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Craig Roberts Physics Division

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1.Rocio BERMUDEZ (U Michoácan); 2.Xiomara GUTIERREZ-GUERRERO (U Michoácan); 3.S. HERNÁNDEZ (U Michoácan); 4.Trang NGUYEN (KSU); 5.Khépani RAYA (U Michoácan); 6.Hannes ROBERTS (ANL, FZJ, UBerkeley); 7.Chien-Yeah SENG (UW-Mad) 8.Kun-lun WANG (PKU); 9.Chen CHEN (USTC, ANL); 10.J. Javier COBOS-MARTINEZ (U.Sonora); 11.Mario PITSCHMANN (Vienna); 12.Si-xue QIN (PKU, U. Frankfurt am Main); 13.Jorge SEGOVIA (ANL); 14.David WILSON (ODU); 15.Lei CHANG (PKU, U.Adelaide); 16.Ian CLOËT (ANL); 17.Bruno EL-BENNICH (São Paulo); 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 2 18.Adnan BASHIR (U Michoácan); 19.Stan BRODSKY (SLAC); 20.Gastão KREIN (São Paulo) 21.Roy HOLT (ANL); 22.Mikhail IVANOV (Dubna); 23.Yu-xin LIU (PKU); 24.Michael RAMSEY-MUSOLF (UW-Mad) 25.Alfredo RAYA (U Michoácan); 26.Sebastian SCHMIDT (IAS-FZJ & JARA); 27.Robert SHROCK (Stony Brook); 28.Peter TANDY (KSU); 29.Tony THOMAS (U.Adelaide) 30.Shaolong WAN (USTC) Students Postdocs Asst. Profs.

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 3 Pretend from now on that I am a vegetarian with a pony-tail, who was born in Australia and enjoys Belgian beer.

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 4

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Exploit opportunities provided by new data on hadron elastic and transition form factors –Chart infrared evolution of QCD’s coupling and dressed-masses –Reveal correlations that are key to baryon structure –Expose facts & fallacies in modern descriptions of hadron structure 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 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 5

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 6

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Very likely a self-contained, nonperturbatively renormalisable and hence well defined Quantum Field Theory This is not true of QED – cannot be defined nonperturbatively No confirmed breakdown over an enormous energy domain: 0 GeV < E < 8 TeV Increasingly likely that any extension of the Standard Model will be based on the paradigm established by QCD –Extended Technicolour: electroweak symmetry breaks via a fermion bilinear operator in a strongly-interacting non-Abelian theory. ( Andersen et al. “Discovering Technicolor” Eur.Phys.J.Plus 126 (2011) 81 )Eur.Phys.J.Plus 126 (2011) 81 Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg- Landau theory of superconductivity 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 7

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Contrast: so-called Effective Field Theories EFTs applicable over a very restricted energy domain; e.g., ChPT known to breakdown for E > 2m π Can be used to help explore how features of QCD influence observables 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 8 QCD appears valid at all energy scales that have been tested so far: no breakdown below E ≈ m π Cannot be used to test QCD Any mismatch between EF-Theory and experiment owes to an error in the formulation of one or conduct of the other CanCannot

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 9

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Light quarks & Confinement A unit area placed midway between the quarks and perpendicular to the line connecting them intercepts a constant number of field lines, independent of the distance between the quarks. This leads to a constant force between the quarks – and a large force at that, equal to about 16 metric tons.” 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 10 Folklore … Hall-D Conceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes.

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Light quarks & Confinement Problem: 16 tonnes of force makes a lot of pions. 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 11

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Light quarks & Confinement Problem: 16 tonnes of force makes a lot of pions. 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 12

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Light quarks & Confinement In the presence of light quarks, pair creation seems to occur non-localized and instantaneously No flux tube in a theory with light- quarks. Flux-tube is not the correct paradigm for confinement in hadron physics 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 13 G. Bali et al., PoS LAT2005 (2006) 308PoS LAT2005 (2006) 308

