Dynamical Coupled-Channels Approach for Single- and Double-Pion Electroproductions: Status and Plans Hiroyuki Kamano Research Center for Nuclear Physics (RCNP) Osaka University EmNN*2012 USC, USA, August 13-15, 2012

Outline 1. Background and motivation for N* spectroscopy 2.ANL-Osaka Dynamical Coupled-Channels (DCC) approach for N* spectroscopy 3. Status and plans for single- and double-pion electroproduction reactions 4. Related hadron physics program at J-PARC

Background and motivation for N* spectroscopy (1 / 4)

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, …

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

ANL-Osaka Dynamical Coupled-Channels (DCC) approach for N* spectroscopy (2 / 4)

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 ANL-Osaka Dynamical Coupled-Channels Approach for N* Spectroscopy 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

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 analysis ( )  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 Double-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) Corresponds to hadron states from static hadron models

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 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 < 2.2 GeV # of channels Fully combined analysis of  N,  N   N,  N, K , K  reactions !! Kamano, Nakamura, Lee, Sato (2012) (more than 20,000 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

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

π - p  ηn reactions Analyzed data up to W = 2 GeV.   p   n data are selected according to Durand et al. PRC Kamano, Nakamura, Lee, Sato, 2012

πN  KY reactions (1/2) Kamano, Nakamura, Lee, Sato, 2012 π - p  K 0 Σ 0 π - p  K 0 Λ π + p  K + Σ +

πN  KY reactions (2/2) Kamano, Nakamura, Lee, Sato, 2012 π - p  K 0 Σ 0 π - p  K 0 Λ π + p  K + Σ +

γp  πN reactions(1/2) γp  π + n γp  π 0 p Kamano, Nakamura, Lee, Sato, 2012

γp  πN reactions(2/2) γp  π + nγp  π 0 p Kamano, Nakamura, Lee, Sato, 2012

γp  ηp reaction Kamano, Nakamura, Lee, Sato, 2012

γp  K + Σ 0, K 0 Σ + reactions Kamano, Nakamura, Lee, Sato, 2012 γp  K + Σ 0 γp  K 0 Σ +

γp  K + Λ reaction (1/4) Kamano, Nakamura, Lee, Sato, 2012

γp  K + Λ reaction (2/4) Kamano, Nakamura, Lee, Sato, 2012

γp  K + Λ reaction (3/4) Kamano, Nakamura, Lee, Sato, 2012

γp  K + Λ reaction (4/4) Kamano, Nakamura, Lee, Sato, 2012

Status and plans for single- and double-pion electroproduction rections (3 / 4)

Status and plans for analysis of electroproduction reactions 6-channel ( ) 8-channel ( ) γp  πN γp  ππN ep  e’πN ep  e’ππN W < 1.6 GeV (the data analyzed) W < 1.6 GeV (cross sections predicted) W < 1.6 GeV, Q 2 < 1.5 (GeV/c) 2 (the data analyzed) W < 2 GeV (the data analyzed) Not yet done [Plan 1]: After completing 8-ch analysis, immediately proceed to the analysis of CLAS p(e,eπ)N data and extract N-N* e.m. transition form factors up to Q 2 ~ 4 (GeV/c) 2. [Plan 2]: After Plan 1, we can give prediction for p(e,eππ)N cross sections. [Combined analysis of p(e,eπ)N and p(e,eππ)N will be a long term project.] VERY preliminary results available (Q 2 = 0 point) (nonzero Q 2 )

γp  ππN calculation with 8-ch. DCC model Prediction for γp  ππ N total cross sections (not yet included in the fit) 8-ch. DCC Full (Kamano, Nakamura, Lee, Sato 2012) 6-ch. DCC Full [PRC (2010)] 8-ch. DCC Nonresonant only 6-ch. DCC Nonresonant only VERY PRELIMINARY !!

