1. Craig Roberts, Physics Division

2. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 2 Valence quarks

3. Parton Structure of Hadrons  Valence-quark structure of hadrons –Definitive of a hadron. After all, it’s how we distinguish a proton from a neutron –Expresses charge; flavour; baryon number; and other Poincaré- invariant macroscopic quantum numbers –Via evolution, determines background at LHC  Foreseeable future will bring precision experimental study of (far) valence region, and theoretical computation of distribution functions and distribution amplitudes –Computation is critical –Without it, no amount of data will reveal anything about the theory underlying the phenomena of strong interaction physics Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 3

4. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 4

5. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 5

6. Light-front Quantisation  Hamiltonian formulation of quantum field theory. –Fields are specified on a particular initial surface: Light front x + = x 0 + x 3 = 0 Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 6  Using LF quantisation: quantum mechanics-like wave functions can be defined; quantum-mechanics-like expectation values can be defined and evaluated Parton distributions are correlation functions at equal LF-time x + ; namely, within the initial surface x + = 0, and can thus be expressed directly in terms of ground state LF wavefunctions

7. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 7

8. Pion’s valence-quark Distribution Amplitude  Following a workshop in Caraguatatuba (2012), methods were developed that enable direct computation of the pion’s light-front wave function  φ π (x) = twist-two parton distribution amplitude = projection of the pion’s Poincaré-covariant wave-function onto the light-front  Results have been obtained with rainbow-ladder DSE kernel, simplest symmetry preserving form; and the best DCSB-improved kernel that is currently available. x α (1-x) α, with α≈0.5 Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 8 Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]

9. Pion’s valence-quark Distribution Amplitude  Both kernels agree: marked broadening of φ π (x), which owes to DCSB Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 9 Asymptotic RL DB  This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB.  Difference between RL and DB results is readily understood: B(p 2 ) is more slowly varying with DB kernel and hence a more balanced result Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]

10. Pion’s valence-quark Distribution Amplitude  Both kernels agree: marked broadening of φ π (x), which owes to DCSB Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 10 Asymptotic RL DB  This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB.  Difference between RL and DB results is readily understood: B(p 2 ) is more slowly varying with DB kernel and hence a more balanced result Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]

11. Features of Ground-state PDAs  A diverse array of studies since Caraguatatuba (2012) have shown that ground-state meson PDAs are broad, concave functions  Camel-humped distributions – popular for many years – are physically unreasonable because they correspond to bound-state amplitudes that disfavour equal momentum partitioning between valence-quark degrees of freedom Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 11 Concave function: no line segment lies above any point on the graph arXiv:1301.0324 [nucl-th]arXiv:1301.0324 [nucl-th], arXiv:1306.2645 [nucl-th], arXiv:1311.1390 [nucl-th], arXiv:1405.0289 [nucl-th], arXiv:1406:3353 [nucl-th]arXiv:1306.2645 [nucl-th] arXiv:1311.1390 [nucl-th]arXiv:1405.0289 [nucl-th] arXiv:1406:3353 [nucl-th]

12. Hard Exclusive Processes & PDAs  In the theory of strong interactions, the cross-sections for many hard exclusive hadronic reactions can be expressed in terms of the PDAs of the hadrons involved  Example: pseudoscalar-meson elastic electromagnetic form factor o α S (Q 2 ) is the strong running coupling, o φ π (u) is the meson’s twist-two valence-quark PDA o f P is the meson's leptonic decay constant Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 12 It was promised that JLab would verify this fundamental prediction

13. Pion electromagnetic form factor  In 2001 – seven years after beginning operations, Jefferson Lab provided the first high precision pion electroproduction data for F π between Q 2 values of 0.6 and 1.6 (GeV/c) 2. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 13  2006 & 2007 – new result, at Q 2 =2.45 (GeV/c) 2  Authors of the publications stated: “still far from the transition to the Q 2 region where the pion looks like a simple quark- antiquark pair”  disappointment and surprise Result imagined by many to be QCD prediction JLab Data Evaluated with φ π = 6x(1-x) lQCD only provides access to this small domain, already well-mapped by experiments

14. Pion electromagnetic form factor  Year 2000 prediction for F π (Q 2 ) –P.Maris & P.C. Tandy, Phys.Rev. C62 (2000) 055204  Problem … used brute-force computational method … unable to compute for Q 2 >4GeV 2 Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 14 Result imagined by many to be QCD prediction JLab Data  Shape of prediction suggested to many that one might never see parton model scaling and QCD scaling violations Factor of three discrepancy Evaluated with φ π = 6x(1-x)

