Resonance nature of light-flavor baryons Hiroyuki Kamano (RCNP, Osaka U.) RCNP/Kyushu U. Workshop, Kyushu U., Sep. 4-6, 2013 Contents:  Recent direction & topics of the N* spectroscopy.  New aspects of excited nucleons (N*) in terms of unstable resonant particles.

: First systematic study of N* spectrum with constituent quark model [Isgur & Karl, PRD18(1978)4187, 19(1979)2653] 80’s- : N* spectrum and form factors are widely studied with various static models 00’s- : N* spectroscopy with multichannel unitary coupled-channels approaches Brief history of N* spectroscopy (theory)  Bag models, Skyrme models, Dyson-Schwinger approaches, Holographic QCD,…  Excited hadrons are treated as stable particles  The resulting N* masses are real.  ANL-Osaka/EBAC-JLab, Bonn-Gatchina, Dubna-Mainz-Taipei, GWU, Juelich…  Determining N* properties by comprehensive analyses of meson production reactions off a nucleon target.  Examining role of reaction dynamics in understanding the nature of N* states as unstable resonances. u u d Constituent quark model Dawn of theoretical studies of the N* spectroscopy with static hadron structure models !! In reality, the excited nucleons are “unstable” and can exist only as resonances (decaying states) in hadron reactions !! What is the role of reaction dynamics in interpreting the N* spectrum, structures, and dynamical origins ??

Pion- and photon-induced meson production reactions off nucleon N N*... πN ηN ππN KΛ KΣ ωN … π, γ (*) N-N* e.m. transition form factors N*  πN, ηN, ππN, … coupling constants  Most useful reactions for studying N* resonances ! N* mass, width γp reaction total cross sections in N* region A huge amount of precise data is available from JLab, CBELSA, MAMI, SPring-8, … !! Comprehensive & simultaneous partial wave analysis of ALL the relevant meson production reactions is required !! Analysis based on multichannel scattering theory including three-body ππN channel is necessary !! “Dynamical coupled-channels model of meson production reactions” A. Matsuyama, T. Sato, T.-S. H. Lee, Phys. Rep. 439 (2007) 193 H. Kamano, S.X. Nakamura, T.-S. H. Lee, T. Sato, arXiv: (to appear in PRC)

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 ANL-Osaka 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   Would be related with hadron states of the static hadron models (quark models, DSE, etc.) excluding meson-baryon continuums. core meson cloud meson baryon Physical N*s will be a “mixture” of the two pictures:

ANL-Osaka 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  ) < 2.3 GeV < 2.1 GeV # of coupled channels Fully combined analysis of  N,  N   N,  N, K , K  reactions !! Kamano, Nakamura, Lee, Sato arXiv: (to appear in PRC) (more than 22,000 data of unpolarized & polarized observables to fit)

πN scattering Differential cross section (W = GeV) Kamano, Nakamura, Lee, Sato, arXiv:1305:4351 to appear in PRC

πN scattering Target polarization (W = GeV) Kamano, Nakamura, Lee, Sato, arXiv:1305:4351 to appear in PRC

Extraction of N* parameters Definitions of N* masses (spectrum)  Pole positions of the amplitudes N*  MB,  N coupling constants  Residues 1/2 at the pole N* pole position ( Im(E 0 ) < 0 ) N* pole position ( Im(E 0 ) < 0 ) N*  b coupling constant N*  b coupling constant Analytic continuation to (lower-half) complex energy plane. Suzuki, Sato, Lee PRC79(2009) 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/ (complex) energy eigenvalues = pole values transition matrix elements= (residue) 1/2 of the poles

Consequences of reaction dynamics (1/3): Complex nature of resonance parameters Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki PRC (2009) Suzuki, Sato, Lee, PRC (2010) Real partImaginary part Nucleon - 1 st D13(I=1/2, J P = 3/2 - ) e.m. transition form factors Extracted from analyzing the p(e,e’  )N data (~ 20,000) from CLAS N*N  (q 2 = -Q 2 ) q Coupling to meson-baryon continuum states makes N* form factors complex !! Fundamental nature of resonant particles (decaying states)

Consequences of reaction dynamics (2/3): Meson cloud effect Re[G M (Q 2 )] for  N   (1232) transition Full dressed Bare Julia-Diaz, Lee, Sato, Smith, PRC (2007) N*N  (q 2 = -Q 2 ) q N-N* e.m. transition form factor = Bare Meson cloud + Most of the available static hadron models INDEED give G M (Q 2 ) close to the “Bare” form factor !! core (bare) meson cloud