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Confinement QFT Paradigm: –Confinement is expressed through a dramatic change in the analytic structure of propagators for coloured states –It can almost be read from a plot of the dressed- propagator for a coloured state 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 14 complex-P 2 o Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities, (or other qualitatively analogous structures chracterised by a dynamically generated mass-scale) o State described by rapidly damped wave & hence state cannot exist in observable spectrum Normal particle Confined particle timelike axis: P 2 <0 s ≈ 1/Im(m) ≈ 1/2Λ QCD ≈ ½fm

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1st Sino-Americas Workshop and School on the Bound- State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 15

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1st Sino-Americas Workshop and School on the Bound- State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 16

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Dynamical Chiral Symmetry Breaking DCSB is a fact in QCD –Dynamical, not spontaneous Add nothing to QCD, no Higgs field, nothing! Effect achieved purely through the quark+gluon dynamics. –It’s the most important mass generating mechanism for visible matter in the Universe. Responsible for ≈98% of the proton’s mass. Higgs mechanism is ( almost ) irrelevant to light-quarks. –Just like gluons and quarks, and for the same reasons, condensates are confined within hadrons. There are no vacuum condensates. 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 17 Confinement contains condensates, S.J. Brodsky, C.D. Roberts, R. Shrock and P.C. Tandy, arXiv: [nucl-th], Phys. Rev. C85 (2012) arXiv: [nucl-th]Phys. Rev. C85 (2012)

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DCSB 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 18 Mass from nothing! 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) AIP Conf.Proc. 842 (2006) In QCD, all “constants” of quantum mechanics are actually strongly momentum dependent: couplings, number density, mass, etc. So, a quark’s mass depends on its momentum. Mass function can be calculated and is depicted here. Continuum- and Lattice-QCD are in agreement: the vast bulk of the light-quark mass comes from a cloud of gluons, dragged along by the quark as it propagates.

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Where does the mass come from? Deceptively simply picture Corresponds to the sum of a countable infinity of diagrams. NB. QED has 12,672 α 5 diagrams Impossible to compute this in perturbation theory. The standard algebraic manipulation tools are just inadequate 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 19 α S 23

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 20

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Bound-states in Quantum Field Theory Mass and “Wave Function” are obtained from a Bethe- Salpeter equation –Generalisation of the Lippmann-Schwinger equation The pion … Nature’s strong-interaction messenger … is a critical example 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 21 Sketching the Bethe-Salpeter kernel, Lei Chang and Craig D. Roberts, arXiv: [nucl-th], Phys. Rev. Lett. 103 (2009) (4 pages) arXiv: [nucl-th]Phys. Rev. Lett. 103 (2009) (4 pages)

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Pion’s Goldberger -Treiman relation Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 22 Pion’s Bethe-Salpeter amplitude Solution of the Bethe-Salpeter equation Dressed-quark propagator Axial-vector Ward-Takahashi identity entails Pseudovector components necessarily nonzero. Cannot be ignored! Exact in Chiral QCD 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Miracle: two body problem solved, almost completely, once solution of one body problem is known Maris, Roberts and Tandy nucl-th/ nucl-th/ , Phys.Lett. B420 (1998)

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Dichotomy of the pion Goldstone mode and bound-state Goldstone’s theorem has a pointwise expression in QCD; Namely, in the chiral limit the wave-function for the two- body bound-state Goldstone mode is intimately connected with, and almost completely specified by, the fully-dressed one-body propagator of its characteristic constituent The one-body momentum is equated with the relative momentum of the two-body system 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 23

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The quark level Goldberger-Treiman relation shows that DCSB has a very deep and far reaching impact on physics within the strong interaction sector of the Standard Model; viz., Goldstone's theorem is fundamentally an expression of equivalence between the one-body problem and the two-body problem in the pseudoscalar channel. This emphasises that Goldstone's theorem has a pointwise expression in QCD Hence, pion properties are an almost direct measure of the dressed-quark mass function. Thus, enigmatically, the properties of the massless pion are the cleanest expression of the mechanism that is responsible for almost all the visible mass in the universe. 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 24

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In QCD, Gluons, too, become massive Not just quarks … Gluons also have a gap equation … 1/k 2 behaviour signals essential singularity in the running coupling: Impossible to reach in perturbation theory 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 25 Interaction model for the gap equation Si-xue Qin, Lei Chang, Y.-x.Liu, C.D. Roberts and D.J. Wilson arXiv: [nucl-th], Phys. Rev. C 84 (2011) (R) [5 pages] arXiv: [nucl-th]Phys. Rev. C 84 (2011) (R) [5 pages]