Related hadron physics program at J-PARC (4 / 4)

Hadron physics program at J-PARC WG on “Hadron physics with high-momentum beam line at J-PARC” Currently J-PARC has high-momentum proton (< 30 GeV/c) and pion (~ 15 GeV/c) beams.  Now considered as one of the highest priority projects at KEK/J-PARC from April Hadron properties in nuclear medium pQCD, partonic structure of nucleon and nuclei Charmed-hadron physics Exotic hadrons and nuclei N* physics (N*, Δ*,...) High-energy spin physics Short-range NN correlations Transition from hadron to quark degrees of freedom Exclusive processes (GPD, quark counting,...) Quark/hadron interactions in nuclear medium (parton-energy loss, color transparency) J/ψ production mechanisms and its interactions in nuclear medium Pion distribution amplitude, hadron-transition distribution amplitudes Intrinsic charm and strange … AND MORE TO COME!!

 πN  ππN: “Critical missing piece” in N* spectroscopy. Measurement of πN  ππN & KY in high-mass N* region (K. Hicks, K. Imai et al.) The idea originates from “US-Japan Joint Workshop on Meson Production Reactions at Jefferson Lab and J-PARC” Hawaii, Oct  There is NO practical data that can be used for partial wave analysis above W > 1.5 GeV.  Above W > 1.5 GeV, πN  ππN becomes the dominant process of the πN reactions.  Most of the N*s decay dominantly to the ππN channel. Hadron physics program at J-PARC The current N* mass spectrum might receive significant modifications and even new N* states might be discovered by the combined analysis including this new πN  ππN data !!

Hadron physics program at J-PARC Measurement of forward p(π,ρ)X, p(π, K*)X reactions (T. Ishikawa, T. Nakano et al.) p virtual π N*, Δ* (slow) Q2Q2 high-p π ρ (fast) p virtual K Y* (slow) high-p π K* (fast) Can be used for extracting N-N* axial transition form factors Can access to Λ(1405) region below KN threshold. Could be used for extracting strangeness changing axial form factors. Crucial for constructing reliable neutrino-nucleon/nucleus reaction models in resonance and DIS region.  Branch of KEK Theory Center [Y. Hayato, M. Hirai, H. Kamano, S. Kumano, S. Nakamura, K. Saito, M. Sakuda, T. Sato] ( Q2Q2

Summary ; ;  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 < 2.2 GeV # of channels Summary  After completing the combined analysis of πp, γp  πN, ηN, KΛ, KΣ reactions, immediately proceed to the analysis of CLAS p(e,eπ)N data and extract N-N* e.m. transition form factors up to Q 2 ~ 4 (GeV/c) 2.  Combined analysis of p(e,eπ)N and p(e,eππ)N is considered as a long term project in future. [Combined analysis of p(e,e’π)N, p(e,e’η)p, p(e,e’K)Y could be done quickly.] With the new 8-channels model, nucleon resonance parameters (mass spectrum, decay widths, etc.) are being investigated. (As presented in T. Sato’s talk)

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Phenomenological prescriptions of constructing conserved-current matrix elements As commonly done in practical calculations in nuclear and particle physics, currently we take a phenomenological prescription to construct conserved current matrix elements [T. Sato, T.-S. H. Lee, PRC (2001)]: : Full e.m. current matrix elements obtained by solving DCC equations : photon momentum : an arbitrary four vector A similar prescription is applied, e.g., in Kamalov and Yang, PRL83, 4494 (1999). There are also other prescriptions that enable practical calculations satisfying current conservation or WT identity:  Gross and Riska, PRC36, 1928 (1987)  Ohta, PRC40, 1335 (1989)  Haberzettl, Nakayama, and Krewald, PRC74, (2006).

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 !!

N* states and PDG *s ? ? ? ? ? Arndt, Briscoe, Strakovsky, Workman PRC (2006) Most of the N*s were extracted from Need comprehensive analysis of channels !! From PDG 2010

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

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

γp  πN reactions 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

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