Consequences of reaction dynamics (3/3): Dynamical origin of nucleon resonances (Complex) pole masses and dynamical origin of I=1/2, J P = 1/2 + resonances Suzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL (2010) 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) Would be related with N*s in static hadron structure models

Summary and future works (1/2) Within the ANL-Osaka DCC approach, we examined the role of the reaction dynamics in understanding of various properties (spectrum, form factors, production mechanism,.. ) of N* states as unstable resonances The reaction dynamics is indispensable for having a correct answer for various properties of N* resonances both qualitatively and quantitatively. A critical issue in the N* spectroscopy is how the complex nature of N* resonances can be interpreted. (  Need to study with Gamow vectors?)

Summary and future works (2/2) Y* spectroscopy via the analysis of kaon-induced reactions Spectroscopy of 3-body light-flavor mesons Neutrino-nucleon/nucleus reactions in N* resonance region Application of ANL-Osaka DCC approach to DIS region QE region RES region CP phase & mass hierarchy studies with atmospheric exp. T2K Developing a unified neutrino reaction model describing overlapping regions between QE, RES, and DIS regions !! Branch of KEK Theory Center Y. Hayato (ICRR, U. of Tokyo), M. Hirai (Tokyo U. of Sci.) W. Horiuchi (Hokkaido U.), H. Kamano (RCNP, Osaka U.) S. Kumano (KEK), S. Nakamura (YITP, Kyoto U.), K. Saito (Tokyo U. of Sci.), M. Sakuda (Okayama U.) T. Sato (Osaka U.) Kamano, Nakamura, Lee, Sato, PRD84(2011) Nakamura, Kamano, Lee, Sato, PRD86(2012) Kamano, Nakamura, Lee, Sato, PRD86(2012)097503

Thank you for your attention !!

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Light-flavor baryon spectroscopy : Physics of broad & overlapping resonances Δ (1232) Width: a few hundred MeV. [ (width/mass) ~ ] Resonances are highly overlapping in energy except  (1232). Width: ~10 keV to ~10 MeV [ (width/mass) ~ ] Each resonance peak is clearly separated. Contain ~ 20 N*s & Δ*s Contain ~ 20 N*s & Δ*s

Approaches for reaction analysis for light-flavor baryon spectroscopy Multichannel unitary condition:  Ensures conservation of probabilities in multichannel reaction processes.  Ensures proper analytic structure of amplitudes (branch points etc) in complex energy plane. Heitler equation: K(E) should be hermitian.  K-matrix (on-shell) approach:  Dynamical approach: ANL-Osaka/EBAC-JLab, Dubna-Mainz-Taipei, Juelich Bonn-Gatchina, Carnegie Mellon-Berkely, George Washington U, Karlsruhe-Helsinki For the historical summary for the N* baryon spectroscopy, see: Numerical cost: cheap Cannot address dynamical contents (structure, production mechanism) of resonances Numerical cost: cheap Cannot address dynamical contents (structure, production mechanism) of resonances Numerical cost: expensive Suitable for studying dynamical contents of resonances Numerical cost: expensive Suitable for studying dynamical contents of resonances Our approach !!

Current status of reaction analysis groups for N* spectroscopy (As of August 2013) Reaction data ○ = Included △ = Included some part of the available data × = Not included

Strategy for the N* spectroscopy Step 3 Examine role of multichannel reaction dynamics in understanding the spectrum, internal structure and production mechanisms of the N* resonances. Step 1 Determine model parameters by making χ 2 -fit of the world data of meson production reactions. Step 2 Extract resonance parameters (pole masses, form factors etc.) from the constructed model by performing the analytic continuation of the amplitudes to the complex energy plane. Couplings, cutoffs, masses of bare N*s, etc.

