nucleon resonances from dcc analysis of collaboration@ebac for confinement physics t.-s. harry lee...
TRANSCRIPT
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Nucleon Resonances from DCC Analysis of
Collaboration@EBAC for Confinement Physics
T.-S. Harry LeeArgonne National Laboratory
Workshop on “Confinement Physics” Jefferson Laboratory, March 12-15, 2012
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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* within QCD
Excited Baryon Analysis Center (EBAC) of Jefferson Lab
N* properties
QCD
Lattice QCDHadron Models
Dynamical Coupled-Channels Analysis @ EBAC
Reaction Data
http://ebac-theory.jlab.org/Founded in January 2006
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1. What is the dynamical coupled-channel (DCC) approach ?
2. What are the latest results from Collaboration@EBAC ?
3. How are DCC-analysis results related to Confinement ?
4. Summary and future directions
5. Remarks on numerical tasks
Explain :
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Experimental fact:
Excited Nucleons (N*) are unstable and coupledwith meson-baryon continuum to formnucleon resonances
Nucleon resonances contain information ona. Structure of N* b. Meson-baryon Interactions
What are nucleon resonances ?
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Extraction of Nucleon Resonances from data is animportant subject and has a long history
How are Nucleon Resonances extracted from data ?
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Assumptions of Resonance ExtractionsPartial-wave amplitudes are analytic functions F (E) on the complex E-plane
F (E) are defined uniquely by the partial-wave amplitudes A (W) determined from accurate and complete experiments on physical W-axis
The Poles of F(E) are the masses of Resonances of the underlying fundamental theory (QCD).
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W =
F (E)
F (E) A (W) Data
Analytic continuation
A (W)
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Theoretical justification: (Gamow, Peierls, Dalitz, Moorhouse, Bohm….)
Resonances are the eigenstates of the Hamiltonianwith outgoing-wave boundary condition
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If high precision partial-wave amplitudes A (W) from complete and accurate experiments are available
Fit A (W) by using any parameterization of analytic function F(E) in E = W region Extract resonance poles and residues from F (E)
Procedures:
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Examples of this approach:
F (E) = polynominals of k
F (E) = g2(k)/(E – M0)+ i Γ(E)/2)
g0 (k2/(k2+C2))2n
k : on-shell momentum
Breit-Wigner form
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Reality:
Data are incomplete and have errors
Extracted resonance parameters depend on theparameterization of F (E) in fittingthe Data A (W) in E = W physical region
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N* Spectrum in PDG
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Solution:
Constraint the parameterization of F (E) by theoretical assumptions
Reduce the errors due to the fit to Incomplete data
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Approaches:
Impose dispersion-relations on F (E) F (E) : K-matrix + tree-diagrams
F (E) : Dynamical Scattering Equations Collaboration @ EBAC Juelich, Dubna-Mainz-Taiwan Sato-Lee, Gross-Surya, Utrech-Ohio etc…
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Objectives of the Collaboration@EBAC :
• Reduce errors in extracting nucleon resonances in the fit of incomplete data • Implement the essential elements of non-perturbative QCD in determining F(E) : Confinement Dynamical chiral symmetry breaking
Provide interpretations of the extracted resonance parameters.
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Develop Dynamical Reaction Model basedon the assumption:
Baryon is made of a confined quark-coreand meson cloud
Meson cloud
Confined core
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Model Hamiltonian :(A. Matsuyama, T. Sato, T.-S. H. Lee, Phys. Rept, 2007)
H = H0 + Hint
Hint = hN*, MB + vMB,M’B’
N* : Confined quark-gluon coreMB : Meson-Baryon states
Note: An extension of Chiral Cloudy Bag Modelto study multi-channel reactions
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Solve
T(E)= Hint+ Hint Hint
T(E) observables of Meson-Baryon Reactions
First step:How many Meson-Baryon states ????
