Results of Nucleon Resonance Extraction via Dynamical Coupled-Channels Analysis from EBAC Hiroyuki Kamano (RCNP, Osaka U.) QNP2012, Palaiseau, France, April 16-20, 2012

Outline 1. Background and motivation for N* spectroscopy 2.Results of nucleon resonance extraction from 3. Summary and future works  Description of Dynamical Coupled-Channels (DCC) model  Results of DCC analysis ( )  Results of DCC analysis ( )

N* spectroscopy : Physics of broad & overlapping resonances Δ (1232) Width: a few hundred MeV. Resonances are highly overlapping in energy except  (1232). Width: ~10 keV to ~10 MeV Each resonance peak is clearly separated. N* : 1440, 1520, 1535, 1650, 1675, 1680,...  : 1600, 1620, 1700, 1750, 1900, … N* : 1440, 1520, 1535, 1650, 1675, 1680,...  : 1600, 1620, 1700, 1750, 1900, …

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

Hadron spectrum and reaction dynamics Various static hadron models have been proposed to calculate hadron spectrum and form factors. In reality, excited hadrons are “unstable” and can exist only as resonance states in hadron reactions.  Quark models, Bag models, Dyson-Schwinger approaches, Holographic QCD,…  Excited hadrons are treated as stable particles.  The resulting masses are real. What is the role of reaction dynamics in interpreting the hadron spectrum, structures, and dynamical origins ?? “Mass” becomes complex !!  “pole mass” u u d Constituent quark model N* bare state meson cloud “molecule-like” states core (bare state) + meson cloud

Objectives and goals: Through the comprehensive analysis of world data of  N,  N, N(e,e’) reactions, Determine N* spectrum (pole masses) 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 Collaboration at Excited Baryon Analysis Center (EBAC) of Jefferson Lab Spectrum, structure,… of N* states QCDQCDQCDQCD Lattice QCDHadron Models Analysis Based on Reaction Theory Reaction Data “Dynamical coupled-channels model of meson production reactions” A. Matsuyama, T. Sato, T.-S.H. Lee Phys. Rep. 439 (2007) 193 Founded in January 2006

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 Meson-Baryon Green functions Stable channels Quasi 2-body channels N         N N  N N,  s-channel u-channel t-channelcontact Exchange potentials Z-diagrams Bare N* states N* bare   N    N   Can be related to hadron states of the static hadron models (quark models, DSE, etc.) excluding meson-baryon continuum. core meson cloud meson baryon Physical N*s will be a “mixture” of the two pictures:

DCC EBAC ( )  N   N : Analyzed to construct a hadronic part of the model up to W = 2 GeV Julia-Diaz, Lee, Matsuyama, Sato, PRC (2007)  N   N : Analyzed to construct a hadronic part of the model up to W = 2 GeV Durand, Julia-Diaz, Lee, Saghai, Sato, PRC (2008)  N    N : Fully dynamical coupled-channels calculation up to W = 2 GeV Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009)   N   N : Analyzed to construct a E.M. part of the model up to W = 1.6 GeV and Q 2 = 1.5 GeV 2 (photoproduction) Julia-Diaz, Lee, Matsuyama, Sato, Smith, PRC (2008) (electroproduction) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009)  N    N : Fully dynamical coupled-channels calculation up to W = 1.5 GeV Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009) Extraction of N* pole positions & new interpretation on the dynamical origin of P11 resonances Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL (2010) Stability and model dependence of P11 resonance poles extracted from pi N  pi N data Kamano, Nakamura, Lee, Sato, PRC (2010) Extraction of  N  N* electromagnetic transition form factors Suzuki, Sato, Lee, PRC (2009); PRC (2010) Hadronic part Electromagnetic part Extraction of N* parameters  N,  N,  N, ,  N,  N coupled-channels calculations were performed.  N,  N,  N, ,  N,  N coupled-channels calculations were performed.

