1. Observing Dynamical Chiral Symmetry Breaking Craig Roberts Physics Division

2. QCD’s Challenges  Dynamical Chiral Symmetry Breaking Very unnatural pattern of bound state masses; e.g., Lagrangian (pQCD) quark mass is small but... no degeneracy between J P =+ and J P =− (parity partners)  Neither of these phenomena is apparent in QCD’s Lagrangian Yet they are the dominant determining characteristics of real-world QCD.  Both will be important herein  QCD QCD – Complex behaviour arises from apparently simple rules. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 2  Quark and Gluon Confinement No matter how hard one strikes the proton, one cannot liberate an individual quark or gluon Understand emergent phenomena

3. Universal Truths SSpectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron's characterising properties amongst its QCD constituents. DDynamical Chiral Symmetry Breaking (DCSB) is most important mass generating mechanism for visible matter in the Universe. Higgs mechanism is ( almost ) irrelevant to light-quarks. RRunning of quark mass entails that calculations at even modest Q 2 require a Poincaré-covariant approach. Covariance requires existence of quark orbital angular momentum in hadron's rest-frame wave function. CConfinement is expressed through a violent change of the propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator. It is intimately connected with DCSB. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 3

4. Dyson-Schwinger Equations  Well suited to Relativistic Quantum Field Theory  Simplest level: Generating Tool for Perturbation Theory... Materially Reduces Model- Dependence … Statement about long-range behaviour of quark-quark interaction  NonPerturbative, Continuum approach to QCD  Hadrons as Composites of Quarks and Gluons  Qualitative and Quantitative Importance of:  Dynamical Chiral Symmetry Breaking – Generation of fermion mass from nothing  Quark & Gluon Confinement – Coloured objects not detected, Not detectable? Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 4  Approach yields Schwinger functions; i.e., propagators and vertices  Cross-Sections built from Schwinger Functions  Hence, method connects observables with long- range behaviour of the running coupling  Experiment ↔ Theory comparison leads to an understanding of long- range behaviour of strong running-coupling

5. Confinement  Quark and Gluon Confinement –No matter how hard one strikes the proton, or any other hadron, one cannot liberate an individual quark or gluon  Empirical fact. However –There is no agreed, theoretical definition of light-quark confinement –Static-quark confinement is irrelevant to real-world QCD There are no long-lived, very-massive quarks  Confinement entails quark-hadron duality; i.e., that all observable consequences of QCD can, in principle, be computed using an hadronic basis. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 5 X

6. Confinement  Confinement is expressed through a violent change in the analytic structure of propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator –Gribov (1978); Munczek (1983); Stingl (1984); Cahill (1989); Krein, Roberts & Williams (1992); … Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 6 complex-P 2 o Real-axis mass-pole splits, moving into pair(s) of complex conjugate poles or branch points o Spectral density no longer positive semidefinite & hence state cannot exist in observable spectrum Normal particle Confined particle

7. Dressed-gluon propagator  Gluon propagator satisfies a Dyson-Schwinger Equation  Plausible possibilities for the solution  DSE and lattice-QCD agree on the result –Confined gluon –IR-massive but UV-massless –m G ≈ 2-4 Λ QCD Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 7 perturbative, massless gluon massive, unconfined gluon IR-massive but UV-massless, confined gluon A.C. Aguilar et al., Phys.Rev. D80 (2009) 085018Phys.Rev. D80 (2009) 085018

8. S(p) … Dressed-quark propagator - nominally, a 1-body problem  Gap equation  D μν (k) – dressed-gluon propagator  Γ ν (q,p) – dressed-quark-gluon vertex Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 8

9. With QCD’s dressed-gluon propagator  What is the dressed-quark mass function? Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 9

10. 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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 10

11. 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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 11 DSE prediction of DCSB confirmed Mass from nothing!

