplitudes of N* → γN and ∆*→ γN transitions

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, γ* n → πN

4. Inclusive N(e,e') reactions : p(e,e'), n(e,e')

5. 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.

Selected fits to the data are shown in the listed figures.

The predicted PWA for each process are given in tables.

The formula for using the PWA to calculate the MB->M'B' cross sections can be found here: crst-mbmb

[ 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).

Selected fits to the data are shown in the listed figures.

The predicted multipole amplitudes for each process are given in tables.

Formula for using the predicted multipole amplitudes to calculate γp → MB cross sections can be found here: crst-gnmb

[ 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, γ*n → π N

Note: Unit of multipole amplitudes is (Fermi/1000)

The standard definition of multipole amplitudes is used, and can be found here: crst-eepi

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

[ γ*n → π0 n ]
Table

[ γ*n → π- p ]
Table

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Structure functions of N(e,e')X, N(e,e'π)X

Note: Unit of structure functions W_1 and W_2 is (1/MeV).

The definitions of structure functions can be found here crst-incl

The predicted structure functions are given in tables. The fits to the data are shown in the listed figures.

[p(e,e')X, p(e,e')πN ]
Fit: dσ/dΩdE', Q2=0.3 (GeV/c)**2
Fit: dσ/dΩdE', Q2=1.1 (GeV/c)**2
Fit: dσ/dΩdE', Q2=2.3 (GeV/c)**2
Table

[ n(e,e')X, n(e,e')πN ]
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Table

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PWA of πN -> π∆, ρN, σN -> ππN

Selected comparisons with the πN -> ππN data are shown in the listed figures.

The predicted PWA for each process are given in tables.

The formula for using the presented PWA to calculate the πN -> π∆, ρN, σN -> ππN cross sections can be found here: crst-pipin

[ 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);
N. Suzuki, T. Sato, T.-S. H. Lee, Phys. Rev. C 79, 025205 (2009);
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);
N. Suzuki, T. Sato, T.-S. H. Lee, Phys. Rev. C 82, 045206 (2010);
H. Kamano, S.X. Nakamura, T.-S. H. Lee, T. Sato, Phys. Rev. C 88, 035209(2013);
S.X. Nakamura, H.Kamano, T. Sato, Phys. Rev. D 92, 074024 (2015);
H. Kamano, S.X. Nakamura, T.-S. H. Lee, T. Sato, Phys. Rev. C 94, 015201 (2016);

Contact Person: Tsung-Shung Harry Lee (tshlee@anl.gov)
Last update: September 25, 2019