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1st Sino-Americas Workshop and School on the Bound- State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 26 Valence quarks

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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 Sea-quark distributions –Flavour content, asymmetry, intrinsic: yes or no? Answers are essentially nonperturbative features of QCD 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 27

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Parton Structure of Hadrons Need for calculation is emphasised by Saga of pion’s valence-quark distribution: o 1989: u v π ~ (1-x) 1 – inferred from LO-Drell-Yan & disagrees with QCD; o 2001: DSE- QCD predicts u v π ~ (1-x) 2 argues that distribution inferred from data can’t be correct; 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 28 Valence quark distributions in the pion, M.B. Hecht, Craig D. Roberts, S.M. Schmidt, nucl- th/ , Phys.Rev. C63 (2001) nucl- th/ Phys.Rev. C63 (2001)

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Parton Structure of Hadrons Need for calculation is emphasised by Saga of pion’s valence-quark distribution: o 1989: u v π ~ (1-x) 1 – inferred from LO-Drell-Yan & disagrees with QCD; o 2001: DSE- QCD predicts u v π ~ (1-x) 2 argues that distribution inferred from data can’t be correct; o 2010: NLO reanalysis including soft-gluon resummation, inferred distribution agrees with DSE and QCD 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 29 Soft-gluon resummation and the valence parton distribution function of the pion, M. Aicher, A. Schafer, W. Vogelsang, Phys.Rev.Lett. 105 (2010) , arXiv: [hep-ph] Phys.Rev.Lett. 105 (2010) arXiv: [hep-ph] Valence quark distributions in the pion, M.B. Hecht, Craig D. Roberts, S.M. Schmidt, nucl- th/ , Phys.Rev. C63 (2001) nucl- th/ Phys.Rev. C63 (2001)

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1st Sino-Americas Workshop and School on the Bound- State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 30

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Pion’s valence-quark Distribution Amplitude Developed DSE methods to compute φ π (x) = 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=0.3 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 31 Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv: [nucl-th], Phys. Rev. Lett. 110 (2013) (2013) [5 pages].arXiv: [nucl-th] Phys. Rev. Lett. 110 (2013) (2013) [5 pages]

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Pion’s valence-quark Distribution Amplitude Both kernels agree: marked broadening of φ π (x), which owes to DCSB 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 32 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: [nucl-th], Phys. Rev. Lett. 110 (2013) (2013) [5 pages].arXiv: [nucl-th] Phys. Rev. Lett. 110 (2013) (2013) [5 pages]

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Pion’s valence-quark Distribution Amplitude Both kernels agree: marked broadening of φ π (x), which owes to DCSB 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 33 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: [nucl-th], Phys. Rev. Lett. 110 (2013) (2013) [5 pages].arXiv: [nucl-th] Phys. Rev. Lett. 110 (2013) (2013) [5 pages]

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Pion’s valence-quark Distribution Amplitude 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 34 Established a one-to-one connection between DCSB and the pointwise form of the pion’s wave function. Dilation measures the rate at which dressed-quark approaches the asymptotic bare-parton limit Experiments at JLab12 can empirically verify the behaviour of M(p), and hence chart the IR limit of QCD C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50Prog. Part. Nucl. Phys. 61 (2008) 50 Dilation of pion’s wave function is measurable in pion’s electromagnetic form factor at JLab12 A-rated: E E Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv: [nucl-th], Phys. Rev. Lett. 110 (2013) (2013) [5 pages].arXiv: [nucl-th] Phys. Rev. Lett. 110 (2013) (2013) [5 pages]

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1st Sino-Americas Workshop and School on the Bound- State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 35

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Valence-quark Distribution Amplitudes of light-quark mesons from lattice-QCD PDA Moments from lattice-QCD Best available results show no distinction between pseudoscalar and vector, nor between light-front parallel and perpendicular polarisations DSE studies underway: Shi-chao, Peter Tandy et al. 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 36 R. Arthur et al., Phys.Rev. D83 (2011) 07450Phys.Rev. D83 (2011) 07450

