The Constituent-Quark Model History

Low-energy QCD – RCQM

Spectroscopy Nowadays Multiplets

Structure Nucleon E.m. Baryon E.m. Willibald Plessas Axial FFs Gravitational FF Strong πNN, πN∆ FFs Theoretical Physics / Institute of Physics CC Model University of Graz, Austria

Summary 4th International Conference on New Frontiers in Physics OAC Kolymbari, August 23rd, 2015 Pre-Quark History

Hadrons known around 1960:

History

Low-energy QCD

RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model

Summary

Yu. Ne’eman and M. Gell-Mann: ’Eightfold Way’, i.e. SU(3) symmetry The Eightfold Way and SU(3)F

Around 1964 one found SU(3) as a (preliminary) order system for mesons and baryons History (independently by M. Gell-Mann and Y. Ne’eman and G. Zweig): Low-energy QCD It implied multiplets of baryon ground states with ﬂavors u, d, s: RCQM octet decuplet Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model

Summary

and in addition: singlet Λ0 Valence-Quark Picture of Hadrons

M. Gell-Mann in 1964∗): Mesons and baryons can be constructed from quarks: History Low-energy Mesons QQ¯ Baryons QQQ QCD { } { } RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model

Summary

Mesons and baryons are formed as colorless objects of quarks conﬁned inside the hadrons. ∗) M. Gell-Mann: Phys. Lett. 8, 2014 (1964) M. Gell-Mann: Quarks – G. Zweig: Aces

History

Low-energy QCD

RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model

Summary Success of SU(3) Symmetry of u, d, s

− I The Ω was predicted (independently) by Ne’eman and Gell-Mann History in 1962. Low-energy I It was discovered at Brookhaven Natl. Lab. by Nicholas Samios et QCD al. in 1964. RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model

Summary

The Ω− earned M. Gell-Mann the Nobel Prize in 1969 "for his contributions and discoveries concerning the classiﬁcation of elementary particles and their interactions". Quark Interactions - Quantum Chromodynamics 1972/1973: Invention of quantum chromodynamics (QCD) M. Gell-Mann and H. Fritzsch: Proceedings of the Int. Conf. on High-Energy History Physics (Rochester Conf.), Chicago 1972 Low-energy H. Fritzsch, M.Gell-Mann, and H. Leutwyler: Phys. Lett. B47, 365 (1973) QCD see also H. Fritzsch in: http://cerncourier.com/cws/article/cern/50796 RCQM

Spectroscopy Multiplets Present methods for non-perturbative hadrons in QCD: Structure I QCD on a lattice (works but faces computational Nucleon E.m. Baryon E.m. limitations) Axial FFs Gravitational FF Strong πNN, πN∆ I Chiral perturbation theory (works at low energies, as a FFs

CC Model systematic expansion but is limited to a few terms)

Summary I Effective ﬁeld theories or functional methods (depend on assumptions and regularizations)

I Effective models, e.g. constituent-quark models (depend on assumptions and input parameters) Outline

Origin of the Quark Picture of Hadrons & QCD X

History Low-Energy QCD / Relevant Degrees of Freedom Low-energy QCD Relativistic Constituent-Quark Model (RCQM) RCQM Baryon Spectroscopy Spectroscopy Multiplets Baryon Classiﬁcation into Flavor Mulitplets Structure Nucleon E.m. Baryon Structure Baryon E.m. Axial FFs Nucleon e.m. form factors - Flavor content Gravitational FF Strong πNN, πN∆ Baryon electromagnetic form factors FFs

CC Model Nucleon and baryon axial form factors / charges

Summary Nucleon gravitational form factors Microscopic πNN and πN∆ vertex form factors Coupled-Channels Theory Summary, Conclusions, and Outlook Low-Energy QCD / Effective D.o.F.

Low-energy QCD of three ﬂavors u, d, s is characterized by:

History spontaneous breaking of chiral symmetry (SBχS): Low-energy • QCD SU(3)L SU(3)R SU(3)V RCQM × → Spectroscopy appearance of (N2 1) = 8 Goldstone bosons φ~ Multiplets → f − Structure generation of quasiparticles with dynamical mass, Nucleon E.m. → Baryon E.m. i.e. constituent quarks ψ Axial FFs Gravitational FF Strong πNN, πN∆ thus (effective) interaction Lagrangian: FFs • CC Model F int igψγ¯ 5~λ φψ~ Summary L ∼ ·

A. Manohar and H. Georgi: Nucl. Phys. B 234 (1984) 189 E.V. Shuryak: Phys. Rep. 115, 151 (1984) L.Ya. Glozman and D.O. Riska: Phys. Rep. 268, 263 (1996) see also: S. Weinberg: Phys. Rev. Lett. 105, 261601 (2010) Baryons

Baryons are considered as colorless bound states of three constituent quarks. History Low-energy Here the proton: QCD

RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs I ’Constituent’ quarks are quasiparticles with dynamical CC Model mass, NOT the original QCD d.o.f. (i.e. ’current’ Summary quarks).

I ’Constituent’ quarks are conﬁned and interact via hyperﬁne interactions associated with SBχS, i.e. Goldstone-boson exchange. Relativistically Invariant Theory

Relativistic quantum mechanics (RQM) History Low-energy i.e. quantum theory respecting Poincaré invariance QCD RCQM (theory on a Hilbert space corresponding to a ﬁnite H Spectroscopy number of particles, not a ﬁeld theory) Multiplets

Structure Nucleon E.m. Baryon E.m. Invariant mass operator Axial FFs Gravitational FF ˆ ˆ ˆ Strong πNN, πN∆ M = Mfree + Mint FFs

CC Model

Summary Eigenvalue equations ˆ ˆ 2 ˆ µ ˆ M P, J, Σ = M P, J, Σ , M = P Pµ | i | i Pˆ µ P, J, Σ = Pµ P, J, Σ , Pˆ µ = Mˆ Vˆ µ | i | i Relativistic Constituent-Quark Model (RCQM)

Interacting mass operator

History ˆ ˆ ˆ M = Mfree + Mint Low-energy q QCD ˆ ˆ 2 ~ˆ 2 Mfree = H P RCQM free − free 3 3 Spectroscopy X X Multiplets ˆ rest frame ˆ ˆ conf ˆ hf Mint = Vij = [Vij + Vij ] Structure Nucleon E.m. i

Phenomenologically, baryons with 5 ﬂavors: u, d, s, c, b

History 3 X q Low-energy H = m2 + ~k 2 QCD ⇒ free i i RCQM i=1 Spectroscopy conf Multiplets V (~rij ) = B + C rij Structure Nucleon E.m. " 24 # Baryon E.m. hf X f f 0 0 Axial FFs V (~rij ) = V24(~rij ) λi λj + V0(~rij )λi λj ~σi ~σj Gravitational FF · Strong πNN, πN∆ f =1 FFs

CC Model Summary I i.e., for Nf = 5, we have the exchange of a 24-plet plus a singlet of Goldstone bosons.