Dynamical origin of nucleon resonances Pole positions and dynamical origin of P11 resonances Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL (2010) pole A:  unphys. sheet pole B:  phys. sheet Two-pole nature of the Roper is found also from completely different approaches: Eden, Taylor, Phys. Rev. 133 B1575 (1964) Multi-channel reactions can generate many resonance poles from a single bare state !! For evidences in hadron and nuclear physics, see e.g., in Morgan and Pennington, PRL (1987)

N-N* transition form factors at resonance poles Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki PRC (2009) Suzuki, Sato, Lee, PRC (2010) Real partImaginary part Nucleon - 1 st D13 e.m. transition form factors Coupling to meson-baryon continuum states makes N* form factors complex !! Fundamental nature of resonant particles (decaying states) Extracted from analyzing the p(e,e’  )N data (~ 20000) from CLAS

Dynamical coupled-channels (DCC) analysis  p   N  p   N  p   N  p   p  p  K ,   p  K +  K  channels (  N,  N,  N, ,  N,  N) < 2 GeV < 1.6 GeV < 2 GeV ― channels (  N,  N,  N, ,  N,  N,K ,K  ) < 2.1 GeV < 2 GeV < 2.1 GeV < 2.2 GeV # of coupled channels Fully combined analysis of  N,  N   N,  N, K , K  reactions !! Kamano, Nakamura, Lee, Sato (2012) (~ 28,000 data points to fit)

Partial wave amplitudes of pi N scattering 8ch DCC-analysis (Kamano, Nakamura, Lee, Sato 2012) 6ch DCC-analysis (fitted to  N   N data only) [PRC (2007)] Real partImaginary part

Single pion photoproduction 6ch DCC-analysis [PRC (2008)] up to 1.6 GeV (fitted to  N   N data up to 1.6 GeV) Angular distribution Photon asymmetry 8ch DCC-analysis Kamano, Nakamura, Lee, Sato 2012

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. PRC Photon asymmetry Kamano, Nakamura, Lee, Sato, 2012

KY production reactions Kamano, Nakamura, Lee, Sato, MeV 1785 MeV Polarizations are calculated using the formulae in Sandorfi, Hoblit, Kamano, Lee, J. Phys. G 38, (2011)

Spectrum of N* resonances (Current status) Real parts of N* pole values L 2I 2J PDG 4* PDG 3* Ours Kamano, Nakamura, Lee, Sato, 2012

Note: Some freedom exists on the definition of partial width from the residue of the amplitudes. Width of N* resonances (Current status) Kamano, Nakamura, Lee, Sato, 2012

Summary and future works (1/2) ; ;  p   N  p   N  p   N  p   p  p  K ,   p  K +  K  channels (  N,  N,  N, ,  N,  N) < 2 GeV < 1.6 GeV < 2 GeV ― channels (  N,  N,  N, ,  N,  N,K ,K  ) < 2.1 GeV < 2 GeV < 2.1 GeV < 2.2 GeV # of coupled channels Summary  Two-pole structure of the Roper resonance.  One-to-multi correspondence between bare N*s (= static hadrons) and physical resonances.  Reaction dynamics can produce sizable mass shift for N*s.  May be a key to understanding the issues in the static hadron models.  Complex nature of the resonance form factors. Mass spectrum, decay widths, and N-N* e.m. transition form factors, etc. have been determined for N* resonances in W < 2 GeV. Multi-channel reaction dynamics plays a crucial role for understanding the N* parameters (spectrum, form factors etc) !!

EBAC J.Durand (Saclay) B.Julia-Diaz (Barcelona U.) H.Kamano (RCNP, Osaka U.) T.-S. H. Lee (Argonne Nat’l Lab.) A.Matsuyama (Shizuoka U.) S.Nakamura (JLab) B.Saghai (Saclay) T.Sato (Osaka U./KEK) C.Smith (Virginia, JLab) N.Suzuki (Osaka U.) K.Tsushima (Adelaide U.)

Add  N channel and complete the 9 coupled-channels analysis of the  p,  p   N,  N, KY,  N data. (Kamano, Nakamura, Lee, Sato) Applications to p(,  ), p(,  ) reactions beyond the  region (W > 1.3 GeV) and study axial form factors of N*. A part of the new collaboration “Toward unified description of lepton-nucleus reactions from MeV to GeV region” at J-PARC branch of KEK theory center: (Y. Hayato, M. Hirai, H. Kamano, S. Kumano, S. Nakamura, K. Saito, M. Sakuda, T. Sato) Summary and future works (2/2) Future works Applications to strangeness production reactions (Kamano, Nakamura, Lee, Oh, Sato)  Y* spectroscopy, YN & YY interactions, hypernucleus,.. (related to J-PARC physics) Applications to meson spectroscopy via heavy-meson decays Kamano, Nakamura, Lee, Sato, PRD (2011) pp  X Exotic hybrids? GlueX experiment at f0, ,.. J/  Heavy meson decays  X Details are given in S. Nakamura’s talk (Today’s session B 16:35-16:55) Details are given in S. Nakamura’s talk (Today’s session B 16:35-16:55)  N,  N,  N, ,  N,  N, K , K ,  N

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Since the late 90s, huge amount of high precision data of meson photo-production reactions on the nucleon target has been reported from electron/photon beam facilities. JLab, MAMI, ELSA, GRAAL, LEPS/SPring-8, … Experimental developments E. Pasyuk’s talk at Hall-B/EBAC meeting Opens a great opportunity to make quantitative study of the N* states !!

