Coupled-channels analysis of hadronic and electromagnetic p , h , two- p production reactions
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Transcript of Coupled-channels analysis of hadronic and electromagnetic p , h , two- p production reactions
Coupled-channels analysis of hadronic and Coupled-channels analysis of hadronic and electromagneticelectromagnetic
, , , two-, two- production reactions production reactions
Hiroyuki KamanoHiroyuki KamanoExcited Baryon Analysis Center, Jefferson LabExcited Baryon Analysis Center, Jefferson Lab
in collaboration within collaboration withB. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. SatoB. Julia-Diaz, T.-S. H. Lee, A. Matsuyama, T. Sato
DNP08 Oct. 23-26
Approaches to determining N-N* form factors
ElectromagneticN-N* form factors
QQCCDD
Lattice QCDHadron Models
Dynamical Coupled-Channels Analysis @ EBAC
Reaction Data
Partial wave (LSJ) amplitude of a b reaction:
Reaction channels:
Potential:
coupled-channels effect
Coupled-channels model @ EBAC
meson exchange bare N* state
For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
Corresponds to the e.m. N-N* transition form factor!
Through the dynamical reaction processes, * N N* bare vertex functions get dressed:
+=
bare mesoncloud
1. Fixing hadronic parameters
2. Good model to describe N reactions at Q2 = 0.
What is needed for extracting electromagnetic N-N* form factors?
Pure hadronic process; Determined fromN N, N, N
Before analyzing eN e’ N, e’ N, … , we need
Determined fromN N, N, N
Critical for the model construction Starting point to explore Q2 > 0 region
Current status of the analysis @ EBAC
N N : fitted to the SAID PWA up to 2 GeV.Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)
N N : cross sections calculated; not fitted yet.Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC
N N : fitted to the data up to 2 GeV ( varied only bare N* N )Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)
N N : fitted to the data up to 1.6 GeV ( varied only )Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008)
N N : in progress
N N : in progress
Hadronic part
Electromagnetic part
pi N pi N & eta NJulia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)
Five coupled-channels:
Fitted up to 2 GeV
Differential cross sections and polarizations are also well reproduced !
gamma N pi Nσ T
OT (
b)
Comparison to data– Total cross section– Differential cross section– Photon asymmetry
Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008) Fitted up to 1.6 GeV.
Only is varied.
pi N pi pi NKamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC
Parameters used in the calculation are from N N analysis.
Need combined analysis of N and N !
N-D13(1520) electromagnetic transition amplitude
meson cloudbare
total ( preliminary ) ( preliminary )
Need *N N analysis to determine Q2 dependence of the bare amplitude !
Q2 dependence comes from NN, , etc. ( well determined )
Outlook
Retune parameters using the data of all three reactions. Extends energy region of N N : 1.6 2 GeV
Combined analysis of N N, N and N N
*N N (Julia-Diaz, Kamano, Lee, Matsuyama, Sato)
(*)N N (Julia-Diaz, Kamano, Lee, Matsuyama, Sato)
N N (Durand, Julia-Diaz, Lee, Saghai, Sato)
Improved parameters are applied to (& further retuned by)
Extract N-N* electromagnetic transition form factors beyond !!
(Julia-Diaz, Kamano, Lee, Matsuyama, Sato)
Back up
Pion-nucleon elastic scattering
N
Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)
Polarization1340 MeV1440 MeV1540 MeV1680 MeV1760 MeV1860 MeV
pi N eta NDurand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)
full result
phase space
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC
pi N pi pi N reaction
invariant mass distributions
Data handled with the help of D. Arndt
Key to improving parameters: distributions at low W of
0 90 180 0 90 180
0 90 180 0 90 180
-1
1
0
-1
1
0
0
1154 MeV1232 MeV1285 MeV1417 MeV1513 MeV
Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008)
Single pion photoproduction reaction
pi N pi pi N reaction
full result
c.c. effect off
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, submitted to PRC
Parameters used in the calculation are from N N analysis.
W = 1420 MeV W = 1780 MeV
Shape is reasonable. Magnitude overestimates the data.
In most energy,
gamma N pi pi N reaction
invariant mass distributions(very preliminary)
Dynamical coupled-channels model for double pion production reactions
Attach appropriate Attach appropriate Green functionsGreen functions ( ) and ( ) and vertex functionsvertex functions ( ) ( )to to NN (on-shell) (on-shell) → → MBMB (off-shell) amplitude (off-shell) amplitude ( )( )
All ingredients already prepared in 2-body calculation !!
Dynamical coupled-channels model for double pion production reactions
+
2 2 → → 3 effective potential3 effective potential
= + …+
Not included inNot included inNo new parameter introducedNo new parameter introduced
Approximate treatment of direct term
part of V23 part of
+=
Dynamical coupled-channels modelfor double pion production reactions
To obtain N → N amplitude, just make replacement below:
where
Results
full
c.c. effect off
res. only
nonres. only
Results
W = 1790 MeVW = 1790 MeVfull
res. only
nonres. only
Results
W = 1440 MeVW = 1440 MeVfull
res. only
nonres. only