L.Ya. Glozman and D.O. Riska: Nucl. Phys. A 603, 326 (1996) J.P. Day, K.-S. Choi, and W. Plessas: arXiv:1205.6918 J.P. Day, K.-S. Choi, and W. Plessas: Few-Body Syst. 54, 329 (2013) Universal GBE RCQM Parametrization

conf V (~rij ) = B + C rij History

Low-energy 2 g −µβ rij QCD β 1 2 e Vβ(~rij ) = µβ 4πδ(~rij ) RCQM 4π 12mi mj rij − Spectroscopy 2 −µβ rij −Λβ rij Multiplets gβ 1 e e = µ2 Λ2 Structure 4π 12m m β r β r Nucleon E.m. i j ij − ij Baryon E.m. Axial FFs Gravitational FF −2 Strong πNN, πN∆ B = − 402 MeV, C = 2.33 fm FFs

CC Model 2 g24 β = 24 : 4π = 0.7, µ24 = µπ = 139 MeV, Λ24 = 700.5 MeV Summary 2 g0 β = 0 : = 1.5, µ0 = µη0 = 958 MeV, Λ0 = 1484 MeV g24

mu = md = 340 MeV, ms = 480 MeV,

mc = 1675 MeV, mb = 5055 MeV Remarks/Caveats on the Setting of the RCQM

I Relativistic (i.e. Poincaré-invariant) framework History I Hamiltonian theory with a ﬁnite number of d.o.f. Low-energy QCD I based on relativistically invariant mass operator

RCQM I solvable with advanced few-body methods

Spectroscopy (differential and / or integral equations) Multiplets

Structure I Observes eminent low-energy QCD dynamics: Nucleon E.m. Baryon E.m. I conﬁnement Axial FFs Gravitational FF I spontaneous chiral-symmetry breaking (SBχS) Strong πNN, πN∆ FFs

CC Model I The Relativistic Constituent Quark Model (RCQM) Summary I is a model of a given dynamics, here QCD I thus, is not itself a (fundamental) dynamical theory I has a limited range of validity ( non-perturbative regime of QCD) ∼ History

Low-energy QCD RCQM Excitation Spectra Spectroscopy Multiplets

Structure Nucleon E.m. of Baryons with All Flavors Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs u, d, s, c, b CC Model

Summary Light Baryon Spectra

M [MeV] History 1800 ...... Low-energy ...... 1700 ...... QCD ...... 1600 ...... RCQM ...... 1500 Spectroscopy ...... Multiplets ...... 1400 Structure Nucleon E.m. 1300 Baryon E.m. 1200 Axial FFs Gravitational FF 1100 Strong πNN, πN∆ FFs 1000 CC Model 900 + + + + Summary 1 1 − 3 3 − 5 5 − 1 − 3 3 − 2 2 2 2 2 2 2 2 2 N ∆

red Universal GBE RCQM

green PDG 2013 (experiment) Strange Baryon Spectra

...... History ...... M ...... M ...... [MeV] ...... [MeV] ...... Low-energy 1800 ...... 1800 ...... QCD ...... 1700 ...... 1700 ...... RCQM ...... 1600 ...... 1600 Spectroscopy 1500 1500 Multiplets 1400 ...... 1400

...... Structure 1300 1300

Nucleon E.m. 1200 ...... 1200 Baryon E.m. 1100 1100 Axial FFs Gravitational FF 1000 1000 Strong πNN, πN∆ 900 900 FFs 1 + 1 3 + 3 5 + 5 1 + 1 3 + 3 5 + 5 + + + − − − − − − 1 1 − 3 3 − 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 CC Model Λ Σ Ξ Ω Summary red Universal GBE RCQM

green PDG 2013 (experiment) Charm Baryon Spectra

M M [MeV] [MeV] 3100 4400 History 3000 4300 ...... 2900 4200 Low-energy ...... 4100 QCD 2800 ...... 2700 4000 3900 RCQM 2600

3800 ...... 2500 ...... Spectroscopy ...... 3700 ...... Multiplets 2400 ...... 3600 2300 Structure 3500 2200 1 + 1 3 + 3 5 + 1 + 1 3 + 3 1 + 3 + + + + + Nucleon E.m. − − ? − − ? 1 1 − 3 3 − 1 1 − 3 3 − 2 2 2 2 2 ? 2 2 2 2 ? 2 2 2 2 2 2 2 2 2 2 Baryon E.m. Λc Σc Ωc Ξcc Ωcc Axial FFs Gravitational FF Strong πNN, πN∆ Left panels – single charm: FFs red Universal GBE RCQM prediction CC Model green PDG 2013 (experiment) Summary

Right panel – double charm: green M. Mattson et al.: Phys. Rev. Lett. 89 (2002) 112001 (SELEX experiment)

cyan S. Migura, D. Merten, B. Metsch, and H.-R. Petry: Eur. Phys. J. A 28 (2006) 41 (Bonn RCQM)

magenta L. Liu et al.: Phys. Rev. D 81 (2010) 094505 (Lattice QCD)

% Bottom Baryon Spectra

History

Low-energy QCD

RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model Left panel – single bottom:

Summary red Universal GBE RCQM prediction green PDG 2013 (experiment)

Right panel – double bottom: green W. Roberts and M. Pervin: Int. J. Mod. Phys. A 23 (2008) 2817 (nonrel. one-gluon-exchange CQM)

orange D. Ebert, R.N. Faustov, V.O. Galkin, and A.P. Martynenko: Phys. Rev. D 66 (2002) 014008 (RCQM) Triple-Heavy Baryon Spectra

History

Low-energy QCD

RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model red Universal GBE RCQM Summary green W. Roberts and M. Pervin: Int. J. Mod. Phys. A 23 (2008) 2817 (nonrelativistic one-gluon-exchange CQM)

blue S. Migura, D. Merten, B. Metsch, and H.-R. Petry: Eur. Phys. J. A 28 (2006) 41 (Bonn RCQM)

cyan A.P. Martynenko: Phys. Lett. B 663 (2008) 317 (RCQM)

magenta S. Meinel: Phys. Rev. D 82 (2010) 114502 (lattice QCD) Rest-Frame Baryon States