15. Pion electromagnetic form factor  Plans were made and an experiment approved that use the higher-energy electron beam at the 12 GeV Upgrade at Jefferson Lab.  The Upgrade will allow an extension of the F π measurement up to a value of Q 2 of about 6 (GeV/c) 2, which will probe the pion at double the resolution. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 15 Projected JLab reach  Will there be any hint of a trend toward the asymptotic pQCD prediction? Result imagined by many to be QCD prediction Evaluated with φ π = 6x(1-x)

16. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 16

17. Result imagined by many to be QCD prediction Evaluated with φ π = 6x(1-x) Pion electromagnetic form factor  Solution – Part 1 –Compare data with the real QCD prediction; i.e. the result calculated using the broad pion PDA predicted by modern analyses of continuum QCD Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 17 Real QCD prediction – obtained with realistic, computed PDA

18. Pion electromagnetic form factor  Solution – Part 1 –Compare data with the real QCD prediction; i.e. the result calculated using the broad pion PDA predicted by modern analyses of continuum QCD  Solution – Part 2 –Algorithm used to compute the PDA can also be employed to compute F π (Q 2 ) directly, to arbitrarily large Q 2 Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 18 Real QCD prediction – obtained with realistic, computed PDA  Predictions:  JLab will see maximum  Experiments to 8GeV 2 will see parton model scaling and QCD scaling violations for the first time in a hadron form factor Pion electromagnetic form factor at spacelike momenta L. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013) arXiv:1307.0026 [nucl-th]Phys. Rev. Lett. 111, 141802 (2013) maximum Agreement within 15%

19. Implications  Verify the theory of factorisation in hard exclusive processes, with dominance of hard contributions to the pion form factor for Q 2 >8GeV 2.  Notwithstanding that, normalisation of F π (Q 2 ) is fixed by a pion wave-function whose dilation with respect to φ π asy (x)=6x(1-x) is a definitive signature of DCSB –Empirical measurement of the strength of DCSB in the Standard Model – the origin of visible mass  Close the book on a story that began thirty-five years ago  Paves the way for a dramatic reassessment of pictures of proton & neutron structure, which is already well underway Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 19

20. New Challenges  Computation of spectrum of hybrid and exotic mesons  Equally pressing, some might say more so, is the three-body problem; viz., baryons in QCD Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 20 exotic mesons: quantum numbers not possible for quantum mechanical quark-antiquark systems hybrid mesons: normal quantum numbers but non- quark-model decay pattern BOTH suspected of having “constituent gluon” content ↔

21. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 21

22. Unification of Meson & Baryon Properties  Correlate the properties of meson and baryon ground- and excited- states within a single, symmetry-preserving framework  Symmetry-preserving means: Poincaré-covariant & satisfy relevant Ward-Takahashi identities  Constituent-quark model has hitherto been the most widely applied spectroscopic tool; whilst its weaknesses are emphasized by critics and acknowledged by proponents, it is of continuing value because there is nothing better that is yet providing a bigger picture.  Nevertheless,  no connection with quantum field theory & therefore not with QCD  not symmetry-preserving & therefore cannot veraciously connect meson and baryon properties Craig Roberts: (3) Hadrons... as they really are 22 Hadron Physics XIII: 22-27 Mar. 2015 (76pp)

23. DSEs & Baryons  Dynamical chiral symmetry breaking (DCSB) – has enormous impact on meson properties.  Must be included in description and prediction of baryon properties.  DCSB is essentially a quantum field theoretical effect. In quantum field theory  Meson appears as pole in four-point quark-antiquark Green function → Bethe-Salpeter Equation  Nucleon appears as a pole in a six-point quark Green function → Faddeev Equation.  Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarks  Tractable equation is based on the observation that an interaction which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channel Craig Roberts: (3) Hadrons... as they really are 23 R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145 Hadron Physics XIII: 22-27 Mar. 2015 (76pp) SU c (3):

24.  Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarks  Confinement and DCSB are readily expressed  Prediction: strong diquark correlations exist within baryons as a dynamical consequence of DCSB in QCD  Diquark correlations are not pointlike –Typically, r 0+ ~ r π & r 1+ ~ r ρ (actually 10% larger) –They have soft form factors Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 24

25. Faddeev Equation  Linear, Homogeneous Matrix equation  Yields wave function (Poincaré Covariant Faddeev Amplitude) that describes quark-diquark relative motion within the nucleon  Scalar and Axial-Vector Diquarks...  Both have “correct” parity and “right” masses  In Nucleon’s Rest Frame Amplitude has s−, p− & d−wave correlations Craig Roberts: (3) Hadrons... as they really are 25 diquark quark quark exchange ensures Pauli statistics composed of strongly- dressed quarks bound by dressed-gluons Hadron Physics XIII: 22-27 Mar. 2015 (76pp) R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145

