Dynamical coupled-channels approach to light-flavor baryon spectroscopy

Resonance nature of light-flavor baryonsHiroyuki Kamano(RCNP, Osaka U.)RCNP/Kyushu U. Workshop, Kyushu U., Sep. 4-6, 2013Contents: Recent direction & topics of the N* spectroscopy.

New aspects of excited nucleons (N*) in terms of unstable resonant particles.1978-79: First systematic study of N* spectrum with constituent quark model [Isgur & Karl, PRD18(1978)4187, 19(1979)2653]

80s- : N* spectrum and form factors are widely studied with various static models

00s- : N* spectroscopy with multichannel unitary coupled-channels approachesBrief 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.uudConstituent quark modelDawn of theoretical studies of the N* spectroscopy with static hadron structure models !!In reality, the excited nucleons are unstable and can existonly as resonances (decaying states) in hadron reactions !!What is the role of reaction dynamics in interpretingthe N* spectrum, structures, and dynamical origins ??2Pion- and photon-induced meson production reactions off nucleonNN*...NNNKKN, (*)N-N* e.m. transition form factorsN* N, N, N, coupling constants Most useful reactions for studying N* resonances !N* mass, width

p reaction total cross sections in N* regionA 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 scatteringtheory including three-body N channel is necessary !!Dynamical coupled-channels model of meson production reactionsA. Matsuyama, T. Sato, T.-S. H. Lee, Phys. Rep. 439 (2007) 193H. Kamano, S.X. Nakamura, T.-S. H. Lee, T. Sato, arXiv:1305.4351 (to appear in PRC)

Partial wave (LSJ) amplitudes of a b reaction:

Reaction channels:

Transition Potentials:coupled-channels effectExchange potentialsbare N* statesFor details see Matsuyama, Sato, Lee, Phys. Rep. 439,193 (2007)

Z-diagramsANL-Osaka Dynamical Coupled-Channels (DCC) model for meson production reactions

Meson-Baryon Green functions

Stable channelsQuasi 2-body channels

NpDpDpppr, sr, sNN

p, r, s, w,..NN, D, ...s-channelu-channelt-channelcontactExchange potentialsZ-diagramsBare N* statesN*bareDpNppDDNp

r, sWould be related with hadron states of the static hadron models (quark models, DSE, etc.) excluding meson-baryon continuums.coremeson cloud

mesonbaryon

Physical N*s will be a mixture of the two pictures:ANL-Osaka Dynamical Coupled-Channels (DCC) analysis p N gp N p hN gp hp pp KL, KS gp K+L, KS2006 - 20096 channels (gN,pN,hN,pD,rN,sN)< 2 GeV< 1.6 GeV< 2 GeV2010 - 20128 channels (gN,pN,hN,pD,rN,sN,KL,KS)< 2.3 GeV< 2.1 GeV< 2.1 GeV< 2.1 GeV< 2.1 GeV< 2.1 GeV # of coupled channelsFully combined analysis of pN , gN N , hN , KL, KS reactions !! Kamano, Nakamura, Lee, SatoarXiv:1305.4351 (to appear in PRC)(more than 22,000 data of unpolarized & polarized observables to fit)N scattering

Differential cross section (W = 1.08-2.3 GeV)Kamano, Nakamura, Lee, Sato, arXiv:1305:4351to appear in PRCN scattering

Target polarization (W = 1.08-2.3 GeV)Kamano, Nakamura, Lee, Sato, arXiv:1305:4351to appear in PRCExtraction of N* parametersDefinitions of

N* masses (spectrum) Pole positions of the amplitudes

N* MB, gN coupling constants Residues1/2 at the poleN* pole position ( Im(E0) < 0 )N* b coupling constant

Analytic continuation to (lower-half) complex energy plane.

Suzuki, Sato, Lee PRC79(2009)025205Consistent with the resonance theory based on Gamow vectorsG. 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 polesConsequences of reaction dynamics (1/3):Complex nature of resonance parametersJulia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki PRC80 025207 (2009)Suzuki, Sato, Lee, PRC82 045206 (2010)Real partImaginary part

Nucleon - 1st D13(I=1/2, JP = 3/2-) e.m. transition form factorsExtracted from analyzing the p(e,ep)N data (~ 20,000) from CLASN*Ng(q2 = -Q2)qCoupling to meson-baryon continuum states makes N* form factors complex !!Fundamental nature of resonant particles (decaying states)9Consequences of reaction dynamics (2/3):Meson cloud effectRe[GM(Q2)] for g N D (1232) transitionFull dressedBareJulia-Diaz, Lee, Sato, Smith, PRC75 015205 (2007)N*Ng(q2 = -Q2)qN-N* e.m. transition form factor=BareMeson cloud+Most of the available static hadron models INDEED give GM(Q2) close to the Bare form factor !!core (bare)meson cloudConsequences of reaction dynamics (3/3): Dynamical origin of nucleon resonances(Complex) pole masses and dynamical origin of I=1/2, JP = 1/2+ resonancesSuzuki, Julia-Diaz, Kamano, Lee, Matsuyama, Sato, PRL104 065203 (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, PRL59 2818 (1987)Would be related with N*s in statichadron structuremodelsSummary 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 regionApplication of ANL-Osaka DCC approach to