Mass operator eigenstates

History Mˆ P, J, Σ, T , M = M P, J, Σ, T , M | T i | T i Low-energy QCD represented in conﬁguration space RCQM D E Spectroscopy ξ,~ ~η P, J, Σ, T , MT = ΨPJΣTM (ξ,~ ~η) Multiplets T Structure Nucleon E.m. with ~ and the usual Jacobi coordinates. Baryon E.m. ξ ~η Axial FFs Gravitational FF Strong πNN, πN∆ FFs Picture the baryon wave functions through CC Model spatial probability density distributions Summary Z 2 2 ρ(ξ, η) = ξ η dΩξdΩη Ψ? ( Ω Ω )Ψ ( Ω Ω ) PJΣTMT ξ, ξ, η, η PJΣTMT ξ, ξ, η, η Pictures of Baryons (rest frame)

N N GBE CQM 2

1.5

History Η 1 Low-energy QCD 0.5 RCQM Η Spectroscopy 0 0 0.5 1 1.5 2 Multiplets Ξ Ξ units are [fm] Structure Nucleon E.m. Baryon E.m. N 1440 GBE CQM NH1440L Axial FFs H L 2 Gravitational FF Strong πNN, πN∆ FFs 1.5

CC Model Η 1 Summary 0.5 Η 0 0 0.5 1 1.5 2 Ξ Ξ units are [fm]

T. Melde, W. Plessas, and B. Sengl: Phys. Rev. D 77 (2008) 114002 Spatial Probability Density Distributions

1 + ρ(ξ, η) for the 2 octet baryon ground states N(939), Λ(1116), Σ(1193), Ξ(1318):

N 2 2 2 2 History 1.5 1.5 1.5 1.5 Low-energy QCD Η 1 Η 1 Η 1 Η 1

RCQM 0.5 0.5 0.5 0.5

Spectroscopy 0 0 0 0 Multiplets 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Ξ Ξ Ξ Ξ Structure Nucleon E.m. Baryon E.m. 1 + Axial FFs ρ(ξ, η) for the 2 octet baryon states N(1440), Λ(1600), Σ(1660), Ξ(1690): Gravitational FF Strong πNN, πN∆ NH1440L H1600L H1660L H1690L FFs 2 2 2 2

CC Model 1.5 1.5 1.5 1.5

Summary Η 1 Η 1 Η 1 Η 1

0.5 0.5 0.5 0.5

0 0 0 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Ξ Ξ Ξ Ξ

T. Melde, W. Plessas, and B. Sengl: Phys. Rev. D 77 (2008) 114002 Spatial Probability Density Distributions

3 + ρ(ξ, η) for the 2 decuplet baryon states ∆(1232), Σ(1385), Ξ(1530), Ω(1672):

H1232L H1385L H1530L H1672L 2 2 2 2 History 1.5 1.5 1.5 1.5 Low-energy QCD Η 1 Η 1 Η 1 Η 1

RCQM 0.5 0.5 0.5 0.5

Spectroscopy 0 0 0 0 Multiplets 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Ξ Ξ Ξ Ξ Structure Nucleon E.m. Baryon E.m. 3 + Axial FFs ρ(ξ, η) for the 2 decuplet baryon states ∆(1600), Σ(1690): Gravitational FF Strong πNN, πN∆ H1600L H1690L FFs 2 2

CC Model 1.5 1.5

Summary Η 1 Η 1

0.5 0.5

0 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Ξ Ξ

T. Melde, W. Plessas, and B. Sengl: Phys. Rev. D 77 (2008) 114002 N and ∆ Rest-Frame Wave Functions

Rest-frame spatial distribution of constituent quarks in terms of 3-body Jacobi coordinates ξ~ and ~η : History Z Low-energy 2 2 QCD ρ(ξ, η) = ξ η dΩξdΩη

RCQM Ψ? ( Ω Ω )Ψ ( Ω Ω ) Spectroscopy PJΣTMT ξ, ξ, η, η PJΣTMT ξ, ξ, η, η Multiplets

Structure N H1232L 2 2 Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF 1.5 1.5 Strong πNN, πN∆ FFs Η 1 Η 1 CC Model

Summary 0.5 0.5

0 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Ξ Ξ Units on abscissa and ordinates are [fm] Root-Mean-Square Radii

The root-mean-square radius (in the rest frame): 1 q Z 2 2 3 D 2 E History = = = Σ ˆ = Σ rrms ri d ri P 0, J, r i P 0, J, Low-energy QCD

RCQM Is NOT an observable! Is NOT relativistically invariant! Spectroscopy Idea about the spatial distribution of constituent quarks. Multiplets → N H1232L Structure 2 2 Nucleon E.m. Baryon E.m. 1.5 1.5 Axial FFs Gravitational FF Η 1 Η 1 Strong πNN, πN∆ FFs 0.5 0.5 CC Model 0 0 Summary 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Ξ Ξ N ∆ rrms= 0.304 fm rrms= 0.390 fm

p ∆++ ∆+ ∆− Exp.: rE ∼ 0.88 fm rE = rE = rE = 0.656 fm n 2 2 ∆0 (rE ) ∼ – 0.12 fm rE =0 fm New Quark-Model Classiﬁcation

multiplet (LS)JP History 1 1 + 100 100 100 100 octet (0 2 ) 2 N(939) Λ(1116) Σ(1193) Ξ(1318) Low-energy 1 1 + 100 96 100 100 octet (0 2 ) 2 N(1440) Λ(1600) Σ(1660) Ξ(1690) QCD 1 1 + 100 99 octet (0 2 ) 2 N(1710) Σ(1880) RCQM 1 1 − 100 72 94 octet (1 2 ) 2 N(1535) Λ(1670) Σ(1560) 3 1 − 100 100 100 Spectroscopy octet (1 2 ) 2 N(1650) Λ(1800) Σ(1620) 1 3 − 100 72 94 97 Multiplets octet (1 2 ) 2 N(1520) Λ(1690) Σ(1670) Ξ(1820) − ( 3 ) 3 ( )100 Σ( )100 Structure octet 1 2 2 N 1700 1940 3 5 − 100 100 100 100 Nucleon E.m. octet (1 2 ) 2 N(1675) Λ(1830) Σ(1775) Ξ(1950) Baryon E.m. 3 3 + 100 100 100 100 Axial FFs decuplet (0 2 ) 2 ∆(1232) Σ(1385) Ξ(1530) Ω(1672) 3 3 + 100 99 Gravitational FF decuplet (0 2 ) 2 ∆(1600) Σ(1690) − Strong πNN, πN∆ decuplet (1 1 ) 1 ∆(1620)100 Σ(1750)94 FFs 2 2 − decuplet (1 1 ) 3 ∆(1700)100 CC Model 2 2 − singlet (1 1 ) 1 Λ(1405)71 Summary 2 2 1 3 − 71 singlet (1 2 ) 2 Λ(1520) 1 1 + 92 singlet (0 2 ) 2 Λ(1810)