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Valence-quark Distribution Amplitudes of light-quark mesons from lattice-QCD 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 37 Reconstruct PDAs using method described in Pion distribution amplitude from lattice- QCD, I. C. Cloët, L. Chang, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv: [nucl- th], Phys. Rev. Lett. 111 (2013) [5 pages]arXiv: [nucl- th]Phys. Rev. Lett. 111 (2013) [5 pages] SU(3) breaking is measured by shift in peak: ratio =1.09 x max =0.545 for φ K (x max ) cf. x max =φ π (½) for φ π (x) cf. ratio of 1.15 for peak of [x s v K (x max )]/[x u v K (x max )] φ π ~ x α (1-x) α α= = = 0.11 φ π ~ x α (1-x) β α=0.39±0.10 β=0.47 -/ Lei Chang et al. In progress.

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When is asymptotic PDA valid? PDA is a wave function not directly observable but PDF is. φ π asy (x) can only be a good approximation to the pion's PDA when it is accurate to write u v π (x) ≈ δ(x) for the pion's valence- quark distribution function. This is far from valid at currently accessible scales 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 38 Q 2 =27 GeV 2 This is not δ(x)! Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. Roberts

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When is asymptotic PDA valid? When is asymptopia reached? If u v π (x) ≈ δ(x), then = ∫ 0 1 dx x u v π (x) = 0; i.e., the light-front momentum fraction carried by valence-quarks is ZERO Asymptopia is reached when is “small” As usual, the computed valence-quark distribution produces (π = u+d bar ) 2 2GeV = 44% When is small? 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 39 Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. Roberts NLO evolution of PDF, computation of. Even at LHC energies, light-front fraction of the π momentum: dressed valence-quarks = 25% glue = 54%, sea-quarks = 21% LHC: 16TeV Evolution in QCD is LOGARITHMIC JLab 2GeV

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When is asymptotic PDA valid? When is asymptopia reached? If u v π (x) ≈ δ(x), then = ∫ 0 1 dx x u v π (x) = 0; i.e., the light-front momentum fraction carried by valence-quarks is ZERO Asymptopia is reached when is “small” As usual, the computed valence-quark distribution produces (π = u+d bar ) 2 2GeV = 44% When is small? 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 40 Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. Roberts NLO evolution of PDF, computation of. Even at LHC energies, light-front fraction of the π momentum: dressed valence-quarks = 25% glue = 54%, sea-quarks = 21% LHC: 16TeV Evolution in QCD is LOGARITHMIC JLab 2GeV

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At the “Planck scale” 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 41 Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. Roberts Evolution in QCD is LOGARITHMIC In the truly asymptotic domain, way, way beyond LHC energy scales, gluons and sea- quarks share the momentum of a hadron, each with roughly 50% of the momentum

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 42

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1st Sino-Americas Workshop and School on the Bound- State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 43

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 44 Single interaction kernel, determined by just 1 parameter and preserving the one-loop RG- behaviour of QCD, had unified F π (Q 2 ) and φ π (x) (and many other quantities) However, using brute-force numerical techniques it was impossible to proceed reliably beyond Q 2 =4GeV 2 DSE 2013 pQCD obtained with φ π asy (x) pQCD obtained with φ π (x;2GeV), i.e., the PDA appropriate to the scale of the experiment 15% DSE 2000

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 45

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 46 Single interaction kernel, determined by just 1 parameter and preserving the one-loop RG- behaviour of QCD, has unified F π (Q 2 ) and φ π (x) (and many other quantities) Prediction of pQCD obtained when the pion valence-quark PDA has the form appropriate to the scale accessible in modern experiments is markedly different from the result obtained using the asymptotic PDA Pion electromagnetic form factor at spacelike momenta, Lei Chang et al. arXiv: [nucl-th],arXiv: [nucl-th] Phys. Rev. Lett. 111 (2013) [5 pages]Phys. Rev. Lett. 111 (2013) [5 pages] DSE 2013 pQCD obtained with φ π asy (x) pQCD obtained with φ π (x;2GeV), i.e., the PDA appropriate to the scale of the experiment 15% Near agreement between the pertinent perturbative QCD prediction and DSE-2013 prediction is striking. Dominance of hard contributions to the pion form factor for Q 2 >8GeV 2. Normalisation is fixed by a pion wave-function whose dilation with respect to φ π asy (x) is a definitive signature of DCSB

