1. EBAC-DCC analysis of world data on pN, gN, and N(e,e’) reactions
Hiroyuki Kamano
Osaka City University
(Excited Baryon Analysis Center, Jefferson Lab)
( Presented by T.-S. H. Lee)
NSTAR2011

2. Outline Strategy for N* study at EBAC
EBAC-DCC analysis of pN and gN reactions ( )
EBAC-DCC analysis of pN and gN reactions ( )
Summary
Highlights of the fits to data
Extracted N* spectrum (poles)
N-N* transition form factors (residues)

3. Strategy for N* study at EBAC

4. Excited Baryon Analysis Center (EBAC) of Jefferson Lab
Founded in January 2006
Reaction Data
Objectives :
Perform a comprehensive analysis
of world data of pN, gN, N(e,e’) reactions,
Determine N* spectrum (pole positions)
Extract N-N* form factors (residues)
Identify reaction mechanisms
for interpreting the properties
and dynamical origins of N*
Dynamical Coupled-Channels EBAC
N* properties
Hadron Models
Lattice QCD
QCD

5. Dynamical coupled-channels model of EBAC
N* spectrum, structure, …
Meson production data
Reaction mechanisms
Dynamical coupled-channels model of meson production reactions
A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439 (2007) 193 a
Singular!

6. Dynamical coupled-channels model of EBAC
For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
Partial wave (LSJ) amplitude of a  b reaction:
Reaction channels:
Transition potentials:
coupled-channels effect
Meson-exchange potentials
(Derived from Lagrangians)
bare N* states

7. Dynamical coupled-channels model of EBAC
For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
Partial wave (LSJ) amplitude of a  b reaction:
Reaction channels:
Transition potentials:
core
meson cloud
meson
baryon
Physical N*s will be a “mixture” of the two pictures:
coupled-channels effect
exchange potentials
of ground state
mesons and baryons
bare N* states

8. Strategy for N* study at EBAC
Stage 1
Perform comprehensive analysis of meson production reactions
Develop analytic continuation of
amplitudes to complex energy plane
 Suzuki, Sato, Lee PRC ; PRC
Stage 2
N* spectrum (poles); N*  gN, MB transition form factors (residues)
Extract resonance information from the determined
partial-wave amplitudes
Stage 3
Interpret the extracted resonance information in terms
of hadron structure calculations .
Quark models, Dyson-Schwinger approaches, LQCD,…

9. EBAC-DCC analysis of pN and gN reactions: 2006-2009

10. pN, hN, ppN (pD,rN,sN) coupled- channels calculations were performed.
EBAC-DCC analysis ( )
pN, hN, ppN (pD,rN,sN) coupled-
channels calculations were performed.
Hadronic part
p N  p N : Used for constructing a hadronic model up to W = 2 GeV.
Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)
p N  h N : Used for constructing a hadronic model up to W = 2 GeV
Durand, Julia-Diaz, Lee, Saghai, Sato, PRC (2008)
p N  p p N : First full dynamical coupled-channels calculation up to W = 2 GeV.
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009)
g(*) N  p N : Used for constructing a E.M. model up to W = 1.6 GeV and Q2 = 1.5 GeV2
(photoproduction) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC (2008)
(electroproduction) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009)
g N  p p N : First full dynamical coupled-channels calculation up to W = 1.5 GeV.
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009)
Electromagnetic part

11. pi N amplitudes (2006-2009) Isospin 1/2 Imaginary T
Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)
Isospin 1/2
Imaginary T

12. Single pion photoproduction (Q2 = 0)
Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC (2008)
Fit up to
W = 1.6 GeV.
Only
is varied.

13. Single pion electroproduction (Q2 > 0)
Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009)
Fit to the structure function data (~ 20000) from CLAS
p (e,e’ p0) p
W < 1.6 GeV
Q2 < 1.5 (GeV/c)2
is determined
at each Q2.

14. Single pion electroproduction (Q2 > 0)
Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009)
Five-fold differential cross sections at Q2 = 0.4 (GeV/c)2
p (e,e’ p0) p
p (e,e’ p+) n

15. pi N  pi pi N reaction Full result C.C. effect off
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009)
Parameters used in the calculation are from pN  pN analysis.
Full result
C.C. effect off

16. Double pion photoproduction
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009)
Parameters used in the calculation are from pN  pN & gN  pN analyses.
Good description near threshold
Reasonable shape of invariant
mass distributions
Above 1.5 GeV, the total cross
sections of p00 and p+-
overestimate the data.