N* resonances from analyses with the old 6ch and current 8ch models 6ch DCC analysis [PRL104(2010)042302] 8ch DCC analysis [arXiv: ]

Spectrum of N* resonances Kamano, Nakamura, Lee, Sato, arXiv: “N” resonances (I=1/2) PDG: 4* & 3* states assigned by PDG2012 AO : ANL-Osaka J : Juelich (DCC, fit πN reactions only) [EPJA49(2013)44, Model A] BG : Bonn-Gatchina (on-shell K-matrix) [EPJA48(2012)5] Re(M R ) -2Im(M R ) (“width”) M R : Resonance pole mass (complex) NOTE: Plot only N*s with Re(M R ) < 2 GeV -2Im(M R ) < 0.4 GeV J P (L 2I 2J )

Spectrum of N* resonances Kamano, Nakamura, Lee, Sato, arXiv: “Δ” resonances (I=3/2) Re(M R ) -2Im(M R ) (“width”) M R : Resonance pole mass (complex) PDG: 4* & 3* states assigned by PDG2012 AO : ANL-Osaka J : Juelich (DCC) [EPJA49(2013)44, Model A] BG : Bonn-Gatchina (K-matrix) [EPJA48(2012)5] NOTE: Plot only N*s with Re(M R ) < 2 GeV -2Im(M R ) < 0.4 GeV J P (L 2I 2J ) πN  πN P33 amp. Re Im

Residues of πN scattering amplitudes at resonance poles Kamano, Nakamura, Lee, Sato, arXiv: “N” resonances (I=1/2) “Δ” resonances (I=3/2) J P (Re[M R ]) Residue Interpreted as square of “N*Nπ coupling constant” (complex value !!) = resonances showing good agreement for pole masses

Helicity amplitudes of γp  N* transition at resonance poles Kamano, Nakamura, Lee, Sato, arXiv: Good agreement: 1 st P33 Qualitative agreement: 1 st S11 2 nd S11 1 st P11 1 st D13 1 st D15 1 st S31 1 st F37 (10 -3 GeV -1/2 ) Coupling consts. & helicity amps. seem much more sensitive to the analysis than the pole masses !!

 Extraction of N-N* e.m. transition form factors via the analysis of electroproduction reactions  Study of photoproduction reactions off a “neutron” target Ongoing projects & future plans with ANL-Osaka DCC approach (1/4) - Extend our early analysis [PRC80(2009)025207] of p(e,e’π)N data from CLAS6 to higher Q 2 region: 1.5  6.0 (GeV/c) 2 - Further extend up to 10(GeV/c) 2 after the JLab12-GeV upgrade (JLab CLAS12 experiment E ). (Hopefully) see how the transition between hadron and quark-gluon degrees of freedom occurs as Q 2 increases. Further study of N* spectroscopy with the current ANL-Osaka DCC model N*N  (q 2 = -Q 2 ) q N-N* e.m. transition form factor Expected to be a crucial source of information on internal structure of N*s !! -For I=1/2 N* states, BOTH proton-N* and neutron-N* e.m. transition form factors are needed for decomposing to isoscalar and isovector form factors. -Explore a possible existence of N* states that strongly couple to “neutron”-target photoproductions.  Necessary for neutrino-induced reactions !! e.g.) Nucleon - 1 st D13 e.m. transition form factors Julia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki PRC80(2009) Suzuki, Sato, Lee, PRC82(2010) ● Real ■ Imaginary VERY PRELIMINARY γ “n”  π - p DCS

DIS region QE region RES region CP phase & mass hierarchy studies with atmospheric exp. T2K Ongoing projects & future plans with ANL-Osaka DCC approach (2/4) Application to neutrino-induced reactions in GeV-energy region Precise knowledge of neutrino-nucleon/nucleus interactions is necessary for reliable extractions of neutrino parameters (CP phase, mass hierarchy, etc.) from the future neutrino-oscillation experiments. Need to tackle overlapping regions between QE, RES, and DIS regions !! Branch of KEK Theory Center Y. Hayato (ICRR, U. of Tokyo), M. Hirai (Tokyo U. of Sci.) H. Kamano (RCNP, Osaka U.), S. Kumano (KEK) S. Nakamura (YITP, Kyoto U.), K. Saito (Tokyo U. of Sci.) M. Sakuda (Okayama U.), T. Sato (Osaka U.) [  arXiv: ] Kamano, Nakamura, Lee, Sato, PRD86(2012) πN ππN KΛ KΣ ηN First application of 8ch DCC model to neutrino-nucleon reactions in N* region (forward angle limit) Full