26.  Why should a pole approximation produce reliable results? Faddeev Equation Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 26 quark-quark scattering matrix - a pole approximation is used to arrive at the Faddeev-equation

27.  Consider the rainbow-gap and ladder-Bethe-Salpeter equations  In this symmetry-preserving truncation, colour-antitriplet quark-quark correlations (diquarks) are described by a very similar homogeneous Bethe-Salpeter equation  Only difference is factor of ½  Hence, an interaction that describes mesons also generates diquark correlations in the colour-antitriplet channel Diquarks Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 27 Calculation of diquark masses in QCD R.T. Cahill, C.D. Roberts and J. Praschifka Phys.Rev. D36 (1987) 2804

28. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 28

29.  Vector-vector contact interaction m G = 800MeV is a gluon mass-scale – dynamically generated in QCD  Gap equation:  DCSB: M ≠ 0 is possible so long as α IR >α IR critical =0.4π  Observables require α IR = 0.93π Contact-Interaction Kernel Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 29

30. Contact Interaction  arXiv:1411.2052, Phys. Rev D in press [ 20pages ] arXiv:1411.2052, Phys. Rev D in press [ 20pages ] Nucleon tensor charges and electric dipole moments M. Pitschmann, C.-Y. Seng, C.D. Roberts, S.M. Schmidt  arXiv:1212.2212 [nucl-th], Phys. Rev. C 87 92013) 045207 [15 pages] arXiv:1212.2212 [nucl-th], Phys. Rev. C 87 92013) 045207 [15 pages] Features and flaws of a contact interaction treatment of the kaon Chen Chen, L. Chang, C. D. Roberts, S. M. Schmidt, Shaolong Wan and D. J. Wilson,  arXiv:1209.4352 [nucl-th], Phys. Rev. C87 (2013) 015205 [12 pages] arXiv:1209.4352 [nucl-th]Phys. Rev. C87 (2013) 015205 [12 pages] Electric dipole moment of the rho-meson M. Pitschmann, C.-Y. Seng, M. J. Ramsey-Musolf, C. D. Roberts, S. M. Schmidt and D. J. Wilson  arXiv:1204.2553 [nucl-th], Few Body Syst. (2012) DOI: 10.1007/s00601-012-0466-3 arXiv:1204.2553 [nucl-th]Few Body Syst. (2012) DOI: 10.1007/s00601-012-0466-3 Spectrum of Hadrons with Strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson  arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages] arXiv:1112.2212 [nucl-th]Phys. Rev. C85 (2012) 025205 [21 pages] Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts  arXiv:1102.4376 [nucl-th], Phys. Rev. C 83, 065206 (2011) [12 pages], arXiv:1102.4376 [nucl-th]Phys. Rev. C 83, 065206 (2011) [12 pages] π- and ρ-mesons, and their diquark partners, from a contact interaction, H.L.L. Roberts, A. Bashir, L.X. Gutiérrez-Guerrero, C.D. Roberts and David J. Wilson  arXiv:1101.4244 [nucl-th], Few Body Syst. 51 (2011) pp. 1-25 arXiv:1101.4244 [nucl-th]Few Body Syst. 51 (2011) pp. 1-25 Masses of ground and excited-state hadrons H.L.L. Roberts, Lei Chang, Ian C. Cloët and Craig D. Roberts  arXiv:1009.0067 [nucl-th], Phys. Rev. C82 (2010) 065202 [10 pages] arXiv:1009.0067 [nucl-th]Phys. Rev. C82 (2010) 065202 [10 pages] Abelian anomaly and neutral pion production Hannes L.L. Roberts, C.D. Roberts, A. Bashir, L. X. Gutiérrez-Guerrero & P. C. Tandy  arXiv:1002.1968 [nucl-th], Phys. Rev. C 81 (2010) 065202 (5 pages) arXiv:1002.1968 [nucl-th]Phys. Rev. C 81 (2010) 065202 (5 pages) Pion form factor from a contact interaction, L. Xiomara Gutiérrez-Guerrero, A. Bashir, I. C. Cloët & C. D. Roberts Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 30 Symmetry-preserving treatment of vector- vector contact-interaction: series of papers establishes strengths & limitations.