T. Melde, W. Plessas, and B. Sengl: Phys. Rev. D 77, 114002 (2008)

See also the PDG: Phys. Rev. D 86, 010001 (2012) SU(3) Flavor Multiplets – New

Classiﬁcation of baryon resonances by the PDG since 2010 (results from the GBE relativistic CQM marked by asterisks) History

Low-energy QCD

RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model

Summary

PDG: J. Phys. G 37, 075021 (2010); Phys. Rev. D 86, 010001 (2012); Chin. Phys. C 38, 090001 (2014) History

Low-energy QCD

RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon Reactions Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model

Summary Applications of the RCQM

History RCQM studies of various baryon reactions: Low-energy QCD I Nucleon electromagnetic form factors RCQM

Spectroscopy (including analysis of ﬂavor content of the nucleons) Multiplets Structure I Nucleon axial form factors Nucleon E.m. Baryon E.m. Axial FFs I ∆ and hyperon electroweak structures (FFs) Gravitational FF Strong πNN, πN∆ FFs I Nucleon gravitational form factors CC Model Summary I NNπ and N∆π strong vertex form factors

I Strong resonance decays Various Baryon Reactions

Matrix elements of a transition operator Oˆ between baryon eigenstates P, J, Σ, T , T3, Y History | i Low-energy P0, J0, Σ0, T 0, T 0 , Y 0 Oˆ P, J, Σ, T , T , Y QCD h 3 | | 3 i RCQM ˆ ˆµ Spectroscopy O ... Jem electromagnetic FF’s Multiplets → ... Aˆµ axial FF’s Structure axial → Nucleon E.m. ˆ Baryon E.m. ... S scalar FF Axial FFs → Gravitational FF ... Θˆ µν gravitational/tensor FF’s Strong πNN, πN∆ FFs → ... Dˆ µ hadronic decays CC Model λ → Summary To be calculated from microscopic three-quark ME’s

0 0 0 0 0 0 ˆ p , p , p ; σ , σ , σ ; fi0 , fi0 , fi0 O p1, p2, p3; σ1, σ2, σ3; fi , fi , fi h 1 2 3 1 2 3 1 2 3 | | 1 2 3 i boosted 3-body⇑⇑ states boosted 3-body states History

Low-energy QCD RCQM Electroweak Structure Spectroscopy Multiplets

Structure Nucleon E.m. of Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs the Nucleons / Baryons CC Model

Summary Electromagnetic Nucleon Observables

History Covariant predictions for: Low-energy QCD

RCQM

Spectroscopy I Electromagnetic nucleon form factors Multiplets p ( 2) p ( 2) n ( 2) n ( 2) Structure GE Q , GM Q ; GE Q , GM Q Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF I Electric radii and magnetic moments Strong πNN, πN∆ FFs r p, p; r n, n CC Model E µ E µ

Summary

Comparison to experiment → Electron Scattering and E.m. Form Factors

Elastic electron scattering:

History

Low-energy e− QCD e−

RCQM

Spectroscopy γ qµ Multiplets

Structure Nucleon E.m. B′ B Baryon E.m. µ µ Axial FFs P ′ P Gravitational FF Strong πNN, πN∆ FFs CC Model Invariant form factors: Summary ν 2 0 0 ˆν F 0 (Q ) = P , J, Σ , T , M J P, J, Σ, T , M Σ Σ h T | em| T i

with Q2 = q2 ; qµ = Pµ P0µ − − Elastic Sachs Form Factors

1 Spin- 2 baryons: History B 2 1 ν=0 2 Low-energy GE (Q ) = F 1 1 (Q ) QCD 2M 2 2 RCQM 1 B ( 2) = ν=1 ( 2) GM Q F 1 − 1 Q Spectroscopy Q 2 2 Multiplets

Structure 3 Nucleon E.m. Spin- baryons: Baryon E.m. 2 Axial FFs Gravitational FF B 2 1 ν=0 2 ν=0 2 Strong πNN, πN∆ GE (Q ) = [F 1 1 (Q ) + F 3 3 (Q )] FFs 4M 2 2 2 2 CC Model 3 GB (Q2) = [F ν=1 (Q2) + √3F ν=1(Q2)] Summary M 1 − 1 3 1 5Q 2 2 2 2

Electric/charge radius rE : 2 d 2 r = 6 G (Q ) 2 E − d Q2 E Q =0 Transition Matrix Elements in Point Form

Incoming baryon state: |V , M, J, Σi ˆ= |P, J, Σi Outgoing baryon state: |V 0, M0, J0, Σ0i ˆ= |P0, J0, Σ0i ˆ ˆµ History Transition operator: O = Jem Low-energy 0 0 0 0 ˆµ QCD V , M , J , Σ Jem |V , M, J, Σi = Z RCQM 2 X X 3~ 3~ 3~ 0 3~ 0 = 0 d k2d k3d k2d k3 Spectroscopy MM 0 0 σi σ µi µ Multiplets i i s Structure P 03 ω ? 1 Nucleon E.m. i i Y 2 0 0 ? ~ 0 ~ 0 ~ 0 0 0 0 × D 0 0 RW k ; B V Ψ 0 0 0 k , k , k ; µ , µ , µ Baryon E.m. Q 0 σ µ i M J Σ 1 2 3 1 2 3 2ωi i i Axial FFs i σ0 i Gravitational FF Strong πNN, πN∆ 0 0 0 0 0 0 ˆµ FFs × p1, p2, p3; σ1, σ2, σ3 Jrd |p1, p2, p3; σ1, σ2, σ3i s CC Model P 3 ωi 1 i Y 2 ~ ~ ~ Summary × Q Dσi µi {RW [ki ; B (V )]}ΨMJΣ k1, k2, k3; µ1, µ2, µ3 i 2ωi σi 3 ~ 0 ~ 0 ×2MV0δ MV − M V − ~q

q 0 0 0 ~ 2 2 where pi = Bc (V )ki , pi = Bc (V )ki , and ωi = ki + mi Electromagnetic Nucleon Form Factors

