study of nucleon resonances at ebac@jlab · study of nucleon resonances at ebac@jlab ... 2-channel...
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Study of nucleon resonances at Study of nucleon resonances at
EBAC@JLabEBAC@JLab
Hiroyuki KamanoHiroyuki Kamano
(Excited Baryon Analysis Center, Jefferson Lab)(Excited Baryon Analysis Center, Jefferson Lab)
in collaboration within collaboration with
B. JuliaB. Julia--Diaz, T.Diaz, T.--S. H. Lee, A. Matsuyama,S. H. Lee, A. Matsuyama,
S. Nakamura, T. Sato, N. SuzukiS. Nakamura, T. Sato, N. Suzuki
7th Japan-China Joint Nuclear Physics Symposium, Nov. 9-13 2009, Univ. of Tsukuba
Outline
� Excited Baryon Analysis Center (EBAC)
at Jefferson Lab
� Dynamical origin of P11 nucleon resonances
PDG *s and N*’s origin
?
?
?
?
?
Arndt, Briscoe, Strakovsky, Workman PRC 74 045205 (2006)
Need consistent
analysis of
ππππN and ππππππππN channels
Need consistent
analysis of
ππππN and ππππππππN channels
PDG *s and N*’s origin
� Most of their properties were extracted from
?
?
?
?
?
PDG *s and N*’s origin
corecore
meson cloudmeson cloud
mesonmeson
baryonbaryon
?
?
?
?
?
� Most of their properties were extracted from
� Are they all genuine quark/gluon excitations (with meson cloud) ?
� Is their origin dynamical ?
���� some could be understood as arising from
meson-baryon dynamics
Objectives and goals:
Through the comprehensive analysis
of world data of ππππN, γγγγN, N(e,e’) reactions,
� Determine N* spectrum
(masses, widths)
� Extract N* form factors, in particular
the N-N* e.m. transition form factors
� Provide reaction mechanism information
for interpreting the N* properties
Excited Baryon Analysis Center (EBAC)
at Jefferson Lab
N* properties
QQCCDD
Lattice QCDHadron Models
Dynamical Coupled-Channels Analysis @ EBAC
Reaction Data
http://ebac-theory.jlab.org/Founded in January 2006
Theory support for
Excited Baryon Program by CLAS@JLab
(arXiv:0907.1901)
Objectives and goals:
Through the comprehensive analysis
of world data of ππππN, γγγγN, N(e,e’) reactions,
� Determine N* spectrum
(masses, widths)
� Extract N* form factors, in particular
the N-N* e.m. transition form factors
� Provide reaction mechanism information
for interpreting the N* properties
Excited Baryon Analysis Center (EBAC)
at Jefferson Lab
N* properties
QQCCDD
Lattice QCDHadron Models
Dynamical Coupled-Channels Analysis @ EBAC
Reaction Data
http://ebac-theory.jlab.org/Founded in January 2006
Theory support for
Excited Baryon Program by CLAS@JLab
(arXiv:0907.1901)
Careful treatment of couplings between multi-reaction channels is necessary !!
A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439 (2007) 193
“Dynamical coupled-channels model of meson production reactions”
� Partial wave (LSJ) amplitude of a ���� b reaction:
� Reaction channels:
� Potential:
coupled-channels effect
Dynamical coupled-channels model @ EBAC
For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
ground
meson-baryon
exchange
ground
meson-baryon
exchangebare N* statebare N* state
Current status of the EBAC-DCC analysis
� π N � π N : model constructed up to W = 2 GeV.
Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)
� π N � π π N : cross sections calculated with the πN model; fit is ongoing.
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)
� π N � η N : model constructed up to W = 2 GeV
Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)
� γ(∗) N � π N : model constructed up to W = 1.6 GeV (& up to Q2 = 1.5 GeV2)(photoproduction) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008)
(electroproduction) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)
� γ N � π π N : cross sections calculated with the γN & πN model; fit is ongoing.
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, arXiv:0909.1129 [nucl-th]
� γ(∗) N � η N : in progress
� γ N � KY, ωN : in progress
Hadronic partHadronic part
Electromagnetic partElectromagnetic part
Analysis of pi N � pi N & eta N reactions
Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)
Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)
1.4 1.5 1.6 1.7 1.8 1.9 2 2.1
W (GeV)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
σto
t (m
b)
Constructed pi N partial wave amplitudes
Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)
Real partReal part
Imaginary partImaginary part
Isospin = 1/2
EBAC
SAID06
W (MeV)
How can we extract N* information?
PROPER definition of
� N* mass and width ���� Pole position of the amplitudes
� N* ���� MB, γγγγN decay vertices ���� Residue of the pole
N* pole position
( Im(E0) < 0 )
N* pole position
( Im(E0) < 0 )
N* ���� b
decay vertex
N* ���� b
decay vertex
How can we extract N* information?
PROPER definition of
� N* mass and width ���� Pole position of the amplitudes
� N* ���� MB, γγγγN decay vertices ���� Residue of the pole
N* pole position
( Im(E0) < 0 )
N* pole position
( Im(E0) < 0 )
N* ���� b
decay vertex
N* ���� b
decay vertexNeed analytic continuation of the amplitudes !!