31. Contact Interaction Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 31  Symmetry-preserving treatment of vector×vector contact interaction is useful tool for the study of phenomena characterised by probe momenta less-than the dressed-quark mass.  Whilst this interaction produces form factors which are too hard, interpreted carefully, even they can be used to draw valuable insights; e.g., concerning relationships between different hadrons.  Studies employing a symmetry-preserving regularisation of the contact interaction serve as a useful surrogate, exploring domains which analyses using interactions that more closely resemble those of QCD are as yet unable to enter.  They’re critical at present in attempts to use data as tool for charting nature of the quark-quark interaction at long-range; i.e., identifying signals of the running of couplings and masses in QCD.

32.  Studies of π & ρ static properties and π form factor establish that contact-interaction results are not realistically distinguishable from those of renormalisation-group- improved one-gluon exchange for Q 2 <M 2 Interaction Kernel Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 32 contact interaction QCD 1-loop RGI gluon M0.370.34 κπκπ 0.24 mπmπ 0.14 mρmρ 0.930.74 fπfπ 0.100.093 fρfρ 0.130.15 M 2 /m ρ 2 cf. expt. rms rel.err.=13% One-loop RGI-improved QCD-based interaction

33. contact interaction M0.37 κπκπ 0.24 mπmπ 0.14 mρmρ 0.93 fπfπ 0.10 fρfρ 0.13  Contact interaction is not renormalisable  Must therefore introduce regularisation scheme  Use confining proper-time definition  Λ ir = 0.24GeV, τ ir = 1/Λ ir = 0.8fm a confinement radius, which is not varied  Two parameters: m G =0.13GeV, Λ uv =0.91GeV fitted to produce tabulated results Interaction Kernel - Regularisation Scheme Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 33 D. Ebert, T. Feldmann and H. Reinhardt, Phys. Lett. B 388 (1996) 154. No pole in propagator – DSE realisation of confinement

34. Regularisation & Symmetries  In studies of the hadron spectrum it’s critical that an approach satisfy the vector and axial-vector Ward-Green Takahashi identities.  Without this it is impossible to preserve the pattern of chiral symmetry breaking in QCD & hence a veracious understanding of hadron mass splittings is not achievable.  Contact interaction should & can be regularised appropriately  Example: dressed-quark-photon vertex  Contact interaction plus rainbow-ladder entails general form  Vector Ward-Takahashi identity  With symmetry-preserving regularisation of contact interaction, Ward Takahashi identity requires Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 34 P L (Q 2 )=1 & P T (Q 2 =0)=1 Interactions cannot generate an on-shell mass for the photon.

35. BSE – inhomogeneous vector vertex  Solution: P L (Q 2 ) = 1 Readily established using vector Ward-Green-Takahashi identity Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 35 ω(x,α,z) = x + α(1- α)z  Plainly: P T (Q 2 =0) = 1 because K γ (Q 2 =0)=1 Again, power of vector Ward-Green-Takahashi identity revealed

36. Regularisation & Symmetries  Solved Bethe-Salpeter equation for dressed- quark photon vertex, regularised using symmetry-preserving scheme Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are Ward-Takahashi identity ρ-meson pole generated dynamically - Foundation for Vector meson dominance (VMD) “Asymptotic freedom” Dressed-vertex → bare at large spacelike Q 2 Renormalisation-group-improved one-gluon exchange Maris & Tandy prediction of F π (Q 2 ) 36

37.  “Spectrum” of nonpointlike quark-quark correlations  Observed in –DSE studies in QCD –0 + & 1 + in Lattice-QCD  Scalar diquark form factor –r 0+ ≈ r π  Axial-vector diquarks –r 1+ ≈ r ρ Diquarks in QCD Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 37  Zero relation with old notion of pointlike constituent-like diquarks BOTH essential H.L.L. Roberts et al., 1102.4376 [nucl-th]1102.4376 [nucl-th] Phys. Rev. C 83, 065206 (2011) [12 pages] Masses of ground and excited-state hadrons Hannes L.L. Roberts, Lei Chang, Ian C. Cloët and Craig D. Roberts, arXiv:1101.4244 [nucl-th]arXiv:1101.4244 [nucl-th] Few Body Systems (2011) pp. 1-25

38. Spectrum of Baryons SStatic “approximation” IImplements analogue of contact interaction in Faddeev-equation IIn combination with contact-interaction diquark-correlations, generates Faddeev equation kernels which themselves are momentum-independent TThe merit of this truncation is the dramatic simplifications which it produces UUsed widely in hadron physics phenomenology; e.g., Bentz, Cloët, Thomas et al. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 38 Variant of: A. Buck, R. Alkofer & H. Reinhardt, Phys. Lett. B286 (1992) 29. H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts, arXiv:1101.4244 [nucl-th], Few Body Syst. 51 (2011) pp. 1-25 arXiv:1101.4244 [nucl-th]