Covariant predictions of the GBE RCQM:

1.0 Andivahis p Andivahis History p Walker 2.5 G G Sill M Walker E Hoehler Sill Bartel Hoehler Bartel Low-energy PFSA 2.0 NRIA PFSA QCD PFSA-NRC NRIA PFSA-NRC 1.5 RCQM 0.5

Spectroscopy 1.0 Multiplets 0.5 Structure 0.0 0.0 Nucleon E.m. 0 1 2 3 4 0 1 2 3 4 2 2 2 2 Baryon E.m. Q [(GeV/c) ] Q [(GeV/c) ] Axial FFs Gravitational FF Eden Meyerhoff Strong πNN, πN∆ Lung n Herberg FFs -0.5 GE Rohe Ostrick CC Model Becker (corr. Golak) Passchier Zhu Lung 0.05 PFSA -1.0 Markowitz Summary NRIA Rock PFSA-NRC Bruins n Gao G Anklin 98 M Anklin 94 -1.5 Xu Kubon PFSA NRIA PFSA-NRC 0.00 -2.0 0 1 2 3 4 0 1 2 3 4 2 2 2 2 Q [(GeV/c) ] Q [(GeV/c) ]

R.F. Wagenbrunn, S. Bofﬁ, W. Klink, W. Plessas, and M. Radici: Phys. Lett. B511 (2001) 33 Nucleon Electric Radii and Magnetic Moments

2 2 Electric radii rE [fm ] History Baryon GBE RCQM Experiment Low-energy p 0.82 0.7692 ± 0.01231) QCD 0.70870 ± 0.001132) RCQM n −0.13 −0.1161 ± 0.0022 Spectroscopy Multiplets 1) 2) Structure CODATA value (PDG) Pohl et al.: Nature 466 (2010) 213 Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs Magnetic moments µ [n.m.]

CC Model Baryon GBE RCQM Experiment

Summary p 2.70 2.792847356 n −1.70 −1.9130427

K. Berger, R.F. Wagenbrunn, and W. Plessas: Phys. Rev. D 70, 094027 (2004) 2 Nucleon rE and µ – Nonrelativistic !!!

2 2 Electric radii rE [fm ] History Baryon GBE RCQM GBE NRIA Experiment Low-energy 1) QCD p 0.820 .100 .7692 ± 0.0123 2) RCQM 0.70870 ± 0.00113 n −0.13 −0.01 −0.1161 ± 0.0022 Spectroscopy Multiplets

Structure 1) CODATA value (PDG) 2) Pohl et al.: Nature 466 (2010) 213 Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs Magnetic moments µ [n.m.] CC Model Baryon GBE RCQM GBE NRIA Experiment Summary p 2.702 .742 .792847356 n −1.70 −1.82 −1.9130427

K. Berger, R.F. Wagenbrunn, and W. Plessas: Phys. Rev. D 70, 094027 (2004) Flavor Analysis of Nucleon E.m. FFs

History

Low-energy QCD

RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Nucleons N Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model

Summary Proton Electric Form Factor

Gp = 2 Gu 1 Gd E 3 E − 3 E u 2 History 2/3 GE (Q ) d 2 -1/3 GE (Q ) Low-energy p 2 1.5 GE (Q ) QCD u 2 Boinepalli: 2/3 GE (Q ) d 2 RCQM p 2 Boinepalli: -1/3 GE (Q ) G (Q ) Boinepalli: Gp (Q2) Spectroscopy E E Andivahis Multiplets 1 Bartel Structure Hoehler Nucleon E.m. Christy Baryon E.m. Sill Axial FFs Gravitational FF 0.5 Walker Strong πNN, πN∆ Qattan FFs u 2 CJRW: 2/3 GE (Q ) d 2 CC Model CJRW: -1/3 GE (Q ) Summary 0

0 1 2 3 Q2 [GeV2/c2]

M. Rohrmoser, Ki-Seok Choi, and W. Plessas: arXiv:1110.3665 Neutron Electric Form Factor

Gn = 2 Gd 1 Gu E 3 E − 3 E

History

Low-energy 0.5 QCD Gn (Q2) RCQM E

Spectroscopy Multiplets

Structure 0 Nucleon E.m. Baryon E.m.

Axial FFs d 2 Gravitational FF 2/3 GE (Q ) Herberg Ostrick u 2 Strong πNN, πN∆ -1/3 GE (Q ) Becker Passchier FFs n 2 GE (Q ) Glazier Rohe CC Model Boinepalli: Meyerhoff Zhu -0.5 d 2 2/3 GE (Q ) Bermuth Madey Summary d 2 Boinepalli: Eden CJRW: 2/3 GE(Q ) u 2 u 2 -1/3 GE (Q ) Schiavilla CJRW: -1/3 GE(Q ) Boinepalli: Lung n 2 GE (Q ) Bruins 0 1 2 3 Q2 [GeV2/c2]

M. Rohrmoser, Ki-Seok Choi, and W. Plessas: arXiv:1110.3665 Proton Magnetic Form Factor

Gp = 2 Gu 1 Gd M 3 M − 3 M

History u 2 2/3 GM (Q ) 2.5 d 2 Low-energy -1/3 GM (Q ) QCD p 2 GM (Q ) u 2 RCQM Boinepalli: 2/3 GM (Q ) 2 Boinepalli: -1/3 Gd (Q2) Spectroscopy M Boinepalli: Gp (Q2) Multiplets M p 2 Andivahis Structure 1.5 GM (Q ) Bartel Nucleon E.m. Baryon E.m. Hoehler Axial FFs Christy Gravitational FF 1 Sill Strong πNN, πN∆ FFs Walker CC Model Qattan u 2 0.5 CJRW: 2/3 GM (Q ) Summary d 2 CJRW: -1/3 GM (Q )

0 0 1 2 3 Q2 [GeV2/c2]