1E-H+ie
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Unitarity Condition
Coupled-channelapproach is needed
MB : gN, pN, 2p-N, hN, KL, KS, wN
Total cross sections of meson photoproduction
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Partial wave (LSJ) amplitudes of a b reaction:
Reaction channels:
Transition Potentials:
coupled-channels effect
Exchange potentials bare N* states
For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
Z-diagrams
Dynamical coupled-channels (DCC) model for meson production reactions
, , , ,..p r s w
N N, D
s-channel u-channel t-channel contact
Exchange potentials
Z-diagrams
Bare N* statesN*bare
Dp
N p
p
DDNp
,r s
Can be related to hadron structure calculations (quark models, DSE, etc.) excluding meson-baryon continuum.
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Dynamical Coupled-Channels analysis
p N
gp N
-p hn
gp hp
pp KL, KS
gp KL, KS
2006-2009
6 channels (gN,pN,hN,pD,rN,sN)
< 2 GeV
< 1.6 GeV
< 2 GeV
―
―
―
2010-2012
8 channels (gN,pN,hN,pD,rN,sN,KL,KS)
< 2.1 GeV
< 2 GeV
< 2 GeV
< 2 GeV
< 2.2 GeV
< 2.2 GeV
# of coupled channels
Fully combined analysis of gN , N N , hN , KL, KS reactions !!
Kamano, Nakamura, Lee, Sato, 2012
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Analysis Database
Pion-inducedreactions (purely strong reactions)
Photo-productionreactions
~ 28,000 data points to fit
SAID
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Parameters :
1. Bare mass M
2. Bare vertex N* -> MB (C , Λ )
N = 14 [ (1 + 8 2 ) n ], n = 1 or 2 = about 200
Determined by χ -fit to about 28,000 data points
N*
N*,MB N*,MB
N*
2
N*
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Results of 8-channel analysis
Kamano, Nakamura, Lee, Sato, 2010-2012
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Partial wave amplitudes of pi N scattering
Kamano, Nakamura, Lee, Sato, 2012
Previous model (fitted to pN pN data only)[PRC76 065201 (2007)]
Real part
Imaginary part
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Pion-nucleon elastic scattering
Target polarizationTarget polarization
1234 MeV1234 MeV
1449 MeV1449 MeV
1678 MeV1678 MeV
1900 MeV1900 MeV
Angular distribution Angular distribution
Kamano, Nakamura, Lee, Sato, 2012
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Single pion photoproduction
Kamano, Nakamura, Lee, Sato, 2012 Previous model (fitted to gN pN data up to 1.6 GeV) [PRC77 045205 (2008)]
Angular distribution Angular distribution Photon asymmetry Photon asymmetry
1137 MeV 1232 MeV 1334 MeV
1462 MeV 1527 MeV 1617 MeV
1729 MeV 1834 MeV 1958 MeV
Kamano, Nakamura, Lee, Sato, 2012
1137 MeV 1232 MeV 1334 MeV
1462 MeV 1527 MeV 1617 MeV
1729 MeV 1834 MeV 1958 MeV
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Kamano, Nakamura, Lee, Sato, 2012
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Kamano, Nakamura, Lee, Sato, 2012
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Eta production reactions
Kamano, Nakamura, Lee, Sato, 2012
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Kamano, Nakamura, Lee, Sato, 2012
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Kamano, Nakamura, Lee, Sato, 2012
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KY production reactions
1732 MeV
1845 MeV
1985 MeV
2031 MeV
1757 MeV
1879 MeV
1966 MeV
2059 MeV
1792 MeV
1879 MeV
1966 MeV
2059 MeV
Kamano, Nakamura, Lee, Sato, 2012
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Kamano, Nakamura, Lee, Sato, 2012
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Kamano, Nakamura, Lee, Sato, 2012
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8-channel model parameters have been determined by the fits to the data of
πΝ, γΝ -> πΝ, ηΝ, ΚΛ, ΚΣ
Extract nucleon resonances
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Extraction of N* information
Definitions of
N* masses (spectrum) Pole positions of the amplitudes
N* MB, gN decay vertices Residues1/2 of the pole
N* pole position ( Im(E0) < 0 )
N* b decay vertex
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On-shell momentum
Suzuki, Sato, Lee, Phys. Rev. C79, 025205 (2009) Phys. Rev. C 82, 045206 (2010)
E = W
E = M – i Γ R
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Delta(1232) : The 1st P33 resonance
pN unphysical & pD unphysical sheet
pN physical & pD physical sheet
p N
p DpN unphysical & pD physical sheet
Real energy axis“physical world”
Complex E-plane
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010)
Im (E
)
Re (E)
P33
1211-50i
Riemann-sheet for other channels: (hN,rN,sN) = (-, p, -)
pole 1211 , 50
BW 1232 , 118/2=59
In this case, BW mass & width can be a good approximation of the pole position.
