EBAC-DCC analysis of world data on N, N, and N(e,e) reactions Hiroyuki Kamano Osaka City University (Excited Baryon Analysis Center, Jefferson Lab) ( Presented by T.-S. H. Lee) NSTAR2011 Outline 1. Strategy for N* study at EBAC 2. EBAC-DCC analysis of N and N reactions (2006 - 2009) Highlights of the fits to data Extracted N* spectrum (poles) N-N* transition form factors (residues) 3. EBAC-DCC analysis of N and N reactions (2010 - ) 4. Summary Strategy for N* study at EBAC

Excited Baryon Analysis Center (EBAC) of Jefferson Lab http://ebac-theory.jlab.org/ Founded in January 2006 Reaction Data Objectives : Perform a comprehensive analysis of world data of N, N, N(e,e) reactions, Dynamical Coupled-Channels Analysis @ EBAC Determine N* spectrum (pole positions) Extract N-N* form factors (residues) Identify reaction mechanisms for interpreting the properties and dynamical origins of N* N* properties

Hadron Models Lattice QCD QCD 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! a 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: coupled-channels effect Reaction channels: Transition potentials: Meson-exchange potentials (Derived from Lagrangians) bare N* states 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: Physical N*s will be a mixture of the two pictures:

baryon coupled-channels effect meson cloud Reaction channels: meson core Transition potentials: exchange potentials of ground state mesons and baryons bare N* states Strategy for N* study at EBAC Stage 1 Perform comprehensive analysis of meson production reactions

Develop analytic continuation of amplitudes to complex energy plane Stage 2 Suzuki, Sato, Lee PRC79 025205; PRC82 045206 Extract resonance information from the determined partial-wave amplitudes N* spectrum (poles); N* N, MB transition form factors (residues) Stage 3 Interpret the extracted resonance information in terms of hadron structure calculations . Quark models, Dyson-Schwinger approaches, LQCD, EBAC-DCC analysis of N and N reactions: 2006-2009 EBAC-DCC analysis (2006-2009) N, N, N (,N,N) coupledchannels calculations were performed.

Hadronic part N N : Used for constructing a hadronic model up to W = 2 GeV. Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) NN : Used for constructing a hadronic model up to W = 2 GeV Durand, 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) Electromagnetic part 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) pi N amplitudes (2006-2009) Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Isospin 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) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009)

Fit to the structure function data (~ 20000) from CLAS p (e,e 00) 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) Five-fold differential cross sections at Q22 = 0.4 (GeV/c)22 p (e,e 00) p p (e,e +) n pi N pi pi N reaction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009)

Parameters used in the calculation are from N N analysis. Full result C.C. effect off Double pion photoproduction Kamano, 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* b vertex vectors Consistent with the resonance theory baseddecay on Gamow G. Gamow (1928), R. E. Peierls (1959), A brief introduction of Gamow vectors: de la Madrid et al, quant-ph/0201091 (complex) energy eigenvalues = transition matrix elements = pole values

1/2 position N* pole (residue) of the poles ( Im(E0) < 0 ) N* poles from EBAC-DCC analysis Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010) L2I 2J Two resonance poles in the Roper resonance region !! 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)

Pole positions and dynamical origin of P11 resonances pole A: unphys. sheet pole 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 - 1stst 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 EBAC-DCC analysis of N and N reactions: 2010

- EBAC-DCC analysis: 2010 ~ Fully combined analysis of N , N N , N , KY reactions !! 2006 ~ 2009 2010 ~ 5 channels (N,N,,N,N) 7 channels (N,N,,N,N,K,K) N N < 2 GeV < 2.1 GeV N N

< 1.6 GeV < 2 GeV N N < 2 GeV < 2 GeV N N < 2GeV N KY

< 2.1 GeV N K < 2.1 GeV # of coupled channels 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 N N data only) [PRC76 065201 (2007)] Single pion photoproduction Angular distribution 1154 MeV 1232 MeV 1137 MeV 1232 MeV 1416MeV MeV

1462 1519MeV MeV 1527 1729 1690MeV MeV 1834 1798MeV MeV Photon asymmetry 1313 MeV MeV 1334 1154 MeV 1137 MeV

1232 MeV 1232 MeV 1313 MeV 1334 MeV 1416MeV MeV 1462 1527 MeV 1519 1617 1617 MeV MeV 1834 1798MeV MeV

1958 1899MeV MeV 1617 MeV MeV 1617 1958 1899 MeV MeV 1690 MeV 1729 MeV Current model (full combined analysis Previous model (fitted to N N data up to 1.6 GeV)