17. Extraction of N* information
Definitions of
N* masses (spectrum)  Pole positions of the amplitudes
N*  MB, gN decay vertices  Residues1/2 of the pole
Consistent with the resonance theory based on Gamow vectors
G. Gamow (1928), R. E. Peierls (1959), …
A brief introduction of Gamow vectors: de la Madrid et al, quant-ph/
(complex) energy eigenvalues = pole values
transition matrix elements = (residue)1/2 of the poles
N*  b
decay vertex
N* pole position
( Im(E0) < 0 )

18. N* poles from EBAC-DCC analysis
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL (2010)
L2I 2J
Two resonance poles
in the Roper resonance region !!

19. Dynamical coupled-channels effect on N* poles and form factors
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL (2010)
Suzuki, Sato, Lee, PRC (2010)
Pole positions and dynamical origin of P11 resonances
pole A: pD unphys. sheet
pole B: pD phys. sheet

20. Dynamical coupled-channels effect on N* poles and form factors
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL (2010)
Suzuki, Sato, Lee, PRC (2010)
Nucleon - 1st D13 e.m. transition form factors
Crucial role of non-trivial multi-channel reaction
mechanisms for interpreting the structure and
dynamical origin of nucleon resonances !
Real part
Imaginary part

21. EBAC-DCC analysis of pN and gN reactions: 2010 -

22. EBAC-DCC analysis: 2010 ~
Fully combined analysis of gN , N  N , hN , KY reactions !!
2006 ~ 2009
5 channels
(pN,hN,pD,rN,sN)
< 2 GeV
< 1.6 GeV ―
2010 ~
7 channels
(pN,hN,pD,rN,sN,KL,KS)
< 2.1 GeV
< 2 GeV
< 2GeV
# of coupled
channels
N  N
gN  N
N  hN
gN  hN
pN  KY
gN  KL

23. Pion-nucleon elastic scattering
Angular distribution
Target polarization
1234 MeV
1449 MeV
1678 MeV
1900 MeV
Current model
(full combined analysis, PRELIMINARY)
Previous model (fitted to pN  pN data only)
[PRC (2007)]

24. Single pion photoproduction
Angular distribution
Photon asymmetry
1154 MeV
1232 MeV
1313 MeV
1416 MeV
1519 MeV
1617 MeV
1690 MeV
1798 MeV
1899 MeV
1137 MeV
1232 MeV
1334 MeV
1462 MeV
1527 MeV
1617 MeV
1729 MeV
1834 MeV
1958 MeV
1154 MeV
1232 MeV
1313 MeV
1416 MeV
1519 MeV
1617 MeV
1690 MeV
1798 MeV
1899 MeV
1137 MeV
1232 MeV
1334 MeV
1462 MeV
1527 MeV
1617 MeV
1729 MeV
1834 MeV
1958 MeV
Current model
(full combined analysis
Previous model (fitted to gN  pN data up to 1.6 GeV) [PRC (2008)]

25. Eta production reactions
Photon asymmetry
1535 MeV
1674 MeV
1811 MeV
1930 MeV
1549 MeV
1657 MeV
1787 MeV
1896 MeV
Analyzed data up to W = 2 GeV.
p- p  h n data are selected
following Durand et al. PRC

26. pi N  KY reactions Angular distribution Recoil polarization 1732 MeV

27. gamma p  K+ Lambda Measure ALL 16 observables !!
Formulae for calculating polarization observables
 Sandorfi, Hoblit, Kamano, Lee JPG 38, (2011)
(Topical Review)
1781 MeV
1883 MeV
2041 MeV
“(Over-) complete experiment” is ongoing at !
Expected to be a crucial source for establishing N* spectrum !!
Measure ALL 16 observables !!
(ds + 15 polarization asymmetries)

28. Summary

29. Summary and outlook Multi-channel reaction mechanisms plays a crucial
Extraction of N* from EBAC-DCC analysis :
The Roper resonance is associated with two resonance poles.
The two Roper poles and N*(1710) pole are generated from a single
bare state.
N-N* e.m. transition form factors are complex.
Multi-channel reaction mechanisms plays a crucial
role for interpreting the N* spectrum and form factors !!

