ebac-dcc analysis of world data on p n, g n, and n(e,e’) reactions

EBAC-DCC analysis of world data on EBAC-DCC analysis of world data on

N, N, N, and N(e,e’) reactionsN, and N(e,e’) reactions

Hiroyuki KamanoHiroyuki Kamano

Osaka City University Osaka City University

(Excited Baryon Analysis Center, Jefferson Lab)(Excited Baryon Analysis Center, Jefferson Lab)

NSTAR2011

( Presented by T.-S. H. Lee)

Outline

1. Strategy for N* study at EBAC

2. EBAC-DCC analysis of N and N reactions (2006 - 2009)

3. EBAC-DCC analysis of N and N reactions (2010 - )

4. Summary

Highlights of the fits to data

Extracted N* spectrum (poles)

N-N* transition form factors (residues)

Strategy for N* study at EBACStrategy for N* study at EBAC

Objectives :

Perform a comprehensive analysis of world data of N, N, 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*

Excited Baryon Analysis Center (EBAC) of Jefferson Lab

N* properties

QQCCDD

Lattice QCDHadron Models

Dynamical Coupled-Channels Analysis @ EBAC

Reaction Data

http://ebac-theory.jlab.org/Founded in January 2006

A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439 (2007) 193

Dynamical coupled-channels model of meson production reactionsDynamical coupled-channels model of meson production reactions

Singular!

a

a

Dynamical coupled-channels model of EBAC

Meson production dataMeson production dataN* spectrum, structure, … N* spectrum, structure, …

Reaction mechanismsReaction mechanisms

Partial wave (LSJ) amplitude of a b reaction:

Reaction channels:

Transition potentials:

coupled-channels effect


Meson-exchange potentials(Derived from Lagrangians)Meson-exchange potentials(Derived from Lagrangians) bare N* statesbare N* states

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


exchange potentialsof ground state

mesons and baryons

exchange potentialsof ground state

mesons and baryonsbare N* statesbare N* states

For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)

corecore

meson cloudmeson cloud

mesonmeson

baryonbaryon

Physical N*s will be a “mixture” of the two pictures:

Strategy for N* study at EBAC

Stage 3Stage 3

Interpret the extracted resonance information in terms of hadron structure calculations .

Quark models, Dyson-Schwinger approaches, LQCD,…

Stage 1Stage 1

Perform comprehensive analysis of meson production reactions

Stage 2Stage 2

N* spectrum (poles); N* N, MB transition form factors (residues)

Extract resonance information from the determined partial-wave amplitudes

Develop analytic continuation of amplitudes to complex energy plane Suzuki, Sato, Lee PRC79 025205; PRC82 045206

EBAC-DCC analysis of N and N reactions:

2006-2009

EBAC-DCC analysis of N and N reactions:

2006-2009

EBAC-DCC analysis (2006-2009)

N N : Used for constructing a hadronic model up to W = 2 GeV.Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)

N N : Used for constructing a hadronic model up to W = 2 GeVDurand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)

N N : First full dynamical coupled-channels calculation up to W = 2 GeV.Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)

N 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, PRC77 045205 (2008) (electroproduction) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)

N N : First full dynamical coupled-channels calculation up to W = 1.5 GeV. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC80 065203 (2009)

Hadronic partHadronic part

Electromagnetic partElectromagnetic part

N, N, N (,N,N) coupled-channels calculations were performed.

N, N, N (,N,N) coupled-channels calculations were performed.

pi N amplitudes (2006-2009)Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)

Isospin 1/2 Imaginary TIsospin 1/2 Imaginary T

Single pion photoproduction (Q2 = 0)Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC77 045205 (2008)

Fit up to

W = 1.6 GeV.

Only

is varied.

Single pion electroproduction (Q2 > 0)

Fit to the structure function data (~ 20000) from CLASFit to the structure function data (~ 20000) from CLAS

Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)

p (e,e’ 0) pp (e,e’ 0) p

W < 1.6 GeV

Q2 < 1.5 (GeV/c)2

is determined

at each Q2.