39. Spectrum of Baryons Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 39  Faddeev equation for Δ-resonance  One-dimensional eigenvalue problem, to which only the axial-vector diquark contributes  Nucleon has scalar & axial-vector diquarks. It is a five-dimensional eigenvalue problem With the right glasses; i.e., those polished by experience with the DSEs, one can look at this equation and see that increasing the current-quark mass will boost the mass of the bound-state

40. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 40

41. Pion cloud  Kernels constructed in the rainbow-ladder truncation do not contain any long-range interactions –These kernels are built only from dressed-quarks and -gluons  But, QCD produces a very potent long-range interaction; namely that associated with the pion, without which no nuclei would be bound and we wouldn’t be here  The rainbow-ladder kernel produces what we describe as the hadron’s dressed-quark core  The contribution from pions is omitted, and can be added without “double counting”  The pion contributions must be thoughtfully considered before any comparison can be made with the real world Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 41 H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts, arXiv:1101.4244 [nucl-th], Few Body Syst. 51 (2011) pp. 1-25 arXiv:1101.4244 [nucl-th]

42. Pion cloud  The body of results described hitherto suggest that whilst corrections to our truncated DSE kernels may have a material impact on m N and m Δ separately, the modification of each is approximately the same, so that the mass-difference, δm, is largely unaffected by such corrections.  This is consistent with analyses that considers the effect of pion loops, which are explicitly excluded in the rainbow-ladder truncation: whilst the individual masses are reduced by roughly 300MeV, the mass difference, δm, increases by only 50MeV.  With the educated use of appropriate formulae, one finds that pion-loops yields a shift of (−300MeV) in m N and (−270MeV) in m Δ, from which one may infer that the uncorrected Faddeev equations should produce m N = 1.24GeV and m Δ = 1.50GeV Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 42 H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts, arXiv:1101.4244 [nucl-th], Few Body Syst. 51 (2011) pp. 1-25 arXiv:1101.4244 [nucl-th] M.B. Hecht, M. Oettel, C.D. Roberts, S.M. Schmidt, P.C.Tandy and A.W. Thomas, Phys.Rev. C65 (2002) 055204Phys.Rev. C65 (2002) 055204 Pion cloud typically reduces a hadron’s mass

43. Pion cloud  One can actually do better owing to the existence of the Excited Baryon Analysis Center (EBAC), which for five years has worked to understand and quantify the effects of a pseudoscalar meson cloud on baryons  For the Δ-resonance, EBAC’s calculations indicate that the dressed- quark core of this state should have m Δ qqq = 1.39GeV  These observations indicate that the dressed-quark core Faddeev equations should yield m N = 1.14GeV, m Δ = 1.39GeV, δm = 0.25GeV which requires g N = 1.18, g Δ = 1.56 Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 43 All three spectrum parameters now fixed (g SO =0.24)

44. Hadron Spectrum Craig Roberts: (3) Hadrons... as they really are 44 Legend: Particle Data Group H.L.L. Roberts et al. EBAC Jülich o Symmetry-preserving unification of the computation of meson & baryon masses o rms-rel.err./deg-of-freedom = 13% o PDG values (almost) uniformly overestimated in both cases - room for the pseudoscalar meson cloud?! Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Masses of ground and excited-state hadrons H.L.L. Roberts et al., arXiv:1101.4244 [nucl-th]arXiv:1101.4244 [nucl-th] Few Body Systems (2011) pp. 1-25

45. Baryon Spectrum Craig Roberts: (3) Hadrons... as they really are 45  In connection with EBAC's analysis, dressed-quark Faddeev-equation predictions for bare-masses agree within rms-relative-error of 14%.  Notably, EBAC finds a dressed-quark-core for the Roper resonance, at a mass which agrees with Faddeev Eq. prediction. Hadron Physics XIII: 22-27 Mar. 2015 (76pp)

46. Roper Resonance  Consider the N(1440)P 11, J P = (1/2) + “Roper resonance,” whose discovery was reported in 1964 – part of Roper’s PhD thesis  In important respects the Roper appears to be a copy of the proton. However, its (Breit-Wigner) mass is 50% greater.  Features of the Roper have long presented a problem within the context of constituent-quark models formulated in terms of color- spin potentials, which typically produce a mass of 2 M N and the following level ordering: –ground state, J P = (1/2) + with radial quantum number n = 0 and angular momentum l = 0; –first excited state, J P = (1/2) − with (n, l) = (0, 1); –second excited state, J P = (1/2) +, with (n, l) = (1, 0); etc.  The difficulty is that the lightest l = 1 baryon appears to be the N(1535)S 11, which is heavier than the Roper! Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 46