Small background Isolated pole Simple analytic structure of the complex E-plane
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Two-pole structure of the Roper P11(1440)
pN unphysical & pD unphysical sheet
pN physical & pD physical sheet
p N
p DpN unphysical & pD physical sheet
Real energy axis“physical world”
Complex E-plane
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010)
Im (E
)
Re (E)
Pole A cannot generate a resonance shape on“physical” real E axis.
B
A
P11
1356-78i
1364-105i
Riemann-sheet for other channels: (hN,rN,sN) = (p,p,p)
BW 1440 , 300/2 = 150
Two 1356 , 78poles 1364 , 105
In this case, BW mass & width has NO clear relation with the resonance poles:
?
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Dynamical origin of P11 resonances
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (2010)
Bare N* = states of hadron calculationsexcluding meson-baryon continuum(quark models, DSE, etc..)
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Spectrum of N* resonances
Real parts of N* pole values
L2I 2J
PDG Ours
N* with 3*, 4* 1816
N* with 1*, 2* 5
PDG 4*
PDG 3*
Ours
Kamano, Nakamura, Lee, Sato ,2012
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Width of N* resonances
Kamano, Nakamura, Lee, Sato 2012
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N-N* form factors at Resonance poles
Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (2010)Suzuki, Sato, Lee, PRC82 045206 (2010)
Nucleon - 1st D13 e.m. transition form factors
Real part Imaginary partComplex : consequence of analytic continuation
Identified with exact solution of fundamental theory (QCD)
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Interpretations :
Delta (1232) Roper(1440)
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GM(Q2) for g N D (1232) transition
Note:Most of the available static hadron models give GM(Q2) close to “Bare” form factor.
Full
Bare
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g N D(1232) form factors compared with Lattice QCD data (2006)
DCC
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“Static” form factor fromDSE-model calculation.(C. Roberts et al, 2011)
“Bare” form factor determined fromour DCC analysis (2010).
g p Roper e.m. transition
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Much more to be done for interpreting
the extracted nucleon resonances !!!
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Summary and Future Directions
2006 – 2012
a. Complete analysis of πΝ, γΝ -> πΝ, ηN, ΚΛ, ΚΣ
b. N* spectrum in W < 2 GeV has been determined
c. γΝ->N* at Q =0 has been extracted
Has reached 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”
2
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Next tasks :
1. Results from DCC analysis of 2006-2009: 6-channel model can only obtain γΝ->N* form factor from N(e,e’π) data in W < 1.6 GeV
Apply 8-channel model to extract γΝ->N* form factor for N* in W < 2 GeV
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Single pion electroproduction (Q2 > 0)
Fit to the structure function data from CLAS
Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)
p (e,e’ p0) p
W < 1.6 GeV
Q2 < 1.5 (GeV/c)2
is determined
at each Q2.
N*N
g(q2 = -Q2)q
N-N* e.m. transitionform factor
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2. Improve analysis of two-pion production :
Results of 6-channel analysis of 2006-2009: 1. Coupled-channel effects are crucial
2. Only qualitatively describe πΝ -> ππN
3. Over estimate γΝ -> ππN by a factor of 2
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pi N pi pi N reaction
Parameters used in the calculation are from pN pN analysis.
Full result
C.C. effect off
Kamano, Julia-Diaz, Lee, Matsuyama, Sato, Phys. Rev. C, (2008)
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Double pion photoproductionKamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC80 065203 (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 p00 and p+-
overestimate the data by factor of 2
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Difficulty : Lack of sufficient πΝ -> ππ N data to pin down N* -> πΔ, ρΝ, σN -> ππΝ
Two-pion data are not in 8-channel analysis
Progress: A proposal on πΝ -> ππN is being considered at J-PARC
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Next Tasks
1. Complete the extraction of N-N* form factors to reach DOE
milestone HP7:
2. Make predictions for J-PARC projects on πΝ -> ππΝ, ΚΛ…
In progress
3. Analyze the data from “complete experiments”
(in collaboration with A. Sandorfi and S. Holbit)
“Measure the electromagnetic excitations of low-lying baryon
states (< 2GeV) and their transition form factors ….”