Single pion electroproduction (Q2 > 0)Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)

p (e,e’ 0) pp (e,e’ 0) p

p (e,e’ +) np (e,e’ +) n

Five-fold differential cross sections at Q2 = 0.4 (GeV/c)2Five-fold differential cross sections at Q2 = 0.4 (GeV/c)2

pi N pi pi N reaction

Parameters used in the calculation are from N N analysis.

Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)

Full result

C.C. effect off

Double pion photoproductionKamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC80 065203 (2009)

Parameters used in the calculation are from N N & N N 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.

Extraction of N* information

Definitions of

N* masses (spectrum) Pole positions of the amplitudes

N* MB, N decay vertices Residues1/2 of the pole

N* pole position ( Im(E0) < 0 )

N* pole position ( Im(E0) < 0 )

N* b decay vertex

N* b decay vertexConsistent 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/0201091

(complex) energy eigenvalues = pole values

transition matrix elements = (residue)1/2 of the poles

N* poles from EBAC-DCC analysisSuzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010)

L2I 2J Two resonance poles in the Roper resonance region !!

Two resonance poles in the Roper resonance region !!

Dynamical coupled-channels effect on N* poles and form factors

Pole positions and dynamical origin of P11 resonancesPole positions and dynamical origin of P11 resonances

Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (2010)Suzuki, Sato, Lee, PRC82 045206 (2010)

pole A: unphys. sheetpole B: phys. sheet

Dynamical coupled-channels effect on N* poles and form factors

Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (2010)Suzuki, Sato, Lee, PRC82 045206 (2010)

Nucleon - 1st D13 e.m. transition form factorsNucleon - 1st D13 e.m. transition form factors

Real part Imaginary part

Crucial role of non-trivial multi-channel reaction

mechanisms for interpreting the structure and

dynamical origin of nucleon resonances !

EBAC-DCC analysis of N and N reactions: 2010

-

EBAC-DCC analysis of N and N reactions: 2010

-

EBAC-DCC analysis: 2010 ~

N N

N N

N N

N N

N KY

N K

2006 ~ 2009

5 channels (N,N,,N,N)

< 2 GeV

< 1.6 GeV

< 2 GeV

―

―

―

2010 ~

7 channels (N,N,,N,N,K,K)

< 2.1 GeV

< 2 GeV

< 2 GeV

< 2GeV

< 2.1 GeV

< 2.1 GeV

# of coupled channels

Fully combined analysis of N , N N , N , KY reactions !!

Pion-nucleon elastic scattering

Current model

(full combined analysis, PRELIMINARYPRELIMINARY)

Previous model (fitted to N N data only)[PRC76 065201 (2007)]

Target polarizationTarget polarization

1234 MeV1234 MeV

1449 MeV1449 MeV

1678 MeV1678 MeV

1900 MeV1900 MeV

Angular distribution Angular distribution

Single pion photoproduction

Current model (full combined analysis

Previous model (fitted to N N data up to 1.6 GeVup 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

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

1154 MeV 1232 MeV 1313 MeV

1416 MeV 1519 MeV 1617 MeV

1690 MeV

1798 MeV 1899 MeV

1535 MeV

1674 MeV

1811 MeV

1930 MeV

1549 MeV

1657 MeV

1787 MeV

1896 MeV

Eta production reactions

Analyzed data up to W = 2 GeV. p n data are selected following Durand et al. PRC78 025204.

Photon asymmetry

pi N KY reactions

Angular distribution Angular distribution Recoil polarizationRecoil polarization

1732 MeV

1845 MeV

1985 MeV

2031 MeV

1757 MeV

1879 MeV

1966 MeV

2059 MeV

1792 MeV

1879 MeV

1966 MeV

2059 MeV

1732 MeV

1845 MeV

1985 MeV

2031 MeV

1757 MeV

1879 MeV

1966 MeV

2059 MeV

1792 MeV

1879 MeV

1966 MeV

2059 MeV

gamma p K+ LambdaFormulae for calculating polarization observables

Sandorfi, Hoblit, Kamano, Lee JPG 38, 053001 (2011)

(Topical Review)

1781 MeV 1883 MeV 2041 MeV

“(Over-) complete experiment” is ongoing at CLAS@JLab !