47. EBAC & the Roper resonance  EBAC examined the dynamical origins of the two poles associated with the Roper resonance are examined.  Both of them, together with the next higher resonance in the P 11 partial wave were found to have the same originating bare state  Coupling to the meson- baryon continuum induces multiple observed resonances from the same bare state.  All PDG identified resonances consist of a core state and meson-baryon components. Craig Roberts: (3) Hadrons... as they really are 47 N. Suzuki et al., Phys.Rev.Lett. 104 (2010) 042302Phys.Rev.Lett. 104 (2010) 042302 Hadron Physics XIII: 22-27 Mar. 2015 (76pp)

48. EBAC & the Roper resonance  Nuclear Physics: Exploring the Heart of Matter Decadal Report, issued 2012, by the National Academy of Sciences –In a recent breakthrough, theorists at the Excited Baryon Analysis Center (EBAC) at Jefferson Lab – led by T.-S. H. Lee, Argonne – demonstrated that the Roper resonance is the proton's first radial excitation, with its lower-than-expected mass coming from a quark core shielded by a dense cloud of pions and other mesons. –This breakthrough was enabled by both new analysis tools and new high quality data from the CLAS-Collaboration. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 48

49. Recapitulation  One method by which to validate QCD is computation of its hadron spectrum and subsequent comparison with modern experiment. Indeed, this is an integral part of the international effort in nuclear physics.  For example, the N ∗ programme and the search for hybrid and exotic mesons together address the questions: –which hadron states and resonances are produced by QCD? –how are they constituted?  This intense effort in hadron spectroscopy is a motivation to extend the research just described and treat ground- and excited-state hadrons with s-quark content. (New experiments planned in Japan)  Key elements in a successful spectrum computation are: –symmetries and the pattern by which they are broken; –the mass-scale associated with confinement and DCSB; –and full knowledge of the physical content of bound-state kernels. All this is provided by the DSE approach. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 49

50. Bethe-Salpeter amplitudes  Bethe-Salpeter amplitudes are couplings in Faddeev Equation  Magnitudes for diquarks follow precisely the meson pattern Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 50 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson Owing to DCSB, FE couplings in ½ - channels are 25-times weaker than in ½ + !

51. Spectrum of Baryons with Strangeness  Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 51 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson

52. Spectrum of Baryons with Strangeness  Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 52 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson (1/2)+ (1/2)-

53. Spectrum of Baryons with Strangeness  Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 53 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson (1/2)+ (1/2)-  This level ordering has long been a problem in CQMs with linear or HO confinement potentials  Correct ordering owes to DCSB  Positive parity diquarks have Faddeev equation couplings 25- times greater than negative parity diquarks  Explains why approaches within which DCSB cannot be realised (CQMs) or simulations whose parameters suppress DCSB will both have difficulty reproducing experimental ordering

54. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 54

55. Frontiers of Nuclear Science: Theoretical Advances In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies. Craig Roberts: (3) Hadrons... as they really are 55 Hadron Physics XIII: 22-27 Mar. 2015 (76pp) C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50Prog. Part. Nucl. Phys. 61 (2008) 50 M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227AIP Conf.Proc. 842 (2006) 225-227

56. Nucleon Structure Probed in scattering experiments  Electron is a good probe because it is structureless Electron’s relativistic current is  Proton’s electromagnetic current Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 56 F 1 = Dirac form factorF 2 = Pauli form factor G E = Sachs Electric form factor If a nonrelativistic limit exists, this relates to the charge density G M = Sachs Magntic form factor If a nonrelativistic limit exists, this relates to the magnetisation density

57. Nucleon form factors  For the nucleon & Δ-resonance, studies of the Faddeev equation exist that are based on the 1-loop renormalisation-group-improved interaction that was used efficaciously in the study of mesons –Toward unifying the description of meson and baryon properties G. Eichmann, I.C. Cloët, R. Alkofer, A. Krassnigg and C.D. Roberts arXiv:0810.1222 [nucl-th], Phys. Rev. C 79 (2009) 012202(R) (5 pages) arXiv:0810.1222 [nucl-th] –Survey of nucleon electromagnetic form factors I.C. Cloët, G. Eichmann, B. El-Bennich, T. Klähn and C.D. Roberts arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) pp. 1-36 arXiv:0812.0416 [nucl-th] –Nucleon electromagnetic form factors from the Faddeev equation G. Eichmann, arXiv:1104.4505 [hep-ph]arXiv:1104.4505 [hep-ph] –Nucleon and Δ elastic and transition form factors, Jorge Segovia, Ian C. Cloët, Craig D. Roberts and Sebastian M. Schmidt arXiv:1408.2919 [nucl-th], Few Body Syst. 55 (2014) pp. 1185-1222 arXiv:1408.2919 [nucl-th]  Analyses retain the scalar and axial-vector diquark correlations, known to be necessary and sufficient for reliable description  To compute form factors, one needs a photon-nucleon current Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 57

