1. EBAC-DCC combined analysis of world data on pN and gN processes
Hiroyuki Kamano
(Excited Baryon Analysis Center, Jefferson Lab)
Joint EBAC/GWU Seminar, March 14th, 2011

2. Outline Motivation and strategy for N* study at EBAC
EBAC-DCC analysis of pN and gN reactions ( )
EBAC-DCC analysis of pN and gN reactions ( )
Summary and outlook
N* spectrum (pole positions) and residues
Alternative view of dynamical origin of P11 resonances
N-N* e.m. transition form factors

3. Motivation and strategy for N* study at EBAC (1 of 4)

4. N* states and PDG *s channels !! ? Most of the N*s were extracted from
Arndt, Briscoe, Strakovsky, Workman PRC (2006) ?
Most of the N*s were extracted from
Need comprehensive analysis of
channels !!

5. Excited Baryon Analysis Center (EBAC) of Jefferson Lab
Founded in January 2006
Reaction Data
Objectives and goals:
Through the comprehensive analysis
of world data of pN, gN, N(e,e’) reactions,
Determine N* spectrum (pole positions)
Extract N* form factors
(e.g., N-N* e.m. transition form factors)
Provide reaction mechanism information
necessary for interpreting N* spectrum,
structures and dynamical origins
Dynamical Coupled-Channels EBAC
N* properties
Hadron Models
Lattice QCD
Theory support for
Excited Baryon Program at
(arXiv: )
QCD

6. 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!

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
Construct a reaction model through the comprehensive analysis of meson production reactions
Requires careful 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)
Confirm/reject N* with low-star status; Search for new N*
Extract resonance information from the constructed reaction model
Stage 3
Make a connection to hadron structure calculations; Explore the
structure of the N* states.
Quark models, Dyson-Schwinger approaches, Holographic QCD,…

9. EBAC-DCC analysis of pN and gN reactions: 2006-2009 (2 of 4)

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  pi pi N reaction
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009)
Parameters used in the calculation are from pN  pN analysis.
(# of pN  ppN data) / (# of pN  pN data) ~ 1200 / 24000
Above W = 1.5 GeV,
All data were measured more than 3 decades ago.
No differential cross section data are available for
quantitative fits (only the data without error bar exist).
s (mb)
Need help of hadron beam facilities such as J-PARC !!
W (GeV)
Full result
Full result
Phase space

12. 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.

13. 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

14. How can we extract N* information?
PROPER definition of
N* mass (spectrum)  Pole position of the amplitudes
N*  MB, gN decay vertices  Residue1/2 of the pole
Consistent with the resonance theory based on Gamow vectors
G. Gamow (1928), R. E. Peierls (1959), …
A brief introduction of Gamov 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 )

15. 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 !!

16. 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

17. 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

18. EBAC-DCC analysis of pN and gN reactions: 2010 - (3 of 4)

19. 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

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

21. 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)]

22. Single pion photoproduction
Preliminary!!
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, preliminary)
Previous model (fitted to gN  pN data up to 1.6 GeV) [PRC (2008)]

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

24. pi N  KY reactions Preliminary!! Angular distribution
Recoil polarization
1732 MeV
1845 MeV
1985 MeV
2031 MeV
1757 MeV
1879 MeV
1966 MeV
2059 MeV
1792 MeV
1732 MeV
1845 MeV
1985 MeV
2031 MeV
1757 MeV
1879 MeV
1966 MeV
2059 MeV
1792 MeV

25. gamma p  K+ Lambda Preliminary!! Measure ALL 16 observables !!
Formulae for calculating polarization observables
 Sandorfi, Hoblit, Kamano, Lee arXiv:
(To appear in JPG as a topical review)
Preliminary!!
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)

26. Summary and outlook (4 of 4)

27. Summary and outlook (1 of 2)
Extraction of N* from EBAC-DCC analysis during :
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 !!

28. Summary and outlook (1 of 2)
Extraction of N* from EBAC-DCC analysis :
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, wN, … reactions to the combined analysis.
Previous model: Q2 < 1.5 GeV2

29. Summary and outlook (2 of 2)
Other issues we are working on
Construction of a consistent formula with Gamow theory for branching
ratios of N* decays to unstable channels: N*  pD, rN, sN  ppN etc.
Implementation of gauge invariance (current conservation) to the full e.m.
amplitudes within our framework.
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
p2(2100)  ppp decay
f0, r, .. p
B, D, J/Y...
Heavy meson decays g X
Exotic hybrids?
GlueX
Hamiltonian approach based on the method of unitary transformation.
Matsuyama, Sato, Lee Phys. Rep. 439 (2007) 193
Sato, Lee PRC54 (1996) 2660

30. back up

31. 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)

32. 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,

33. 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

34. 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

35. 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

36. 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

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

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

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

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

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

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

43. Phase shift and inelasticity
W (MeV)

44. 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

45. 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

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

47. 2. 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

48. 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