By extending the ANL-Osaka collaboration (since 1996)
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Collaborators
J. Durand (Saclay)B. Julia-Diaz (Barcelona)H. Kamano (RCNP,JLab)T.-S. H. Lee (ANL,JLab)A. Matsuyama(Shizuoka)S. Nakamura (JLab)B. Saghai (Saclay)T. Sato (Osaka)C. Smith (Virginia, Jlab) U. Suzuki (Osaka)K. Tsushima (JLab)
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Remarks on numerical tasks :
1. DCC is not an algebraic approach like analysis based on polynomials or K-matrix
Solve coupled integral equations with 8 channels by inverting 400 400 complex matrix formed by about 150 Feynman diagrams for each partial waves (about 20 partial waves up to L=5)
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2. Fits to about 28,000 data points
3. To fit new data, we usually need to improve or extend the model Hamiltonian theoretically, not just blindly vary the parameters
4. Analytic continuation requires careful analysis of the analytic structure of the driving terms (150 Feynman amplitudes) of the coupled integral equations, no easy rules to use blindly
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5. Typically, we need 240 processors using supercomputer Fusion at ANL NERSC at LBL
We have used 200,000 hours in January-February, 2012 for 8-channel analysis
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ApplicationApplication
FeedbackFeedback
Pass hadronic parameters Pass hadronic parameters
Application Extract N* hN, KY, wN
Application
Extract N* hN, KY, wN
ApplicationApplication
FeedbackFeedback
Strategy for N* study @ EBAC
Fit hadronic part of parameters
Fit electro-magneticpart of parameters
Refit hadronic part of parameters
Refit electro-magneticpart of parameters
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Thanks to the support from JLab !!
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back up
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y(r) r
e-
i(k - ik )R I
f(q)
k , k > 0 R I
r
y(r) f(q)-eik r
r
-ik re +
Resonance
Scattering
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Search poles on 2n sheets of Riemann surface n = 8
Search on the sheets where a. close channels: physical (kI > 0) b. open channels: unphysical (kI < 0)
Near threshold :search on both physical and unphysical
k = kR + i kI on-shell momentum
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Single pion electroproduction (Q2 > 0)Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)
p (e,e’ p0) p
p (e,e’ p+) n
Five-fold differential cross sections at Q2 = 0.4 (GeV/c)2
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Dynamical coupled-channels model of EBACFor details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)
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Improvements of the DCC model
The resulting amplitudes are now completely unitary in
channel space !!
Processes with 3-body ppN unitarity cut
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Re E (MeV)
Im E
(M
eV) pD threshold
C:1820–248i
B:1364–105i
hN threshold
rN thresholdA:1357–76i
Bare state
Dynamical origin of P11 resonancesSuzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010)
(hN, rN, pD) = (u, u, u)
(hN, rN, pD) = (p, u, - )(hN, rN, pD) = (p, u, p)
(hN, rN, pD) = (p, u, u)
Pole trajectoryof N* propagator
(pN,sN) = (u,p)for three P11 poles
self-energy:
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Scattering amplitude is a double-valued function of complex E !!
Essentially, same analytic structure as square-root function: f(E) = (E – Eth)1/2
e.g.) single-channel meson-baryon scattering
unphysical sheet
physical sheet
Multi-layer structure of the scattering amplitudes
physical sheet
Re (E)
Im (E
)
0 0Im (E
)
Re (E)
unphysical sheet
Re(E) + iε =“ physical world”
Eth
(branch point)Eth
(branch point)
N-channels Need 2N Riemann sheets
2-channel case (4 sheets):(channel 1, channel 2) = (p, p), (u, p) ,(p, u), (u, u)
p = physical sheetu = unphysical sheet