���� Suzuki, Sato, Lee, PRC79 025205 (2009); arXiv:0910.1742
Dynamical origin of P11 nucleon resonances
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato arXiv:0909.1356
1. Two almost degenerate poles in the Roper resonance region.
2. All three poles below 2 GeV evolve from a same, single bare state.
ImE (MeV)
Re E (MeV)
100
Findings:
0
-100
-200
-3001400 1600 1800
P11 N* resonances
in the EBAC-DCC model
P11 N* resonances
in the EBAC-DCC model
Dynamical origin of P11 nucleon resonances
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato arXiv:0909.1356
1. Two almost degenerate poles in the Roper resonance region.
2. All three poles below 2 GeV evolve from a same, single bare state.
ImE (MeV)
Re E (MeV)
100
Findings:
0
-100
-200
-3001400 1600 1800
P11 N* resonances
in the EBAC-DCC model
P11 N* resonances
in the EBAC-DCC model
Eden, Taylor, Phys. Rev. 133 B1575 (1964)
Multi-channels reactions can
generate many resonance poles
from a single bare state!!
e.g.)
Two poles for Jππππ = 3/2+ resonance in He5
Hale, Brown, Jarmie, PRL59 763 (1987)
Analytic structure of the scattering amplitudes
×××× ××××
physical sheet
Re (E)
Im(E)
0 0
Im(E)
Re (E)
unphysical sheet
Eth(branch point)
E + iεεεε (“real world”)E + iεεεε (“real world”)
Eth(branch point)
Scattering amplitude is
a double-valued function of E !!
Scattering amplitude is
a double-valued function of E !!
e.g.) single-channel meson-baryon scattering
Analytic structure of the scattering amplitudes
×××× ××××
physical sheet
Re (E)
Im(E)
0 0
Im(E)
Re (E)
unphysical sheet
Eth(branch point)
E + iεεεε (“real world”)E + iεεεε (“real world”)
Eth(branch point)
Scattering amplitude is
a double-valued function of E !!
Scattering amplitude is
a double-valued function of E !!
e.g.) single-channel meson-baryon scattering
N-channels ���� Need 2N Riemann sheetsN-channels ���� Need 2N Riemann sheets
2-channel case (4 sheets):
(channel 1, channel 2) =
(p, p), (u, p) ,(p, u), (u, u)
p = physical sheet
u = unphysical sheet
2-channel case (4 sheets):
(channel 1, channel 2) =
(p, p), (u, p) ,(p, u), (u, u)
p = physical sheet
u = unphysical sheet
Re E (MeV)
ImE (MeV) π∆π∆π∆π∆ threshold
C:1820–248i
B:1364–105i
ηηηηN threshold
ρρρρN thresholdA:1357–76i
Bare state
Dynamical origin of P11 resonances
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010)
Pole trajectory
of N* propagator
Pole trajectory
of N* propagator
(ππππN,σσσσN) = (u,p)
for three P11 poles
Re E (MeV)
ImE (MeV) π∆π∆π∆π∆ threshold
C:1820–248i
B:1364–105i
ηηηηN threshold
ρρρρN thresholdA:1357–76i
Bare state
Dynamical origin of P11 resonances
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010)
Pole trajectory
of N* propagator
Pole trajectory
of N* propagator
(ππππN,σσσσN) = (u,p)
for three P11 poles
self-energy:
Re E (MeV)
ImE (MeV) π∆π∆π∆π∆ threshold
C:1820–248i
B:1364–105i
ηηηηN threshold
ρρρρN thresholdA:1357–76i
Bare state
Dynamical origin of P11 resonances
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010)
(ηηηηN, ρρρρN, π∆π∆π∆π∆) = (u, u, u)
Pole trajectory
of N* propagator
Pole trajectory
of N* propagator
(ππππN,σσσσN) = (u,p)
for three P11 poles
Re E (MeV)
ImE (MeV) π∆π∆π∆π∆ threshold
C:1820–248i
B:1364–105i
ηηηηN threshold
ρρρρN thresholdA:1357–76i
Bare state
Dynamical origin of P11 resonances
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010)
(ηηηηN, ρρρρN, π∆π∆π∆π∆) = (u, u, u)
(ηηηηN, ρρρρN, π∆π∆π∆π∆) = (p, u, －－－－)
Pole trajectory
of N* propagator
Pole trajectory
of N* propagator
(ππππN,σσσσN) = (u,p)
for three P11 poles
Re E (MeV)
ImE (MeV) π∆π∆π∆π∆ threshold
C:1820–248i
B:1364–105i
ηηηηN threshold
ρρρρN thresholdA:1357–76i
Bare state
Dynamical origin of P11 resonances
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010)
(ηηηηN, ρρρρN, π∆π∆π∆π∆) = (u, u, u)
(ηηηηN, ρρρρN, π∆π∆π∆π∆) = (p, u, p)
(ηηηηN, ρρρρN, π∆π∆π∆π∆) = (p, u, u)
Pole trajectory
of N* propagator
Pole trajectory
of N* propagator
(ππππN,σσσσN) = (u,p)
for three P11 poles
Summary
� Continuous effort for exploring the N* states in
Excited Baryon Analysis Center (EBAC) at Jefferson Lab.
� Scattering amplitudes are successfully constructed by
dynamical coupled-channels analysis of meson production reactions.
� Dynamical origin of the P11 nucleon resonances:
� Two resonance poles are found in the Roper energy region.
� (Two) Roper and N*(1710) originate from a same, single bare state.
Treatment of multi-reaction channels is
key to understanding the N* spectrum !!
Treatment of multi-reaction channels is
key to understanding the N* spectrum !!