12. 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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 12 Hint of lattice-QCD support for DSE prediction of violation of reflection positivity

13. 12GeV The Future of JLab 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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 13 Jlab 12GeV: Scanned by 2<Q 2 <9 GeV 2 elastic & transition form factors.

14. Dynamical Chiral Symmetry Breaking SStrong-interaction: Q CD CConfinement –E–Empirical fact –M–Modern theory and lattice-QCD support conjecture that light-quark confinement is real associated with violation of reflection positivity; i.e., novel analytic structure for propagators and vertices –S–Still circumstantial, no proof yet of confinement OOn the other hand, DCSB is a fact in QCD –I–It is the most important mass generating mechanism for visible matter in the Universe. Responsible for approximately 98% of the proton’s mass. Higgs mechanism is ( almost ) irrelevant to light-quarks. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 14

15. Strong-interaction: QCD  Gluons and quarks acquire momentum-dependent masses –characterised by an infrared mass-scale m ≈ 2-4 Λ QCD  Significant body of work, stretching back to 1980, which shows that, in the presence of DCSB, the dressed-fermion-photon vertex is materially altered from the bare form: γ μ. –Obvious, because with A(p 2 ) ≠ 1 and B(p 2 ) ≠ constant, the bare vertex cannot satisfy the Ward-Takahashi identity; viz.,  Number of contributors is too numerous to list completely (300 citations to 1 st J.S. Ball paper), but prominent contributions by: J.S. Ball, C.J. Burden, C.D. Roberts, R. Delbourgo, A.G. Williams, H.J. Munczek, M.R. Pennington, A. Bashir, A. Kizilersu, L. Chang, Y.-X. Liu … Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 15 Dressed-quark-gluon vertex

16.  Single most important feature –Perturbative vertex is helicity-conserving: Cannot cause spin-flip transitions –However, DCSB introduces nonperturbatively generated structures that very strongly break helicity conservation –These contributions Are large when the dressed-quark mass-function is large –Therefore vanish in the ultraviolet; i.e., on the perturbative domain –Exact form of the contributions is still the subject of debate but their existence is model-independent - a fact. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 16

17. Gap Equation General Form  D μν (k) – dressed-gluon propagator  good deal of information available  Γ ν (q,p) – dressed-quark-gluon vertex  Information accumulating  Straightforward to insert Ansatz for Γ ν (q,p) into gap equation & from the solution obtain values for –in-pion condensate –estimate of pion’s leptonic decay constant  However, there’s a little more than that to hadron physics Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 17 Many are still doing only this

18. Gap Equation General Form  D μν (k) – dressed-gluon propagator  Γ ν (q,p) – dressed-quark-gluon vertex  Until 2009, all studies of other hadron phenomena used the leading-order term in a symmetry-preserving truncation scheme; viz., –D μν (k) = dressed, as described previously –Γ ν (q,p) = γ μ … plainly, key nonperturbative effects are missed and cannot be recovered through any step-by-step improvement procedure Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 18 Bender, Roberts & von Smekal Phys.Lett. B380 (1996) 7-12

19. Gap Equation General Form  D μν (k) – dressed-gluon propagator  good deal of information available  Γ ν (q,p) – dressed-quark-gluon vertex  Information accumulating  Suppose one has in hand – from anywhere – the exact form of the dressed-quark-gluon vertex What is the associated symmetry- preserving Bethe-Salpeter kernel?! Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 19 If kernels of Bethe-Salpeter and gap equations don’t match, one won’t even get right charge for the pion.