30. Summary and outlook Extraction of N* from EBAC-DCC analysis 2006-2009:
Fully combined analysis of pN, gN  pN, hN, KY reactions is underway.
The Roper resonance is associated with two resonance poles.
The two Roper poles and N*(1710) pole are generated from a single
bare state.
N-N* e.m. transition form factors are complex.
Re-examine resonance poles
Analyze CLAS ep  epN data with Q2 < ~ 4 GeV2;
 Extract N-N* electromagnetic transition form factors at high Q2
Include pN, gN  ppN, … reactions to the combined analysis.
Previous model: Q2 < 1.5 GeV2

31. Summary and outlook Projected progress Spring of 2012
Complete the combined analysis to reach DOE milestone HP3:
“Complete the combined analysis of available single pion, eta, kaon
photo-production data for nucleon resonances and incorporate
analysis of two-pion final states into the coupled-channels analysis
of resonances”

32. EBAC Collaborations J. Durand B. Julia-Diaz Kamano (Jlab)
T.-S. H. Lee (1/4 EFT)
A. Matsuyama
S. Nakamura (JLab)
B. Saghai
Sato
C. Smith
N. Suzuki

33. Summary and outlook Works need to be accomplished Summer of 2013
Complete the extraction of N-N* form factors to reach DOE
milestone HP7:
End of 2013
Make the EBAC-DCC code available for future analysis of
“complete experiments” and N* experiments with 12 GeV upgrade
“Measure the electromagnetic excitations of low-lying baryon
states (< 2GeV) and their transition form factors over the range
Q2 = 0.1 – 7 GeV2 and measure the electro- and photo-production
of final states with one and two pseudoscalar mesons”

34. back up

35. Summary and outlook New direction
Nakamura, arXiv:
Kamano, Nakamura, Lee, Sato, in preparation
New direction
Application of the DCC approach to meson physics:
(3-body unitarity effect are fully taken into account) p g
B, D, J/Y... X
Exotic hybrids?
f0, r, .. p p
Heavy meson decays
GlueX

36. Summary and outlook New direction
Nakamura, arXiv:
Kamano, Nakamura, Lee, Sato, in preparation
New direction
Application of the DCC approach to meson physics:
(3-body unitarity effect are fully taken into account)
Dalitz plot of a1(1260)  ppp decay from our model
Isobar model
Unitary model
(with full 3-body unitarity)

37. Pion photoproductions Pion electroproductions Double pion productions
Coupled-channels effect in various reactions
Pion photoproductions
Full
c.c. effect of
ppN(pD,rN,sN) &
hN off
Pion electroproductions
Full
c.c. effect of
ppN(pD,rN,sN) &
hN off
Double pion productions
Full
c.c effect off

38. Dynamical coupled-channels model of EBAC
For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)

39. pi N  pi pi N reaction Full result Full result Phase space
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009)
Parameters used in the calculation are from pN  pN analysis.
s (mb)
W (GeV)
Full result
Full result
Phase space

40. Improvements of the DCC model
Processes with 3-body ppN unitarity cut
The resulting amplitudes are now completely unitary in
channel space !!

41. Dynamical origin of P11 resonances
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL (2010)
Pole trajectory
of N* propagator
self-energy:
Bare state
hN threshold
pD threshold
(hN, rN, pD) = (p, u, u)
A:1357–76i
Im E (MeV)
(hN, rN, pD) = (p, u, －)
rN threshold
(hN, rN, pD) = (p, u, p)
(hN, rN, pD) = (u, u, u)
B:1364–105i
C:1820–248i
(pN,sN) = (u,p)
for three P11 poles
Re E (MeV)