Kamano, Nakamura, Lee, Sato, 2012

Kamano, Nakamura, Lee, Sato 2012

Kamano, Nakamura, Lee, Sato 2012

Kamano, Nakamura, Lee, Sato, 2012

Single pion electroproduction (Q 2 > 0) Fit to the structure function data (~ 20000) from CLAS Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009) p (e,e’  0 ) p W < 1.6 GeV Q 2 < 1.5 (GeV/c) 2 is determined at each Q 2. N*N  (q 2 = -Q 2 ) q N-N* e.m. transition form factor

Single pion electroproduction (Q 2 > 0) Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki, PRC (2009) p (e,e’  0 ) p p (e,e’  + ) n Five-fold differential cross sections at Q 2 = 0.4 (GeV/c) 2

Data handled with the help of R. Arndt pi N  pi pi N reaction Parameters used in the calculation are from  N   N analysis. Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (2009) Full result Phase spaceFull result W (GeV)  (mb) C. C. effect off

Double pion photoproduction Kamano, Julia-Diaz, Lee, Matsuyama, Sato, PRC (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 p  0  0 and p  +  - overestimate the data.

Definition of N* parameters Definitions of N* masses (spectrum)  Pole positions of the amplitudes N*  MB,  N decay vertices  Residues 1/2 of the pole N* pole position ( Im(E 0 ) < 0 ) N* pole position ( Im(E 0 ) < 0 ) N*  b decay vertex N*  b decay vertex

Scattering amplitude is a double-valued function of complex E !! Essentially, same analytic structure as square-root function: f(E) = (E – E th ) 1/2 Scattering amplitude is a double-valued function of complex E !! Essentially, same analytic structure as square-root function: f(E) = (E – E th ) 1/2 e.g.) single-channel two-body scattering unphysical sheet physical sheet Multi-layer structure of the scattering amplitudes physical sheet Re (E) Im (E) 0 0 Re (E) unphysical sheet Re(E) + iε ＝ “physical world” E th (branch point) E th (branch point) × × × × N-channels  Need 2 N Riemann sheets 2-channel case (4 sheets): (channel 1, channel 2) = (p, p), (u, p),(p, u), (u, u) p = physical sheet u = unphysical sheet 2-channel case (4 sheets): (channel 1, channel 2) = (p, p), (u, p),(p, u), (u, u) p = physical sheet u = unphysical sheet

N, N* Meson cloud effect in gamma N  N* form factors G M (Q 2 ) for  N   (1232) transition Note: Most of the available static hadron models give G M (Q 2 ) close to “Bare” form factor. Full Bare

“Static” form factor from DSE-model calculation. (C. Roberts et al) A clue how to connect with static hadron models “Bare” form factor determined from our DCC analysis.  p  Roper e.m. transition

Delta(1232) : The 1st P33 resonance  N unphysical &  unphysical sheet  N physical &  physical sheet  N   N unphysical &  physical sheet Real energy axis “physical world” Real energy axis “physical world” Complex E-plane Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL (2010) Im (E) Re (E) Re (T) Im (T) P i Riemann-sheet for other channels: (  N,  N,  N) = (-, 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 Small background Isolated pole Simple analytic structure of the complex E-plane

Two-pole structure of the Roper P11(1440)  N unphysical &  unphysical sheet  N physical &  physical sheet  N   N unphysical &  physical sheet Real energy axis “physical world” Real energy axis “physical world” Complex E-plane Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL (2010) Im (E) Re (E) Pole A cannot generate a resonance shape on “physical” real E axis. Pole A cannot generate a resonance shape on “physical” real E axis. Re (T) Im (T) B A P11  branch point prevents pole B from generating a resonance shape on “physical” real E axis.  branch point prevents pole B from generating a resonance shape on “physical” real E axis i i Riemann-sheet for other channels: (  N,  N,  N) = (p,p,p) BW 1440, 300/2 = 150 Two 1356, 78 poles 1364, 105 In this case, BW mass & width has NO clear relation with the resonance poles: ?