[PRC77 045205 (2008)] Eta production reactions Photon asymmetry 1535 MeV 1549 MeV 1674 MeV 1657 MeV 1811 MeV 1787 MeV 1930 MeV Analyzed data up to W = 2 GeV. p n data are selected following Durand et al. PRC78 025204. 1896 MeV

pi N KY reactions Angular distribution 1732 MeV 1757 MeV Recoil polarization 1792 MeV 1732 MeV 1792 MeV 1757 MeV 1845 MeV 1985 MeV 2031 MeV

1879 MeV 1966 MeV 2059 MeV 1879 MeV 1845 MeV 1879 MeV 1879 MeV 1985 MeV 1966 MeV 1966 MeV

2031 MeV 2059 MeV 2059 MeV 1966 MeV 2059 MeV gamma p K+ Lambda Formulae for calculating polarization observables Sandorfi, Hoblit, Kamano, Lee JPG 38, 053001 (2011) (Topical Review) 1781 MeV 1883 MeV 2041 MeV Measure ALL 16 observables !!

(d + 15 polarization asymmetries) (Over-) complete experiment is ongoing at [email protected] ! Expected to be a crucial source for establishing N* spectrum !! 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 crucial role for interpreting the N* spectrum and form factors !! 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. Fully combined analysis of N, N N, N, KY reactions is underway. Re-examine resonance poles Previous model: Q2 < 1.5 GeV2 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. 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

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 accomplished Summer of 2013 Complete the extraction of N-N* form factors to reach DOE milestone HP7: 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 End of 2013 Make the EBAC-DCC code available for future analysis of complete experiments and N* experiments with 12 GeV upgrade back up Summary and outlook New direction Nakamura, arXiv:1102.5753 Kamano, Nakamura, Lee, Sato, in preparation Application of the DCC approach to meson physics: (3-body unitarity effect are fully taken into account) B, D, J/...

X Exotic hybrids? f0, , .. Heavy meson decays p p GlueX Summary and outlook New direction Nakamura, arXiv:1102.5753 Kamano, Nakamura, Lee, Sato, in preparation Application of the DCC approach to meson physics: (3-body unitarity effect are fully taken into account)

Dalitz plot of a1(1260) decay from our model Isobar model Unitary model (with full 3-body unitarity) Coupled-channels effect in various reactions Pion photoproductions Full c.c. effect of N(,N,N) & N off Double pion productions Full c.c effect off Pion electroproductions Full

c.c. effect of N(,N,N) & N off Dynamical coupled-channels model of EBAC For details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007) pi N pi pi N reaction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) (mb) Parameters used in the calculation are from N N analysis. W (GeV) Full result Full result Phase space

Improvements of the DCC model Processes with 3-body N unitarity cut The resulting amplitudes are now completely unitary in channel space !! Dynamical origin of P11 resonances Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 042302 (2010) Pole trajectory of N* propagator self-energy: Bare state Im E (MeV) N threshold (N, N, ) = (p, u, u)

threshold (N, N, ) = (p, u, ) (N, N, ) = (p, u, p) A:135776i N threshold (N, N, ) = (u, u, u) B:1364105i C:1820248i (N,N) = (u,p) for three P11 poles Re E (MeV) 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,

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 N*(1720) P13 -3 120, --

15 9, -167 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 45, 172 12, -153 38, -- 13, -20

*(1910) P31 *(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

Helicity amplitudes of N-N* e.m. transition (Q2 = 0) EBAC-DCC P33(1211) Ahrens04/02 Arndt04/02 Dugger07 Blanpied01 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 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

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 D13(1521) F15(1674) Q2 dependence of the form factors: 1/3 Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) Suzuki, Sato, Lee, arXiv:0910.1742 GM / (3GD) N- transition GM form factor other analyses real part imaginary part Q2 dependence of the form factors: 2/3

Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) Suzuki, Sato, Lee, arXiv:0910.1742 N-D13 e.m. transition amplitude A3/2 A1/2 real part CLAS imaginary part Q2 dependence of the form factors: 3/3 Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) N-P11 e.m. transition amplitude Suzuki, Sato, Lee, arXiv:0910.1742

CLAS Collaboration PRC78, 045209 (2008) A1/2 real imaginary real imaginary pi N amplitudes (2006-2009) Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Isospin 1/2 Real T Double pion photoproduction Kamano, 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. pi N amplitudes (2006-2009) Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Isospin 1/2 Imaginary T pi N amplitudes (2006-2009) Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Isospin 3/2 Real T pi N amplitudes (2006-2009) Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007)

Isospin 3/2 Imaginary T pi N amplitudes (current model) !!! PRELIMINARY, NOT the final result !!! Real T pi N amplitudes (current model) !!! PRELIMINARY, NOT the final result !!! Imaginary T Phase shift and inelasticity W (MeV) pi N pi pi N reaction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) Parameters used in the calculation are from N N analysis.

Full result C.C. effect off pi N eta N reaction Durand, 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) M N* L 18 12

B L = MB orbital angular mom. S = total spin of MB J=LxS Number of resonant parameters are reduced significantly !!