M. Rohrmoser, Ki-Seok Choi, and W. Plessas: arXiv:1110.3665 Neutron Magnetic Form Factor

Gn = 2 Gd 1 Gu M 3 M − 3 M

History 0 Low-energy QCD

RCQM

Spectroscopy -0.5 Multiplets n 2 Structure GM (Q ) Nucleon E.m. Baryon E.m. Axial FFs -1 Gravitational FF d 2 Strong πNN, πN∆ 2/3 GM (Q ) Boinepalli: Gao FFs u 2 n 2 -1/3 GM (Q ) GM (Q ) Xu 2003 n 2 CC Model GM (Q ) Bartel Xu 2000 Boinepalli: Anklin 94 Lung Summary -1.5 d 2 2/3 GM (Q ) Anklin 98 Bruins d 2 Boinepalli: Kubon CJRW: 2/3 GM (Q ) u 2 u 2 -1/3 GM (Q ) Markowitz CJRW: -1/3 GM (Q ) 0 1 2 3 Q2 [GeV2/c2]

M. Rohrmoser, Ki-Seok Choi, and W. Plessas: arXiv:1110.3665 ∆ and Hyperon E.m. Form Factors

History

Low-energy QCD ∆ RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Λ, Σ, Ξ Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model Summary Σ∗, Ξ∗, Ω Baryon Electric Radii and Magnetic Moments

2 2 Electric radii rE [fm ] Baryon GBE RCQM Experiment History p 0.82 0.7692 ± 0.0123 Low-energy n −0.13 −0.1161 ± 0.0022 QCD Σ− 0.72 0.61 ± 0.12 ± 0.09 RCQM Spectroscopy Magnetic moments µ [n.m.] Multiplets

Structure Baryon GBE RCQM Experiment Nucleon E.m. p 2.70 2.792847356 Baryon E.m. Axial FFs n −1.70 −1.9130427 Gravitational FF Λ −0.64 −0.613 ± 0.004 Strong πNN, πN∆ + FFs Σ 2.38 2.458 ± 0.010 − CC Model Σ −0.93 −1.160 ± 0.025 0 Summary Ξ −1.25 −1.250 ± 0.014 Ξ− −0.70 −0.6507 ± 0.0025 + +1.0 ∆ 2.08 2.7−1.3 ± 1.5 ± 3 ∆++ 4.17 3.7 − 7.5 Ω− −1.59 −2.020 ± 0.05

K. Berger, R.F. Wagenbrunn, and W. Plessas: Phys. Rev. D 70, 094027 (2004) Electric ∆ Form Factors

2 ++ 1.8 ∆ 2 GE (Q ) 1.6 ∆+ 2 History GE (Q ) 1.4 ∆0 2 Low-energy GE (Q ) - QCD 1.2 ∆ 2 GE (Q ) RCQM 1 ∆ 2 Alexandrou: DW 0.8 GE (Q ) Spectroscopy Alexandrou: QW 0.6 Multiplets Alexandrou: hybrid Structure 0.4 Nucleon E.m. 0.2 Baryon E.m. Axial FFs 0 Gravitational FF -0.2 Strong πNN, πN∆ FFs -0.4 CC Model -0.6

Summary -0.8 -1 0 1 2 3 Q2 [GeV2/c2]

GBE RCQM: Ki-Seok Choi: PhD Thesis, Univ. Graz, 2011

Lattice QCD: C. Alexandrou et al. Phys. Rev. D 79 (2009) 014507 Magnetic ∆ Form Factors

4 ∆++ 2 3.6 GM (Q ) ∆+ 2 History 3.2 GM (Q ) ∆0 G (Q2) Low-energy 2.8 M ∆- QCD 2.4 G (Q2) ∆ M RCQM 2 G (Q2) Alexandrou: QW 1.6 M Spectroscopy Alexandrou: hybrid Multiplets 1.2

Structure 0.8 Nucleon E.m. 0.4 Baryon E.m. Axial FFs 0 Gravitational FF -0.4 Strong πNN, πN∆ FFs -0.8

CC Model -1.2 -1.6 Summary -2 0 1 2 3 Q2 [GeV2/c2]

GBE RCQM: Ki-Seok Choi: PhD Thesis, Univ. Graz, 2011

Lattice QCD: C. Alexandrou et al. Phys. Rev. D 79 (2009) 014507 Octet Λ(uds) Electric Form Factor

0.7 u Λ 2 1/3 GE (Q ) d Λ 2 History -1/3 GE (Q ) 0.6 s Λ 2 -1/3 GE (Q ) Low-energy Λ 2 0.5 GE(Q ) QCD u Λ 2 Boinepalli: 1/3 GE (Q ), RCQM 0.4 Λ mπ=306(7)MeV 2 d Λ 2 Spectroscopy GE (Q ) Boinepalli: -1/3 GE (Q ), Multiplets 0.3 mπ=306(7)MeV s Λ 2 Boinepalli: -1/3 GE (Q ), Structure 0.2 mπ=306(7)MeV Nucleon E.m. Λ Boinepalli: G (Q2), Baryon E.m. 0.1 E Axial FFs mπ=306(7)MeV Gravitational FF Strong πNN, πN∆ 0 FFs

CC Model -0.1

Summary -0.2

-0.3

0 1 2 3 Q2 [GeV2/c2] Octet Λ(uds) Magnetic Form Factor

0.1

History 0 Low-energy QCD -0.1 RCQM u Λ 2 1/3 GM (Q ) Spectroscopy d Λ 2 -0.2 -1/3 GM (Q ) Multiplets s Λ 2 -1/3 GM (Q ) Structure Λ 2 -0.3 GM(Q ) Nucleon E.m. Λ Boinepalli: 1/3 Gu (Q2), Baryon E.m. M m =306(7)MeV Axial FFs -0.4 π Gravitational FF Λ d Λ 2 2 Boinepalli: -1/3 GM (Q ), Strong πNN, πN∆ G (Q ) FFs M mπ=306(7)MeV -0.5 s Λ 2 CC Model Boinepalli:-1/3 GM (Q ), mπ=306(7)MeV Summary -0.6 Λ 2 Boinepalli: GM (Q ), mπ=306(7)MeV -0.7 0 1 2 3 Q2 [GeV2/c2] Decuplet Ω−(sss) Electric Form Factor

History -0.1

Low-energy -0.2 QCD -0.3 RCQM -0.4 Spectroscopy Ω- 2 Multiplets -0.5 GE (Q ) Structure Nucleon E.m. -0.6 Baryon E.m. Axial FFs -0.7 - Gravitational FF Ω 2 GE (Q ) Strong πNN, πN∆ FFs -0.8 Alexandrou: mπ=330 MeV Alexandrou: mπ=297 MeV CC Model -0.9 Alexandrou: hybrid Summary -1 0 1 2 3 Q2 [GeV2/c2]