Expected to be a crucial source for establishing N* spectrum !!

Measure ALL 16 observables !!(d + 15 polarization asymmetries)Measure ALL 16 observables !!(d + 15 polarization asymmetries)

Summary Summary

Summary and outlook

Extraction of N* from EBAC-DCC analysis 2006-2009:

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 crucialrole for interpreting the N* spectrum and form factors !!

Summary and outlook

Extraction of N* from EBAC-DCC analysis 2006-2009:

Fully combined analysis of N, N N, N, KY reactions is underway.

Re-examine resonance poles

Analyze CLAS ep eN data with Q2 < ~ 4 GeV2;

Extract N-N* electromagnetic transition form factors at high Q2

Include N, N N, … reactions to the combined analysis.

Previous model: Q2 < 1.5 GeV2

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.

Summary and outlook

Projected progressProjected progress

Spring of 2012

Complete the combined analysis to reach DOE milestone HP3:

““Complete the Complete the combinedcombined analysis of available single pion, eta, kaon analysis of available single pion, eta, kaon

photo-production data for nucleon resonances and incorporate photo-production data for nucleon resonances and incorporate

analysis of two-pion final states into the analysis of two-pion final states into the coupled-channelscoupled-channels analysis analysis

of resonances”of resonances”

EBAC Collaborations

J. Durand

B. Julia-Diaz

H. Kamano (Jlab)

T.-S. H. Lee (1/4 EFT)

A. Matsuyama

S. Nakamura (JLab)

B. Saghai

T. Sato

C. Smith

N. Suzuki

Summary and outlook

Works need to be accomplishedWorks 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 Measure the electromagnetic excitationselectromagnetic excitations of low-lying baryon of low-lying baryon

states (< 2GeV) and their states (< 2GeV) and their transition form factorstransition form factors over the range over the range

QQ22 = 0.1 – 7 GeV = 0.1 – 7 GeV22 and measure the electro- and photo-production and measure the electro- and photo-production

of final states with of final states with oneone and and twotwo pseudoscalar mesons” pseudoscalar mesons”

back upback up

Summary and outlook

New directionNew direction

Application of the DCC approach to meson physics:

(3-body unitarity effect are fully taken into account)

f0, , ..

B, D, J/...

Heavy meson decays

p p

X

Exotic hybrids?

GlueX

Nakamura, arXiv:1102.5753 Kamano, Nakamura, Lee, Sato, in preparation

Summary and outlook

New directionNew direction

Application of the DCC approach to meson physics:

(3-body unitarity effect are fully taken into account)

Nakamura, arXiv:1102.5753 Kamano, Nakamura, Lee, Sato, in preparation

Dalitz plot of a1(1260) decay from our modelDalitz plot of a1(1260) decay from our model

Isobar model

Unitary model(with full 3-body unitarity)

Coupled-channels effect in various reactions

Full

c.c. effect of N(,N,N) & N off

Full

Full

c.c effect off

c.c. effect of N(,N,N) & N off

Pion photoproductionsPion photoproductions

Pion electroproductionsPion electroproductions

Double pion productionsDouble pion productions

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




Full result

Phase spaceFull result

W (GeV)

(m

b)

Improvements of the DCC model

The resulting amplitudes are now completely unitary in

channel space !!

Processes with 3-body N unitarity cutProcesses with 3-body N unitarity cut

Re E (MeV)

Im E

(M

eV) threshold

C:1820–248i

B:1364–105i

N threshold

N thresholdA:1357–76i

Bare state

Dynamical origin of P11 resonancesSuzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010)

(N, N, ) = (u, u, u)

(N, N, ) = (p, u, － )(N, N, ) = (p, u, p)

(N, N, ) = (p, u, u)

Pole trajectoryof N* propagatorPole trajectoryof N* propagator

(N,N) = (u,p)for three P11 poles

self-energy:

Residues of resonance poles in pi N amplitude

EBAC(06-09) Arndt06 Doring09 Hoeler Cutkosky

PDG notation R (MeV), (deg.)