DISregionQEregionRESregionCP phase & mass hierarchy studies with atmospheric exp. T2KDeveloping a unified neutrino reactionmodel describing overlapping regions between QE, RES, and DIS regions !!Collaboration@J-PARC 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)114019Nakamura, Kamano, Lee, Sato, PRD86(2012)114012Kamano, Nakamura, Lee, Sato, PRD86(2012)097503Thank you for your attention !!back up

Light-flavor baryon spectroscopy : Physics of broad & overlapping resonances (1232)

Width: a few hundred MeV. [ (width/mass) ~ 0.1 - 0.2 ]Resonances are highly overlappingin energy except D(1232).Width: ~10 keV to ~10 MeV [ (width/mass) ~ 10-3 - 10-4 ]Each resonance peak is clearly separated.Contain~ 20 N*s & *s16Approaches 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-HelsinkiFor the historical summary for the N* baryon spectroscopy, see:http://pdg.lbl.gov/2012/reviews/rpp2012-rev-n-delta-resonances.pdfNumerical cost: cheapCannot address dynamical contents (structure, production mechanism) of resonancesNumerical cost: expensiveSuitable for studying dynamical contents of resonancesOur approach !!Current status of reaction analysis groupsfor N* spectroscopyGroupApproach3-body unitarityNNNNNNNNNNNNNKNKNKNKNNNNN0NN0NANL-Osaka(ours)DCCBonn-Gatchinaon-shellK-matrixCarnegie Mellon-Berkelyon-shellK-matrixDubna-Mainz-TaipeiDCCGiessenon-shellK-matrixGorge Washington U. (SAID)on-shellK-matrixJuelichDCCKarlsruhe-Helsinkion-shellK-matrix(As of August 2013)Reaction data = Included = Included some part of the available data = Not includedStrategy for the N* spectroscopyStep 3Examine role of multichannel reaction dynamics in understanding the spectrum, internal structure and production mechanisms of the N* resonances.Step 1Determine model parameters by making 2-fit of the world data of meson production reactions.Step 2Extract resonance parameters (pole masses, form factors etc.) fromthe constructed model by performing the analytic continuationof 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:1305.4351]

Spectrum of N* resonancesKamano, Nakamura, Lee, Sato, arXiv:1305.4351N resonances (I=1/2)PDG: 4* & 3* states assigned by PDG2012AO : ANL-OsakaJ : Juelich (DCC, fit N reactions only) [EPJA49(2013)44, Model A]BG : Bonn-Gatchina (on-shell K-matrix) [EPJA48(2012)5]Re(MR)-2Im(MR)(width)MR : Resonance pole mass (complex) NOTE: Plot only N*s with Re(MR) < 2 GeV-2Im(MR) < 0.4 GeVJP(L2I 2J)

Spectrum of N* resonancesKamano, Nakamura, Lee, Sato, arXiv:1305.4351 resonances (I=3/2)Re(MR)-2Im(MR)(width)MR : Resonance pole mass (complex)PDG: 4* & 3* states assigned by PDG2012AO : ANL-OsakaJ : Juelich (DCC) [EPJA49(2013)44, Model A]BG : Bonn-Gatchina (K-matrix) [EPJA48(2012)5] NOTE: Plot only N*s with Re(MR) < 2 GeV-2Im(MR) < 0.4 GeVJP(L2I 2J)

N N P33 amp.ReIm

Residues of N scattering amplitudes at resonance polesKamano, Nakamura, Lee, Sato, arXiv:1305.4351

N resonances (I=1/2) resonances (I=3/2)JP (Re[MR])ResidueInterpreted as square of N*N coupling constant(complex value !!)

= resonances showing good agreement for pole massesHelicity amplitudes of p N* transition at resonance polesKamano, Nakamura, Lee, Sato, arXiv:1305.4351

Good agreement:1st P33

Qualitative agreement:1st S112nd S111st P111st D131st D151st S311st 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 targetOngoing projects & future plans withANL-Osaka DCC approach (1/4) - Extend our early analysis [PRC80(2009)025207] of p(e,e)N data from CLAS6 to higher Q2 region: 1.5 6.0 (GeV/c)2

- Further extend up to 10(GeV/c)2 after the JLab12-GeV upgrade (JLab CLAS12 experiment E12-09-003). (Hopefully) see how the transition between hadron and quark-gluon degrees of freedom occurs as Q2 increases.Further study of N* spectroscopy with the current ANL-Osaka DCC modelN*Ng(q2 = -Q2)qN-N* e.m. transitionform factorExpected 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 - 1st D13 e.m. transition form factorsJulia-Diaz, Kamano, Lee, Matsuyama, Sato, Suzuki PRC80(2009)025207Suzuki, Sato, Lee, PRC82(2010)045206 Real Imaginary