Lattice-QCD: C. Alexandrou et al.: Phys. Rev. D82 (2010) 034504 Decuplet Ω−(sss) Magnetic Form Factor

-0.2 History

Low-energy -0.4 QCD

RCQM -0.6

Spectroscopy -0.8 - Multiplets Ω 2 Structure GM (Q ) Nucleon E.m. -1 Baryon E.m. Axial FFs -1.2 Gravitational FF Ω- Strong πNN, πN∆ G (Q2) FFs -1.4 M Alexandrou: mπ=330 MeV CC Model Alexandrou: mπ=297 MeV -1.6 Summary Alexandrou: hybrid

-1.8 0 1 2 3 Q2 [GeV2/c2]

Lattice-QCD: C. Alexandrou et al.: Phys. Rev. D82 (2010) 034504 Axial Charges and Axial Form Factors

History

Low-energy QCD Axial Charges and Axial Form Factors RCQM

Spectroscopy Multiplets of Structure Nucleon E.m. Baryon E.m. Axial FFs N Ground State and N∗ Resonances Gravitational FF Strong πNN, πN∆ FFs

CC Model as well as

Summary ∆, Σ, Ξ, Σ∗, Ξ∗ Axial Nucleon Form Factors

Covariant predictions of the GBE RCQM: History

Low-energy QCD 1.5 Pion world data Pion Mainz 100 G Neutrino world data A PFSA RCQM NRIA RC/no boosts 10 Spectroscopy 1.0 Multiplets

Structure 1 Nucleon E.m. Bardin 0.5 Choi Baryon E.m. with pion pole G 0.1 P Axial FFs without pion pole Gravitational FF Strong πNN, πN∆ 0.0 0.01 FFs 0 1 2 3 4 5 0.01 0.1 1 2 2 2 2 Q [(GeV/c) ] Q [(GeV/c) ] CC Model

Summary gGBE = 1.15 vs. gexp = 1.2695 0.0029 A A ±

L.Ya. Glozman, M. Radici, R.F. Wagenbrunn, S. Bofﬁ, W. Klink, and W. Plessas: Phys. Lett. B 516, 183 (2001) Axial Charges of N and N∗ Resonances

State JP EGBE Lattice QCD GN NR History 1 + N(939) 2 1.15 1.18 1.31 1.66 1.65 Low-energy ∼ QCD 1 + N(1440) 2 1.16 ? 1.66 1.61 RCQM N(1535) 1 − 0.02 0.00 -0.11 -0.20 Spectroscopy 2 ∼ Multiplets + N(1710) 1 0.35 ? 0.33 0.42 Structure 2 1 Nucleon E.m. − N(1650) 2 0.51 0.55 0.55 0.64 Baryon E.m. ∼ Axial FFs Gravitational FF Strong πNN, πN∆ FFs EGBE Extended GBE RCQM covariant result CC Model Lattice Lattice QCD calculations by LHPC Collaboration, Summary Takahashi-Kunihiro (Kyoto) etc. GN Glozman-Nefediev SU(6) O(3) nonrelativistic QM × NR Non-Relativistic EGBE result

K.-S. Choi, W. Plessas, and R.F. Wagenbrunn: Phys. Rev. C 81, 028201 (2010) Axial Form Factor of the ∆

Covariant predictions of the GBE and OGE RCQMs: History

Low-energy QCD

RCQM

Spectroscopy Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs

CC Model

Summary

K.-S. Choi and W. Plessas: Few-Body Syst. 54, 1055 (2013)

(Lattice QCD data from C. Alexandrou et al., PoS LATTICE2010, 141 (2010)) Axial Charges of ∆, Σ, Ξ, Σ∗, Ξ∗

JP Exp EGBE LO EOT JT NR

History 1 + N 2 1.2695 1.15 1.18 1.314 1.18 1.65 Low-energy 1 + QCD Σ 2 - 0.65 0.636 0.686 0.73 0.93 1 + RCQM Ξ 2 - -0.21 -0.277 -0.299 -0.23 -0.32 Spectroscopy + Multiplets 3 ∆ 2 - -4.48 - - -4.5 -6.00 + ∼ Structure Σ 3 - -1.06 - - - -1.41 Nucleon E.m. ∗ 2 + Baryon E.m. Ξ 3 - -0.75 - - - -1.00 Axial FFs ∗ 2 Gravitational FF Strong πNN, πN∆ FFs CC Model EGBE Extended GBE RCQM covariant result Summary LO Lin and Orginos lattice-QCD calculation EOT Erkol, Oka, and Takahashi lattice-QCD calculation JT Jiang and Tiburzi χPT calculation NR Non-Relativistic EGBE result

K.-S. Choi, W. Plessas, and R.F. Wagenbrunn: Phys. Rev. D 82, 014007 (2010) History

Low-energy QCD

RCQM

Spectroscopy Gravitational Form Factors Multiplets

Structure Nucleon E.m. of Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs the Nucleon CC Model

Summary Gravitational Form Factors

q˜µ History µ µ p1 p1 Low-energy QCD

RCQM

Spectroscopy Multiplets µν Structure Invariant ME of energy-momentum tensor Θˆ : Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF 0 0 ˆ µν ¯ 0 (µ ¯ ν) 2 Strong πNN, πN∆ P JΣ Θ PJΣ = U(P ) γ P A(Q )+ FFs h | | i CC Model µ ν 2 µν i ¯ (µ ν) 2 q q q g 2 Summary P σ B(Q )+ − C(Q ) U(P) 2M M

A(Q2) P0JΣ0 Θ00 PJΣ ∼ h | | i Nucleon Gravitational Form Factor A(Q2)

1.2 History URCQM 2 AdS/QCD Low-energy A(Q ) QCD 1 Domokos et al.

RCQM 0.8 Spectroscopy Multiplets

Structure 0.6 Nucleon E.m. Baryon E.m. Axial FFs 0.4 Gravitational FF Strong πNN, πN∆ FFs 0.2 CC Model

Summary 0 0 1 2 3 4 5 Q2[(GeV/c)2]

J.P. Day: PhD Thesis, Univ. Graz, August 2013 History

Low-energy QCD RCQM Microscopic Description Spectroscopy Multiplets

Structure Nucleon E.m. of Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs Meson-Baryon Interaction Vertices CC Model

Summary Meson-Baryon Interaction Vertices

Interaction vertices

History

Low-energy QCD

RCQM 4 ˆ π Spectroscopy Fi f = (2π) f I (0) i V 0, M0, J0, Σ0 Drd V , M, J, Σ Multiplets → h | L | i ≡ h | | i