N*(1535) S11 44, -42 16, -16 31, -3 120, 15

N*(1650) S11 18, -93 14, -69 54, -44 39, -27 60, -75

N*(1440) P11 37, -110 38, -98 48, -64 40, -- 52, -100

N*(1440) P11 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, 7 38, -5 32, -18 32, -8 35, -12

N*(1675) D15 31, -24 27, -21 (not analyzed) 23, -22 31, -30

N*(1680) F15 40, -11 42, -4 (not analyzed) 44, -17 34, -25

(1232) P33 52, -46 52, -47 47, -37 50, -48 53, -47

*(1620) S31 21, -134 15, -92 12, -108 19, -95 15, -110

*(1910) P31 45, 172 12, -153 38, -- 13, -20

*(1700) D33 12, -59 18, -40 16, -38 10, -- 13, -20

*(1905) F35 5, -79 15, -30 (not analyzed) 25, -- 25, -50

*(1950) F37 41, -33 53, -31 (not analyzed) 47, -32 50, -33

EBAC-DCC Ahrens04/02 Arndt04/02 Dugger07 Blanpied01

P33(1211) A3/2 -269 + 12i -258 +/- 3 -243 +/- 1 -266.9+/-1.6+/-7.8

A1/2 -132 + 38i -137 +/- 5 -129 +/- 1 -135+/-1.3+/-3.7

D13(1521) A3/2 125 + 25i 147 +/- 10 165 +/- 5 143 +/- 2

A1/2 -42 + 8i -38 +/- 3 -20 +/- 7 -28 +/- 2

P11(1357) A1/2 -12 + 21i -63 +/- 5 -51 +/- 2

(1364) A1/2 -14 + 22i

S11(1540) A1/2 -8 + 43i 60 +/- 15 91 +/- 2

(1642) A1/2 29 – 17i 69 +/- 5 22 +/- 7

D15(1654) A3/2 44 – 9i 10 +/- 7 21 +/- 1

A1/2 58 – 0.5i 15 +/-10 18 +/- 2

F15(1674) A3/2 -95 - 3i 145 +/- 5 134 +/- 2

A1/2 -67 + 11i -10 +/- 4 -17 +/- 1

S31(1563) A1/2 137 – 70i 35 +/- 20 50 +/- 2

D33(1604) A3/2 -45+9i 97 +/- 20 105 +/- 3

A1/2 -1 -17i 90 +/- 25 125 +/- 3

Helicity amplitudes of N-N* e.m. transition (Q2 = 0)

Q2 dependence of the form factors: 1/3

real part

imaginary part

GM

/ (3

GD)

Suzuki, Sato, Lee, arXiv:0910.1742


other analyses

N- transition GM form factorN- transition GM form factor


real part

imaginary part

A3/2A3/2

A1/2A1/2

CLAS



N-D13 e.m. transition amplitudeN-D13 e.m. transition amplitude




N-P11 e.m. transition amplitudeN-P11 e.m. transition amplitude

CLAS CollaborationPRC78, 045209 (2008)

realimaginary

realimaginary

A1/2A1/2


Isospin 1/2 Real TIsospin 1/2 Real T

Double pion photoproductionKamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC80 065203 (2009)

Parameters used in the calculation are from N N & N N 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.


Isospin 3/2 Real TIsospin 3/2 Real T

pi N amplitudes (current model) !!! PRELIMINARY, NOT the final result !!!

Real T

Imaginary T

pi N amplitudes (current model) !!! PRELIMINARY, NOT the final result !!!

Phase shift and inelasticity

W (MeV)




Full result

C.C. effect off

pi N eta N reactionDurand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008)

N* N varied

Model constructed from N N analysis only

Modifications of the DCC model

e.g.) Hadronic parameters of D13 state ( I = 1/2, J = 3/2, Parity = minus)

18 12

×

M

B

L

L = MB orbital angular mom.S = total spin of MBJ = L x S

N*

Number of resonant parameters are reduced significantly !!

ebac-dcc analysis of world data on p n, g n, and n(e,e’) reactions

Documents

p n p n

p n p p n

p n h n

g n p p n

spectrum poles nn

baryonsbare n

lagrangiansbare n

n amplitudes