42. Residues of resonance poles in pi N amplitude
EBAC(06-09)
Arndt06
Doring09
Hoeler
Cutkosky
PDG notation
R (MeV), f (deg.)
N*(1535) S11
44, -42
16, -16
31,
120,
N*(1650) S11
18, -93
14, -69
54, -44
39, -27
60,
N*(1440) P11
37, -110
38, -98
48, -64
40,
52, -100
64, -99
86, -46
N*(1710) P11
20, -168
9, -167
N*(1720) P13
25, -94
14, -82
15,
8, -160
N*(1520) D13
38,
38, -5
32, -18
32, -8
35,
N*(1675) D15
31, -24
27, -21
(not analyzed)
23, -22
31,
N*(1680) F15
40, -11
42, -4
44, -17
34,
D (1232) P33
52, -46
52, -47
47, -37
50, -48
53,
D*(1620) S31
21, -134
15, -92
12, -108
19, -95
15, -110
D*(1910) P31
45, 172
12, -153
38,
13,
D*(1700) D33
12, -59
18, -40
16, -38
10,
D*(1905) F35
5, -79
15, -30
25,
25,
D*(1950) F37
41, -33
53, -31
47, -32
50,

43. Helicity amplitudes of N-N* e.m. transition (Q2 = 0)
EBAC-DCC
Ahrens04/02
Arndt04/02
Dugger07
Blanpied01
P33(1211)
A3/2 i
-258 +/- 3
-243 +/- 1
/-1.6+/-7.8
A1/2 i
-137 +/- 5
-129 +/- 1
-135+/-1.3+/-3.7
D13(1521) i
147 +/- 10
165 +/- 5
143 +/- 2 i
-38 +/- 3
-20 +/- 7
-28 +/- 2
P11(1357) i
-63 +/- 5
-51 +/- 2
(1364) i
S11(1540) i
60 +/- 15
91 +/- 2
(1642)
29 – 17i
69 +/- 5
22 +/- 7
D15(1654)
44 – 9i
10 +/- 7
21 +/- 1
58 – 0.5i
15 +/-10
18 +/- 2
F15(1674) i
145 +/- 5
134 +/- 2 i
-10 +/- 4
-17 +/- 1
S31(1563)
137 – 70i
35 +/- 20
50 +/- 2
D33(1604)
-45+9i
97 +/- 20
105 +/- 3
-1 -17i
90 +/- 25
125 +/- 3

44. Q2 dependence of the form factors: 1/3
Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009)
Suzuki, Sato, Lee, arXiv:
N-D transition GM form factor
GM / (3GD)
real part
other analyses
imaginary part

45. Q2 dependence of the form factors: 2/3
Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009)
Suzuki, Sato, Lee, arXiv:
N-D13 e.m. transition amplitude
A3/2
A1/2
real part
CLAS
imaginary part

46. Q2 dependence of the form factors: 3/3
Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009)
Suzuki, Sato, Lee, arXiv:
N-P11 e.m. transition amplitude
A1/2
CLAS Collaboration
PRC78, (2008)
real
imaginary
real
imaginary

47. pi N amplitudes (2006-2009) Isospin 1/2 Real T
Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)
Isospin 1/2
Real T

48. Double pion photoproduction
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009)
Parameters used in the calculation are from pN  pN & gN  pN analyses.
Good description near threshold
Reasonable shape of invariant
mass distributions
Above 1.5 GeV, the total cross
sections of p00 and p+-
overestimate the data.

49. pi N amplitudes (2006-2009) Isospin 1/2 Imaginary T
Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)
Isospin 1/2
Imaginary T

50. pi N amplitudes (2006-2009) Isospin 3/2 Real T
Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)
Isospin 3/2
Real T

51. pi N amplitudes (2006-2009) Isospin 3/2 Imaginary T
Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)
Isospin 3/2
Imaginary T

52. pi N amplitudes (current model) !!! PRELIMINARY, NOT the final result !!!
Real T

53. pi N amplitudes (current model) !!! PRELIMINARY, NOT the final result !!!
Imaginary T

54. Phase shift and inelasticity
W (MeV)

55. pi N  pi pi N reaction Full result C.C. effect off
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009)
Parameters used in the calculation are from pN  pN analysis.
Full result
C.C. effect off

56. pi N  eta N reaction N*  hN varied Model constructed from
Durand, Julia-Diaz, Lee, Saghai, Sato, PRC (2008)
N*  hN varied
Model constructed from
pN  pN analysis only

57. Modifications of the DCC model×
e.g.) Hadronic parameters of D13 state ( I = 1/2, J = 3/2, Parity = minus) M N* L 18
 12 B
Number of resonant
parameters are reduced
significantly !!
L = MB orbital angular mom.
S = total spin of MB
J = L x S