πp  πN γp  πN πp  ηp γp  ηp πp  KΛ, KΣ γp  KΛ, KΣ π - p  ωn γp  ωp channels (γN,πN,ηN,πΔ,ρN,σN) < 2 GeV < 1.6 GeV < 2 GeV ― ― ― ― ― (arXiv: ) 8 channels (6ch + KΛ, KΣ) < 2.3 GeV < 2.1 GeV ― ― # of coupled channels channels (8ch + ωN) < 2.5 GeV < 2.3 GeV Ongoing projects & future plans with ANL-Osaka DCC approach (3/4) Extending DCC analysis Extending DCC analysis γp  ωp DCS π - p  ωn DCS VERY PRELIMINARY Combined analysis including ωN data is in progress !! After the 9-channel analysis, next task is to include ππN data !!  ππN has the largest cross section in πN and γN reactions above W = 1.6 GeV. (Precise data of πN  ππN will be available from J-PARC [K. Hicks et al., J-PARC P45])  Most N*s decay dominantly to ππN. Kamano arXiv: πN  πN F37 amp. π+p  π+π+n 8ch DCC (arXiv: ) Refit F37 amp keeping bare N*  πΔ off Before the combined analysis including ππN data, need further improvement/tune of the analysis code. Ambiguity over N*  ππN decay processes can be eliminated by the πN  ππN data !! Ambiguity over N*  ππN decay processes can be eliminated by the πN  ππN data !!

Ongoing projects & future plans with ANL-Osaka DCC approach (4/4) Y* spectroscopy via DCC analysis of kaon-induced reactions N N, Σ, Λ, … Λ*, Σ* K M B Ξ* N Λ*, Σ* Y π, K N d Y π Y d K (Noumi et al., J-PARC E31)  Nucleon target  Deuteron target + … Simplest reaction processes to study Y* resonances. Extensive data would become available from J-PARC after the extension of Hadron Hall. K - p  K - p TCS VERY PRELIMINARY

α  β reaction amplitude at resonance pole position M R is expressed as The residue is then interpreted as the product of “coupling constants” of N*-β and N*-α: If one tries to get the coupling constants from the residues, the constants can be determined up to a sign. We fix the sign ambiguity by choosing the phase of the pi N scattering residue as Conventions for coupling constants This corresponds to taking the real part of πNN* coupling constants always positive: Re(g_N*,πN) > 0. With this convention, the relative signs of all coupling constants are uniquely fixed. Re Im Re

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).

Database used for the analysis πN  πN Partial wave amp. (SAID EIS) πN  ηN, KΛ, KΣ observables γN  πN, ηN, KΛ, KΣ observables Total 22,348 data points

Partial wave amplitudes of πN scattering 8ch DCC-analysis (Kamano, Nakamura, Lee, Sato, arXiv: ) Real part Imaginary part previous 6ch DCC-analysis (fitted to  N   N data only up to W = 2 GeV and up to F wave) [PRC (2007)] SAID energy independent solution ( )

Partial wave amplitudes of πN scattering Real part Imaginary part 8ch DCC-analysis (Kamano, Nakamura, Lee, Sato, arXiv: ) previous 6ch DCC-analysis (fitted to  N   N data only up to W = 2 GeV and up to F wave) [PRC (2007)] SAID energy independent solution ( )

γ p  π 0 p reaction 8ch DCC-analysis (Kamano, Nakamura, Lee, Sato, arXiv: to appear in PRC) previous 6ch DCC-analysis (fitted to  N   N data only up to W = 1.6 GeV) [PRC (2008)] 1.6 GeV1.9 GeV Unpolarized differential cross section

π- p  ηn reaction DCS NOTE: It is known that there is an inconsistency on the normalization of the π-p  ηn data between different experiments. The data used in our analysis are carefully selected according to the discussion by Durand et al. PRC

π- p  K 0 Λ reaction DCS P β

π + p  K + Σ + reaction DCS P β Note: spin-rotation β is modulo 2π

π- p  K 0 Σ 0 reaction DCS P

γ p  π + n reaction (1/3) DCSΣ

γ p  π + n reaction (2/3) PT

γ p  π + n reaction (3/3) hat EG H

γ p  η p reaction (1/2) DCS

γ p  η p reaction (2/2) T Σ

γ p  K + Λ reaction (1/2) DCS Σ P

γ p  K + Λ reaction (2/2) T Ox’ Oz’ Cx’ Cz’

γ p  K + Σ 0 reaction DCS Σ P Cx’ Cz’

γ p  K 0 Σ + reaction DCS PΣ