Structure where Nucleon E.m. D E Baryon E.m. 0 0 0 0 0 0 ˆ π p , p , p ; σ , σ , σ D p1, p2, p3; σ1, σ2, σ3 = Axial FFs 1 2 3 1 2 3 rd Gravitational FF Strong πNN, πN∆ igqqm 0 0 µ 0 0 ¯ ˜ ~ ~ ~ ~ 0 0 FFs 3NS u(p , σ )γ5γµλmu(p1, σ1)q 2p20δ(p2−p )2p30δ(p3−p )δσ σ δσ σ 3 1 1 2 3 2 2 3 3 2m1 (2π) 2 CC Model

Summary and √ q 0 0 1 m 2π EN + MN F 2 = π i→f GπNN Q p 0 0 fπNN 2MN EN + MN + ω Qz √ 2 1 3 2π mπ Fi→f GπN∆ Q = − q √ fπN∆ 2 0 0 Qz EN + MN 2M∆ πNN and πN∆ Interaction Vertices

History RCQM RCQM Sato-Lee Sato-Lee Polinder-Rijken Polinder-Rijken Low-energy 1 Liu et al. 1 Alexandrou et al. A Alexandrou et al. A Alexandrou et al. B QCD Alexandrou et al. B Alexandrou et al. C Erkol et al. RCQM

Spectroscopy 0.5 0.5 Multiplets

Structure Nucleon E.m. Baryon E.m. Axial FFs 0 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 2 2 Gravitational FF Q Q Strong πNN, πN∆ FFs GπNN GπN∆ CC Model

Summary

T. Melde, L. Canton, and W. Plessas: Phys. Rev. Lett. 102, 132002 (2009) Form-Factor Parametrizations

2 1 2 1 History G ~q = 2 4 G Q = 2 ~q ~q 1+ Q 1+ Λ + Λ ( Λ ) Low-energy 1 2 QCD RCQM RCQM SL PR LIU ERK ALX Spectroscopy f 2 Multiplets N 4π 0.0691 0.08 0.075 0.0649 0.0481 0.0412 Structure N Λ1 0.451 0.453 0.940 Λ 0.747 0.614 1.65 Nucleon E.m. Baryon E.m. Λ2 0.931 0.641 1.102 - - - Axial FFs f 2 Gravitational FF ∆ 0.188 0.334 0.478 Strong πNN, πN∆ 4π FFs ∆ Λ1 0.594 0.458 0.853 CC Model Λ2 0.998 0.648 1.014 Summary

T. Melde, L. Canton, and W. Plessas: Phys. Rev. Lett. 102, 132002 (2009) Way to a Coupled-Channels Quark Model

History

Low-energy QCD

RCQM Spectroscopy Introducing Multiplets

Structure Nucleon E.m. explicit mesonic degrees of freedom Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ (ongoing work with Regina Kleinhappel) FFs

CC Model

Summary Coupled-Channels Approach

History I Coupled-channel mass operator eigenvalue Low-energy equation: QCD I E.g., excited hadron can decay into GS and additional RCQM particle Spectroscopy Multiplets

Structure † Nucleon E.m. Mi K ψi ψi Baryon E.m. | i = m | i Axial FFs KMi+1 ψi+1 ψi+1 Gravitational FF | i | i Strong πNN, πN∆ FFs

CC Model I i=1: Allows, e.g., dressing of bare hadrons by meson loops Summary I i=2: Allows, e.g., dressing of pure qq¯ states by meson loops

I i=3: Allows, e.g., dressing of pure qqq states by meson loops Summary and Conclusions

History

Low-energy I Baryon spectroscopy of all ﬂavors consistently QCD described in a universal RCQM based on GBE RCQM dynamics Spectroscopy Multiplets I The covariant structures of the ground states (N, ∆, Structure Nucleon E.m. Λ, ...) in good agreement with experiment (wherever Baryon E.m. Axial FFs such data are available) Gravitational FF Strong πNN, πN∆ I Predictions by the GBE RCQM reasonable consistent FFs

CC Model with (reliable) lattice-QCD results. Summary I Disturbing shortcomings of the QQQ quark model { } for hadronic decays (π, η, K modes, ...) Achievements and Future Potentials of RCQMs

To be able to describe/understand in a consistent manner • History on the microscopic level • Low-energy in accordance with the properties of low-energy QCD QCD • RCQM such phenomena like

Spectroscopy Multiplets I hadron spectra: Structure baryon ground states & excitations X Nucleon E.m. Baryon E.m. I baryon structure: rE , µ, gA ; GE , GM , GA, GP , ... Axial FFs , Gravitational FF i.e. electroweak form factors etc. Strong πNN, πN∆ X FFs I resonance decays: CC Model ∗ ∗ , Summary N Nπ, ∆ Nπ, Λ KN, ... X → → ∗ →− ∗ I resonance excitations: γN N , e N N , ... → → / I meson-baryon interactions: π N, K N, ... − − I hyperon-hyperon interactions: N N, N Y , ... etc. etc. − − Constituent-Quark-Model Review

History

Low-energy QCD W. Plessas: RCQM Int. J. Mod. Phys. A30 (2015) 02, 1530013 Spectroscopy Multiplets Structure also in: Nucleon E.m. Baryon E.m. Axial FFs Gravitational FF "50 Years of Quarks" Strong πNN, πN∆ FFs ed. by M. Gell-Mann and H. Fritzsch CC Model Summary (World Scientiﬁc, Singapore, 2015) Collaborators

Graz K. Berger, J.P. Day, Ki-Seok Choi, L. Glozman, History R. Kleinhappel, T. Melde, M. Rohrmoser, R.C. Schardmüller, Low-energy QCD B. Sengl, R.F. Wagenbrunn

RCQM (Theoretical Physics, University of Graz)

Spectroscopy Multiplets Pavia Structure S. Bofﬁ and M. Radici Nucleon E.m. Baryon E.m. (INFN, Sezione di Pavia) Axial FFs Gravitational FF Strong πNN, πN∆ FFs Padova CC Model L. Canton Summary (INFN, Sezione di Padova)

Iowa City W. Klink (Department of Physics, University of Iowa, USA History

Low-energy QCD RCQM Thank you very much Spectroscopy Multiplets

Structure Nucleon E.m. for Baryon E.m. Axial FFs Gravitational FF Strong πNN, πN∆ FFs your attention! CC Model

Summary