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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 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 47 R.T. Cahill et al., Austral. J. Phys. 42 (1989) SU c (3):

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Remarks Diquark correlations are not inserted by hand Such correlations are a dynamical consequence of strong- coupling in QCD The same mechanism that produces an almost massless pion from two dynamically-massive quarks; i.e., DCSB, forces a strong correlation between two quarks in colour-antitriplet channels within a baryon – an indirect consequence of Pauli-Gürsey symmetry Diquark correlations are not pointlike –Typically, r 0+ ~ r π & r 1+ ~ r ρ (actually 10% larger) –They have soft form factors 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 48 SU(2) isospin symmetry of hadrons might emerge from mixing half-integer spin particles with their antiparticles. Faddeev Equation

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Nucleon Structure Probed in scattering experiments Electron is a good probe because it is structureless Electron’s relativistic current is Proton’s electromagnetic current 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 49 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

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Structure of Hadrons Elastic form factors –Provide vital information about the structure and composition of the most basic elements of nuclear physics. –They are a measurable and physical manifestation of the nature of the hadrons' constituents and the dynamics that binds them together. Accurate form factor data are driving paradigmatic shifts in our pictures of hadrons and their structure; e.g., –role of orbital angular momentum and nonpointlike diquark correlations –scale at which p-QCD effects become evident –strangeness content –meson-cloud effects –etc. 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 50

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Flavor separation of proton form factors Very different behavior for u & d quarks Means apparent scaling in proton F2/F1 is purely accidental 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 51 Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 (2011) Q4F2q/Q4F2q/ Q 4 F 1 q

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Diquark correlations! Poincaré covariant Faddeev equation –Predicts scalar and axial-vector diquarks Proton's singly-represented d-quark more likely to be struck in association with 1 + diquark than with 0 + –form factor contributions involving 1 + diquark are softer 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 52 Cloët, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36 Few Body Syst. 46 (2009) pp.1-36 Wilson, Cloët, Chang, Roberts, PRC 85 (2012) Doubly-represented u-quark is predominantly linked with harder 0 + diquark contributions Interference produces zero in Dirac form factor of d-quark in proton –Location of the zero depends on the relative probability of finding 1 + & 0 + diquarks in proton –Correlated, e.g., with valence d/u ratio at x=1 d u =Q 2 /M 2

53 Visible Impacts of DCSB 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 53 Apparently small changes in M(p) within the domain 1

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Visible Impacts of DCSB 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 54 I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution, arXiv: [nucl- th], Phys. Rev. Lett. 111 (2013) arXiv: [nucl- th]Phys. Rev. Lett. 111 (2013)

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 55

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Far valence domain x ≃ 1 Endpoint of the far valence domain: x ≃ 1, is especially significant –All familiar PDFs vanish at x=1; but ratios of any two need not –Under DGLAP evolution, the value of such a ratio is invariant. Thus, e.g., –lim x→1 d v (x)/u v (x) is unambiguous, scale invariant, nonperturbative feature of QCD. keen discriminator between frameworks that claim to explain nucleon structure. Furthermore, Bjorken-x=1 corresponds strictly to the situation in which the invariant mass of the hadronic final state is precisely that of the target; viz., elastic scattering. Structure functions inferred experimentally on x ≃ 1 are determined theoretically by target's elastic form factors. 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 56 Nucleon spin structure at very high-x Craig D. Roberts, Roy J. Holt and Sebastian M. Schmidt arXiv: [nucl-th], Phys. Lett. B in press arXiv: [nucl-th]

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Neutron Structure Function at high-x Valence-quark distributions at x=1 –Fixed point under DGLAP evolution –Strong discriminator between theories Algebraic formula –P 1 p,s = contribution to the proton's charge arising from diagrams with a scalar diquark component in both the initial and final state –P 1 p,a = kindred axial-vector diquark contribution –P 1 p,m = contribution to the proton's charge arising from diagrams with a different diquark component in the initial and final state. 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 57 I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th]arXiv: [nucl-th], Few Body Syst. 46 (2009) 1-36Few Body Syst. 46 (2009) 1-36 D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts arXiv: [nucl-th]arXiv: [nucl-th], Phys. Rev. C85 (2012) [21 pages]Phys. Rev. C85 (2012) [21 pages] Measures relative strength of axial-vector/scalar diquarks in proton