58. Photon-nucleon current  Composite nucleon must interact with photon via nontrivial current constrained by Ward-Green-Takahashi identities  DSE → BSE → Faddeev equation plus current → nucleon form factors Craig Roberts: (3) Hadrons... as they really are 58 Oettel, Pichowsky, Smekal Eur.Phys.J. A8 (2000) 251-281 Hadron Physics XIII: 22-27 Mar. 2015 (76pp)  In a realistic calculation, the last three diagrams represent 8-dimensional integrals, which can be evaluated using Monte-Carlo techniques

59. Photon-nucleon current  Comparison between results from contact- interaction and realistic interaction can reveal a great deal  Owing to momentum- independence of the diquark Bethe-Salpeter and Faddeev amplitudes using the contact interaction in “static approximation”, the nucleon photon current simplifies Craig Roberts: (3) Hadrons... as they really are 59 Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Just three terms survive  arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages], Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts arXiv:1112.2212 [nucl-th]Phys. Rev. C85 (2012) 025205 [21 pages]

60. Nucleon Form Factors Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 60 Survey of nucleon electromagnetic form factors I.C. Cloët et al, arXiv:0812.0416 [nucl-th],arXiv:0812.0416 [nucl-th] Few Body Syst. 46 (2009) pp. 1-36 Unification of meson and nucleon form factors. Very good description. Quark’s momentum- dependent anomalous magnetic moment has observable impact & materially improves agreement in all cases.

61. Nucleon Form Factors Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 61 Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts, arXiv:1112.2212 [nucl- th], Phys. Rev. C85 (2012) 025205 [21 pages]arXiv:1112.2212 [nucl- th]Phys. Rev. C85 (2012) 025205 [21 pages] Black solid curve = contact interaction Blue dashed curve = momentum- dependent interaction Green dot-dashed curve = parametrisation of experimental data

62. Nucleon Form Factors Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 62 Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts, arXiv:1112.2212 [nucl- th], Phys. Rev. C85 (2012) 025205 [21 pages]arXiv:1112.2212 [nucl- th]Phys. Rev. C85 (2012) 025205 [21 pages] Black solid curve = contact interaction Blue dashed curve = momentum- dependent interaction Green dot-dashed curve = parametrisation of experimental data

63. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 63 Which is correct? How is the difference to be explained?

64. Craig Roberts: (3) Hadrons... as they really are 64 Nucleon and Δ elastic and transition form factors, Jorge Segovia, Ian C. Cloët, Craig D. Roberts and Sebastian M. Schmidt arXiv:1408.2919 [nucl-th], Few Body Syst. 55 (2014) pp. 1185-1222 arXiv:1408.2919 [nucl-th] Hadron Physics XIII: 22-27 Mar. 2015 (76pp)  DSE –Solid: M(p 2 ) result –Dashed: M constant  Dot-dashed = 2004 parametrisation of data

65.  DSE studies indicate that the proton has a very rich internal structure  The JLab data, obtained using the polarisaton transfer method, are an accurate indication of the behaviour of this ratio  The pre-1999 data (Rosenbluth) receive large corrections from so-called 2-photon exchange contributions Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 65 Proton plus proton-like resonances

66. Craig Roberts: (3) Hadrons... as they really are 66 Nucleon and Δ elastic and transition form factors, Jorge Segovia, Ian C. Cloët, Craig D. Roberts and Sebastian M. Schmidt arXiv:1408.2919 [nucl-th], Few Body Syst. 55 (2014) pp. 1185-1222 arXiv:1408.2919 [nucl-th] Hadron Physics XIII: 22-27 Mar. 2015 (76pp)  DSE: there is plainly a chance that G E can theoretically pass through zero  But, is a zero unavoidable?