20. Bethe-Salpeter Equation Bound-State DSE  K(q,k;P) – fully amputated, two-particle irreducible, quark-antiquark scattering kernel  Textbook material.  Compact. Visually appealing. Correct Blocked progress for more than 60 years. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 20

21. Bethe-Salpeter Equation General Form  Equivalent exact bound-state equation but in this form K(q,k;P) → Λ(q,k;P) which is completely determined by dressed-quark self-energy  Enables derivation of a Ward-Takahashi identity for Λ(q,k;P) Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 21 Lei Chang and C.D. Roberts 0903.5461 [nucl-th] Phys. Rev. Lett. 103 (2009) 081601

22. Ward-Takahashi Identity Bethe-Salpeter Kernel  Now, for first time, it’s possible to formulate an Ansatz for Bethe-Salpeter kernel given any form for the dressed-quark-gluon vertex by using this identity  This enables the identification and elucidation of a wide range of novel consequences of DCSB Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 22 Lei Chang and C.D. Roberts 0903.5461 [nucl-th] Phys. Rev. Lett. 103 (2009) 081601 iγ5iγ5 iγ5iγ5

23. Dressed-quark anomalous magnetic moments  Three strongly-dressed and essentially- nonperturbative contributions to dressed-quark-gluon vertex: Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 23 DCSB Ball-Chiu term Vanishes if no DCSB Appearance driven by STI Anom. chrom. mag. mom. contribution to vertex Similar properties to BC term Strength commensurate with lattice-QCD Skullerud, Bowman, Kizilersu et al. hep-ph/0303176 L. Chang, Y. –X. Liu and C.D. Roberts arXiv:1009.3458 [nucl-th] arXiv:1009.3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001

24. Dressed-quark anomalous chromomagnetic moment  Lattice-QCD –m = 115 MeV  Nonperturbative result is two orders-of-magnitude larger than the perturbative computation –This level of magnification is typical of DCSB –cf. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 24 Skullerud, Kizilersu et al. JHEP 0304 (2003) 047 Prediction from perturbative QCD Quenched lattice-QCD Quark mass function: M(p 2 =0)= 400MeV M(p 2 =10GeV 2 )=4 MeV

25. Dressed-quark anomalous magnetic moments  Three strongly-dressed and essentially- nonperturbative contributions to dressed-quark-gluon vertex: Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 25 DCSB Ball-Chiu term Vanishes if no DCSB Appearance driven by STI Anom. chrom. mag. mom. contribution to vertex Similar properties to BC term Strength commensurate with lattice-QCD Skullerud, Bowman, Kizilersu et al. hep-ph/0303176 Role and importance is novel discovery Essential to recover pQCD Constructive interference with Γ 5 L. Chang, Y. –X. Liu and C.D. Roberts arXiv:1009.3458 [nucl-th] arXiv:1009.3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001

26. Dressed-quark anomalous magnetic moments Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 26  Formulated and solved general Bethe-Salpeter equation  Obtained dressed electromagnetic vertex  Confined quarks don’t have a mass-shell o Can’t unambiguously define magnetic moments o But can define magnetic moment distribution MEME κ ACM κ AEM Full vertex0.44-0.220.45 Rainbow-ladder0.3500.048  AEM is opposite in sign but of roughly equal magnitude as ACM L. Chang, Y. –X. Liu and C.D. Roberts arXiv:1009.3458 [nucl-th] arXiv:1009.3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001 Factor of 10 magnification

27. Dressed-quark anomalous magnetic moments Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 27  Potentially important for elastic and transition form factors, etc.  Significantly, also quite possibly for muon g-2 – via Box diagram, which is not constrained by extant data. L. Chang, Y. –X. Liu and C.D. Roberts arXiv:1009.3458 [nucl-th] arXiv:1009.3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001 Factor of 10 magnification  Formulated and solved general Bethe-Salpeter equation  Obtained dressed electromagnetic vertex  Confined quarks don’t have a mass-shell o Can’t unambiguously define magnetic moments o But can define magnetic moment distribution Contemporary theoretical estimates: 1 – 10 x 10 -10 Largest value reduces discrepancy expt.↔theory from 3.3σ to below 2σ.