VERY PRELIMINARY n -p DCS

DISregionQEregionRESregionCP phase & mass hierarchy studies with atmospheric exp. T2KOngoing projects & future plans withANL-Osaka DCC approach (2/4)

Application to neutrino-induced reactions in GeV-energy regionPrecise knowledge of neutrino-nucleon/nucleusinteractions is necessary for reliable extractionsof neutrino parameters (CP phase, mass hierarchy, etc.)from the future neutrino-oscillation experiments.Need to tackle overlapping regions between QE, RES, and DIS regions !!Collaboration@J-PARC 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:1303.6032]

Kamano, Nakamura, Lee, Sato, PRD86(2012)097503NNKKNFirst application of 8ch DCC model to neutrino-nucleonreactions in N* region (forward angle limit)Full p N p N p p p p p K, K p K, K -p n p p2006-2009

6 channels (N,N,N,,N,N)< 2 GeV< 1.6 GeV< 2 GeV2010-2012(arXiv:1305.4351)8 channels (6ch + K, K)< 2.3 GeV< 2.1 GeV< 2.1 GeV< 2.1 GeV< 2.1 GeV< 2.1 GeV # of coupled channels2013-

9 channels (8ch + N)< 2.5 GeV< 2.3 GeV< 2.3 GeV< 2.3 GeV< 2.3 GeV< 2.3 GeV< 2.3 GeV< 2.3 GeVOngoing projects & future plans withANL-Osaka DCC approach (3/4)Extending DCC analysis

p p DCS-p n DCSVERY PRELIMINARYCombined analysis including N datais in progress !!After the 9-channel analysis, next task is to include N data !!N has the largest cross section in N and N reactions above W = 1.6 GeV. (Precise data of N N will be available from J-PARC [K. Hicks et al., J-PARC P45])Most N*s decay dominantly to N.

Kamano arXiv:1305.6678

NN F37 amp. +p ++n 8ch DCC(arXiv:1305.3451)Refit F37 amp keeping bare N* offBefore the combined analysis including N data,need further improvement/tune of the analysis code.Ambiguity over N* N decay processes can be eliminated by the N N data !!Ongoing projects & future plans withANL-Osaka DCC approach (4/4)Y* spectroscopy via DCC analysis of kaon-induced reactionsNN, , , *, *KMB*N*, *Y, KNdYYdK(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 TCSVERY PRELIMINARY reaction amplitude at resonance pole position MR is expressed as

The residue is then interpreted as the product of coupling constants of N*- and N*-:

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 asConventions for coupling constantsThis corresponds to taking the real part of NN* coupling constants always positive: Re(g_N*,N) > 0. With this convention, the relative signs of all coupling constants are uniquely fixed.

ReImImRePhenomenological prescriptions of constructing conserved-current matrix elementsAs 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, PRC60 055201 (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, 045202 (2006).Database used for the analysis

N N Partial wave amp. (SAID EIS)N N, K, K observablesN N, N, K, K observablesTotal 22,348 data points

Partial wave amplitudes of N scattering8ch DCC-analysis(Kamano, Nakamura, Lee, Sato, arXiv:1305.4351)Real partImaginary part

previous 6ch DCC-analysis (fitted to pN pN data only up to W = 2 GeV and up to F wave)[PRC76 065201 (2007)]SAID energy independent solution( http://gwdac.phys.gwu.edu/ )

Partial wave amplitudes of N scattering

Real partImaginary part8ch DCC-analysis(Kamano, Nakamura, Lee, Sato, arXiv:1305.4351)previous 6ch DCC-analysis (fitted to pN pN data only up to W = 2 GeV and up to F wave)[PRC76 065201 (2007)]SAID energy independent solution( http://gwdac.phys.gwu.edu/ ) p 0 p reaction

8ch DCC-analysis(Kamano, Nakamura, Lee, Sato, arXiv:1305.4351 to appear in PRC)previous 6ch DCC-analysis (fitted to gN pN data only up to W = 1.6 GeV)[PRC77 045205 (2008)]1.6 GeV1.9 GeVUnpolarized differential cross section

- p n reactionDCSNOTE:It is known that there is an inconsistency on the normalization ofthe -p n data between different experiments.

The data used in our analysis are carefully selected according to the discussion by Durand et al. PRC78 025204.

- p K0 reactionDCSP

+ p K+ + reactionDCSPNote: spin-rotation is modulo 2

- p K0 0 reactionDCSP

p + n reaction (1/3)

DCS

p + n reaction (2/3)PT

p + n reaction (3/3)hat EGH

p p reaction (1/2)DCS

p p reaction (2/2)T

p K+ reaction (1/2)DCSP

p K+ reaction (2/2)TOxOzCxCz

p K+ 0 reactionDCSPCxCz

p K0 + reactionDCSP