EBAC-DCC analysis of world data on pN, gN, and N(e,e’) reactions Hiroyuki Kamano Osaka City University (Excited Baryon Analysis Center, Jefferson Lab) ( Presented by T.-S. H. Lee) NSTAR2011

Outline Strategy for N* study at EBAC EBAC-DCC analysis of pN and gN reactions (2006 - 2009) EBAC-DCC analysis of pN and gN reactions (2010 - ) Summary Highlights of the fits to data Extracted N* spectrum (poles) N-N* transition form factors (residues)

Strategy for N* study at EBAC

Excited Baryon Analysis Center (EBAC) of Jefferson Lab Founded in January 2006 http://ebac-theory.jlab.org/ Reaction Data 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* Dynamical Coupled-Channels Analysis @ EBAC 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!

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: coupled-channels effect 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: 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

Strategy for N* study at EBAC Stage 1 Perform comprehensive analysis of meson production reactions Develop analytic continuation of amplitudes to complex energy plane  Suzuki, Sato, Lee PRC79 025205; PRC82 045206 Stage 2 N* spectrum (poles); N*  gN, MB transition form factors (residues) Extract resonance information from the determined partial-wave amplitudes Stage 3 Interpret the extracted resonance information in terms of hadron structure calculations . Quark models, Dyson-Schwinger approaches, LQCD,…

EBAC-DCC analysis of pN and gN reactions: 2006-2009

pN, hN, ppN (pD,rN,sN) coupled- channels calculations were performed. EBAC-DCC analysis (2006-2009) 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, PRC76 065201 (2007) p N  h N : Used for constructing a hadronic model up to W = 2 GeV Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008) p N  p p N : First full dynamical coupled-channels calculation up to W = 2 GeV. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (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, PRC77 045205 (2008) (electroproduction) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) g N  p p N : First full dynamical coupled-channels calculation up to W = 1.5 GeV. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC80 065203 (2009) Electromagnetic part

pi N amplitudes (2006-2009) Isospin 1/2 Imaginary T 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’ p0) 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 Q2 = 0.4 (GeV/c)2 p (e,e’ p0) p p (e,e’ p+) n

pi N  pi pi N reaction Full result C.C. effect off Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) Parameters used in the calculation are from pN  pN 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 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.

Extraction of N* information Definitions of N* masses (spectrum)  Pole positions of the amplitudes N*  MB, gN decay vertices  Residues1/2 of the pole Consistent 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*  b decay vertex N* pole position ( 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: pD unphys. sheet pole B: pD 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 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 pN and gN reactions: 2010 -

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

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) [PRC76 065201 (2007)]

Single pion photoproduction 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 Previous model (fitted to gN  pN data up to 1.6 GeV) [PRC77 045205 (2008)]

Eta production reactions Photon asymmetry 1535 MeV 1674 MeV 1811 MeV 1930 MeV 1549 MeV 1657 MeV 1787 MeV 1896 MeV Analyzed data up to W = 2 GeV. p- p  h n data are selected following Durand et al. PRC78 025204.

pi N  KY reactions Angular distribution Recoil polarization 1732 MeV

gamma p  K+ Lambda Measure ALL 16 observables !! Formulae 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 !! (ds + 15 polarization asymmetries)

Summary

Summary and outlook Multi-channel reaction mechanisms plays a crucial 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: 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, … reactions to the combined analysis. Previous model: Q2 < 1.5 GeV2

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 Kamano (Jlab) T.-S. H. Lee (1/4 EFT) A. Matsuyama S. Nakamura (JLab) B. Saghai 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: End of 2013 Make the EBAC-DCC code available for future analysis of “complete experiments” and N* experiments with 12 GeV upgrade “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”

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Summary and outlook New direction Nakamura, arXiv:1102.5753 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) p g B, D, J/Y... X Exotic hybrids? f0, r, .. p p Heavy meson decays GlueX

Summary and outlook New direction Nakamura, arXiv:1102.5753 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 a1(1260)  ppp decay from our model Isobar model Unitary model (with full 3-body unitarity)

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

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

pi N  pi pi N reaction Full result Full result Phase space Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) Parameters used in the calculation are from pN  pN analysis. s (mb) W (GeV) Full result Full result Phase space

Improvements of the DCC model Processes with 3-body ppN 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 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)

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, -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 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 44, -17 34, -25 D (1232) P33 52, -46 52, -47 47, -37 50, -48 53, -47 D*(1620) S31 21, -134 15, -92 12, -108 19, -95 15, -110 D*(1910) P31 45, 172 12, -153 38, -- 13, -20 D*(1700) D33 12, -59 18, -40 16, -38 10, -- D*(1905) F35 5, -79 15, -30 25, -- 25, -50 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 -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) 125 + 25i 147 +/- 10 165 +/- 5 143 +/- 2 -42 + 8i -38 +/- 3 -20 +/- 7 -28 +/- 2 P11(1357) -12 + 21i -63 +/- 5 -51 +/- 2 (1364) -14 + 22i S11(1540) -8 + 43i 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) -95 - 3i 145 +/- 5 134 +/- 2 -67 + 11i -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

Q2 dependence of the form factors: 1/3 Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) Suzuki, Sato, Lee, arXiv:0910.1742 N-D transition GM form factor GM / (3GD) real part other analyses 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) Suzuki, Sato, Lee, arXiv:0910.1742 N-P11 e.m. transition amplitude A1/2 CLAS Collaboration PRC78, 045209 (2008) real imaginary real imaginary

pi N amplitudes (2006-2009) Isospin 1/2 Real T 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 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.

pi N amplitudes (2006-2009) Isospin 1/2 Imaginary T Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Isospin 1/2 Imaginary T

pi N amplitudes (2006-2009) Isospin 3/2 Real T Julia-Diaz, Lee, Matsuyama, Sato, PRC76 065201 (2007) Isospin 3/2 Real T

pi N amplitudes (2006-2009) Isospin 3/2 Imaginary T 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 Full result C.C. effect off Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) Parameters used in the calculation are from pN  pN analysis. Full result C.C. effect off

pi N  eta N reaction N*  hN varied Model constructed from Durand, Julia-Diaz, Lee, Saghai, Sato, PRC78 025204 (2008) N*  hN varied Model constructed from pN  pN 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 Number of resonant parameters are reduced significantly !! L = MB orbital angular mom. S = total spin of MB J = L x S