28. DSEs and 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 observation that an interaction which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channel Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 28 R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145 r qq ≈ r π

29. 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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 29 R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145 diquark quark quark exchange ensures Pauli statistics composed of strongly- dressed quarks bound by dressed-gluons

30. Photon-nucleon current  Composite nucleon must interact with photon via nontrivial current constrained by Ward-Takahashi identities  DSE, BSE, Faddeev equation, current → nucleon form factors Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 30 Vertex contains dressed-quark anomalous magnetic moment Oettel, Pichowsky, Smekal Eur.Phys.J. A8 (2000) 251-281

31. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 31 I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th]  Highlights again the critical importance of DCSB in explanation of real-world observables.  DSE result Dec 08 DDSE result – including the anomalous magnetic moment distribution I.C. Cloët, C.D. Roberts, et al. In progress

32. Unification of Meson & Baryon Spectra  Correlate the masses 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; and 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 & certainly not with QCD  not symmetry-preserving & therefore cannot veraciously connect meson and baryon properties Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 32

33. Faddeev Equation Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 33 quark-quark scattering matrix - pole-approximation used to arrive at Faddeev-equation o Nucleon states, combination of J=0 and J=1 diquarks o Δ-states, much simpler … only J=1 diquarks

34. Baryons & diquarks Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 34  Provided numerous insights into baryon structure; e.g.,  There is a causal connection between m Δ - m N & m 1+ - m 0+ m Δ - m N mNmN mΔmΔ Physical splitting grows rapidly with increasing diquark mass difference H.L.L. Roberts et al., Masses of ground and excited-state hadronsMasses of ground and excited-state hadrons 1101.4244 [nucl-th], Few Body Syst. 51 (2011) pp. 1-25; DOI:10.1007/s00601-011-0225-x

35. Baryons & diquarks Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 35  Provided numerous insights into baryon structure; e.g.,  m N ≈ 3 M & m Δ ≈ M+m 1+

36. Baryon Spectrum Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 36  Our predictions for baryon dressed-quark-core masses match the bare-masses determined by Jülich with a rms-relative-error of 10%.  Notably, however, we find a quark-core to the Roper resonance, whereas within the Jülich coupled-channels model this structure in the P 11 partial wave is unconnected with a bare three-quark state. H.L.L. Roberts et al., to appear Few Body Syst., 1101.4244 [nucl-th] Masses of ground and excited-state hadrons

37. Baryon Spectrum Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 37 IIn connection with EBAC's analysis, our predictions for the bare- masses agree within a rms-relative-error of 14%. NNotably, EBAC does find a dressed-quark-core for the Roper resonance, at a mass which agrees with our prediction. H.L.L. Roberts et al., to appear Few Body Syst., 1101.4244 [nucl-th] Masses of ground and excited-state hadrons

38. 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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 38 N. Suzuki et al., Phys.Rev.Lett. 104 (2010) 042302Phys.Rev.Lett. 104 (2010) 042302

39. Hadron Spectrum Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 39 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?!

40. Next steps …  In Hand … A documented comparison between the electromagnetic form factors of mesons and those diquarks which play a material role in nucleon structure.  In position to complete reference M=constant computation of nucleon elastic form factors & nucleon → Roper transition form factor  Compare with existing calculations of elastic form factors using M=M(p 2 )  Compute M=M(p 2 ) nucleon → Roper transition form factors  Identify those signals in these observables that are unambiguously related to QCD-behaviour of M=M(p 2 ) Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 40

41. Epilogue  Dynamical chiral symmetry breaking (DCSB) – mass from nothing for 98% of visible matter – is a reality o Expressed in M(p 2 ), with observable signals in experiment  Poincaré covariance Crucial in description of contemporary data  Fully-self-consistent treatment of an interaction Essential if experimental data is truly to be understood.  Dyson-Schwinger equations: o single framework, with IR model-input turned to advantage, “almost unique in providing unambiguous path from a defined interaction → Confinement & DCSB → Masses → radii → form factors → distribution functions → etc.” Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs 41 McLerran & Pisarski arXiv:0706.2191 [hep-ph] Confinement is almost Certainly the origin of DCSB e.g., BaBar anomaly