EBAC-DCC combined analysis of world data on pN and gN processes Hiroyuki Kamano (Excited Baryon Analysis Center, Jefferson Lab) Joint EBAC/GWU Seminar, March 14th, 2011

Outline Motivation and 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 and outlook N* spectrum (pole positions) and residues Alternative view of dynamical origin of P11 resonances N-N* e.m. transition form factors

Motivation and strategy for N* study at EBAC (1 of 4)

N* states and PDG *s channels !! ? Most of the N*s were extracted from Arndt, Briscoe, Strakovsky, Workman PRC 74 045205 (2006) ? Most of the N*s were extracted from Need comprehensive analysis of channels !!

Excited Baryon Analysis Center (EBAC) of Jefferson Lab Founded in January 2006 http://ebac-theory.jlab.org/ Reaction Data Objectives and goals: Through the comprehensive analysis of world data of pN, gN, N(e,e’) reactions, Determine N* spectrum (pole positions) Extract N* form factors (e.g., N-N* e.m. transition form factors) Provide reaction mechanism information necessary for interpreting N* spectrum, structures and dynamical origins Dynamical Coupled-Channels Analysis @ EBAC N* properties Hadron Models Lattice QCD Theory support for Excited Baryon Program at CLAS12@JLab (arXiv:0907.1901) 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: 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 Construct a reaction model through the comprehensive analysis of meson production reactions Requires careful 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) Confirm/reject N* with low-star status; Search for new N* Extract resonance information from the constructed reaction model Stage 3 Make a connection to hadron structure calculations; Explore the structure of the N* states. Quark models, Dyson-Schwinger approaches, Holographic QCD,…

EBAC-DCC analysis of pN and gN reactions: 2006-2009 (2 of 4)

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  pi pi N reaction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC79 025206 (2009) Parameters used in the calculation are from pN  pN analysis. (# of pN  ppN data) / (# of pN  pN data) ~ 1200 / 24000 Above W = 1.5 GeV, All data were measured more than 3 decades ago. No differential cross section data are available for quantitative fits (only the data without error bar exist). s (mb) Need help of hadron beam facilities such as J-PARC !! W (GeV) Full result Full result Phase space

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.

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

How can we extract N* information? PROPER definition of N* mass (spectrum)  Pole position of the amplitudes N*  MB, gN decay vertices  Residue1/2 of the pole Consistent with the resonance theory based on Gamow vectors G. Gamow (1928), R. E. Peierls (1959), … A brief introduction of Gamov 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 - (3 of 4)

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

Improvements of the DCC model Processes with 3-body ppN unitarity cut new ! The resulting amplitudes are now completely unitary in channel space !!

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 Preliminary!! 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, preliminary) 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 Preliminary!! Analyzed data up to W = 2 GeV. p- p  h n data are selected following Durand et al. PRC78 025204.

pi N  KY reactions Preliminary!! Angular distribution Recoil polarization 1732 MeV 1845 MeV 1985 MeV 2031 MeV 1757 MeV 1879 MeV 1966 MeV 2059 MeV 1792 MeV 1732 MeV 1845 MeV 1985 MeV 2031 MeV 1757 MeV 1879 MeV 1966 MeV 2059 MeV 1792 MeV

gamma p  K+ Lambda Preliminary!! Measure ALL 16 observables !! Formulae for calculating polarization observables  Sandorfi, Hoblit, Kamano, Lee arXiv:1010.0455 (To appear in JPG as a topical review) Preliminary!! 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 and outlook (4 of 4)

Summary and outlook (1 of 2) Extraction of N* from EBAC-DCC analysis during 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 (1 of 2) 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, wN, … reactions to the combined analysis. Previous model: Q2 < 1.5 GeV2

Summary and outlook (2 of 2) Other issues we are working on Construction of a consistent formula with Gamow theory for branching ratios of N* decays to unstable channels: N*  pD, rN, sN  ppN etc. Implementation of gauge invariance (current conservation) to the full e.m. amplitudes within our framework. 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 p2(2100)  ppp decay f0, r, .. p B, D, J/Y... Heavy meson decays g X Exotic hybrids? GlueX Hamiltonian approach based on the method of unitary transformation. Matsuyama, Sato, Lee Phys. Rep. 439 (2007) 193 Sato, Lee PRC54 (1996) 2660

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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

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

Single pion electroproduction (Q2 > 0) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC80 025207 (2009) Fit to the structure function data from CLAS p (e,e’ p0) p W < 1.6 GeV Q2 < 1.5 (GeV/c)2 is determined at each Q2.

2. 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

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