67. Origin of the zero & its location  The Pauli form factor is a gauge of the distribution of magnetization within the proton. Ultimately, this magnetisation is carried by the dressed quarks and influenced by correlations amongst them, which are expressed in the Faddeev wave function.  If the dressed quarks are described by a momentum-independent mass function, M=constant, then they behave as Dirac particles with constant Dirac values for their magnetic moments and produce a hard Pauli form factor. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 67

68. Origin of the zero & its location  Alternatively, suppose that the dressed quarks possess a momentum-dependent mass function, M=M(p 2 ), which is large at infrared momenta but vanishes as their momentum increases.  At small momenta they will then behave as constituent-like particles with a large magnetic moment, but their mass and magnetic moment will drop toward zero as the probe momentum grows.  Such dressed quarks produce a proton Pauli form factor that is large for Q 2 ∼ 0 but drops rapidly on the domain of transition between nonperturbative and perturbative QCD, to give a very small result at large Q 2. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 68

69. Origin of the zero & its location  The precise form of the Q 2 dependence will depend on the evolving nature of the angular momentum correlations between the dressed quarks.  From this perspective, existence, and location if so, of the zero in μ p G Ep (Q 2 )/G Mp (Q 2 ) are a fairly direct measure of the location and width of the transition region between the nonperturbative and perturbative domains of QCD as expressed in the momentum dependence of the dressed-quark mass function.  Hard, M=constant → Soft, M=M(p 2 ) Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 69

70. Origin of the zero & its location  One can anticipate that a mass function which rapidly becomes partonic—namely, is very soft—will not produce a zero  We’ve seen that a constant mass function produces a zero at a small value of Q 2  And also seen and know that a mass function which resembles that obtained in the best available DSE studies and via lattice-QCD simulations produces a zero at a location that is consistent with extant data.  There is opportunity here for very constructive feedback between future experiments and theory. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 70

71. Visible Impacts of DCSB Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 71  Apparently small changes in M(p) within the domain 1<p(GeV)<3 have striking effect on the proton’s electric form factor  The possible existence and location of the zero is determined by behaviour of Q 2 F 2 p (Q 2 ), proton’s Pauli form factor  Like the pion’s PDA, Q 2 F 2 p (Q 2 ) measures the rate at which dressed- quarks become parton-like: F 2 p =0 for bare quark-partons Therefore, G E p can’t be zero on the bare-parton domain I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution, arXiv:1304.0855 [nucl-th]arXiv:1304.0855 [nucl-th], Phys. Rev. Lett. 111 (2013) 101803Phys. Rev. Lett. 111 (2013) 101803

72. Visible Impacts of DCSB Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 72 I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution, arXiv:1304.0855 [nucl-th]arXiv:1304.0855 [nucl-th], Phys. Rev. Lett. 111 (2013) 101803Phys. Rev. Lett. 111 (2013) 101803

73. Electric Charge  Proton: if one accelerates the rate at which the dressed-quark sheds its cloud of gluons to become a parton, then zero in G ep is pushed to larger Q 2  Opposite for neutron!  Explained by presence of diquark correlations Craig Roberts: (3) Hadrons... as they really are 73 J. Segovia, I.C. Cloët, C.D. Roberts, S.M. Schmidt: Nucleon and Δ Elastic and Transition Form Factors, arXiv:1408.2919 [nucl-th]arXiv:1408.2919 [nucl-th], Few Body Syst. 55 (2014) 1185 [on-line]on-line  These features entail that at x ≈ 5 the electric form factor of the neutral neutron will become larger than that of the unit-charge proton!  JLab12 will probe this prediction Hadron Physics XIII: 22-27 Mar. 2015 (76pp)

74. Craig Roberts: (3) Hadrons... as they really are 74

75.  QCD is the most interesting part of the Standard Model and Nature’s only example of an essentially nonperturbative fundamental theory  Dyson-Schwinger equations: o Exact results proved in QCD, amongst them: Quarks are not Dirac particles and gluons are nonperturbatively massive Dynamical chiral symmetry breaking is a fact. It’s responsible for 98% of the mass of visible matter in the Universe Goldstone’s theorem is fundamentally an expression of equivalence between the one-body problem and the two-body problem in the pseudoscalar channel Confinement is a dynamical phenomenon It cannot in principle be expressed via a potential The list goes on …  DSEs are a single framework, with IR model-input turned to advantage, “almost unique in providing an unambiguous path from a defined interaction → Confinement & DCSB → Masses → radii → form factors → distribution functions → etc.” Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 75 McLerran & Pisarski arXiv:0706.2191 [hep-ph]

76. Hadron Physics XIII: 22-27 Mar. 2015 (76pp) Craig Roberts: (3) Hadrons... as they really are 76