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Neutron Structure Function at high-x 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 58 d/u=1/2 SU(6) symmetry pQCD, uncorrelated Ψ 0 + qq only, d/u=0 Deep inelastic scattering – the Nobel-prize winning quark-discovery experiments Reviews: S. Brodsky et al. NP B441 (1995) W. Melnitchouk & A.W.Thomas PL B377 (1996) 11 N. Isgur, PRD 59 (1999) R.J. Holt & C.D. Roberts RMP (2010) d/u=0.28 DSE: “realistic” Distribution of neutron’s momentum amongst quarks on the valence-quark domain DSE: “contact” d/u=0.18 Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) x>0.9 Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th]arXiv: [nucl-th], Few Body Syst. 46 (2009) 1-36Few Body Syst. 46 (2009) 1-36 D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts arXiv: [nucl-th]arXiv: [nucl-th], Phys. Rev. C85 (2012) [21 pages]Phys. Rev. C85 (2012) [21 pages]

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Neutron Structure Function at high-x 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 59 d/u=1/2 SU(6) symmetry pQCD, uncorrelated Ψ 0 + qq only, d/u=0 Deep inelastic scattering – the Nobel-prize winning quark-discovery experiments Reviews: S. Brodsky et al. NP B441 (1995) W. Melnitchouk & A.W.Thomas PL B377 (1996) 11 N. Isgur, PRD 59 (1999) R.J. Holt & C.D. Roberts RMP (2010) d/u=0.28 DSE: “realistic” Distribution of neutron’s momentum amongst quarks on the valence-quark domain DSE: “contact” d/u=0.18 Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) x>0.9 Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) I.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th]arXiv: [nucl-th], Few Body Syst. 46 (2009) 1-36Few Body Syst. 46 (2009) 1-36 D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts arXiv: [nucl-th]arXiv: [nucl-th], Phys. Rev. C85 (2012) [21 pages]Phys. Rev. C85 (2012) [21 pages]

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Neutron Structure Function at high-x “While it is quite hazardous to extrapolate from our limited x B range all the way to x B = 1, these results appear to disfavor models of the proton with d/u=0 at x B = 1” 1st Sino-Americas Workshop and School on the Bound- State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 60 Short Range Correlations and the EMC Effect, L.B. Weinstein et al., Phys.Rev.Lett. 106 (2011) , arXiv: [hep-ph]Phys.Rev.Lett. 106 (2011) arXiv: [hep-ph] Figure courtesy of D.W. Higinbotham Observation: EMC effect measured in electron DIS at

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Nucleon spin structure at very high x 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 61 Similar formulae for nucleon longitudinal structure functions. Plainly, existing data cannot distinguish between modern pictures of nucleon structure Empirical results for nucleon longitudinal spin asymmetries on x ≃ 1 promise to add greatly to our capacity for discriminating between contemporary pictures of nucleon structure. NB. pQCD is actually model-dependent: assumes SU(6) spin-flavour wave function for the proton's valence-quarks and the corollary that a hard photon may interact only with a quark that possesses the same helicity as the target. Nucleon spin structure at very high-x Craig D. Roberts, Roy J. Holt and Sebastian M. Schmidt arXiv: [nucl-th], Phys. Lett. B in press arXiv: [nucl-th]

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Tensor Charge: σ μν current h 1T = distribution of transversely polarized quarks inside a transversely polarised proton δq = Light-front number-density of quarks with transverse polarisation parallel to that of the proton minus that of quarks with transverse polarisation antiparallel –Bias in quark polarisation induced by polarisation of parent proton Value of tensor charge places constraints on some extensions of the Standard Model PRD85 (2012) > Current knowledge of transversity: COMPASS, JLab No gluon transversity distribution => transversity is suppressed at low-x, so large-x behavior important => JLab12 a useful tool. So, transversity will be measured at JLab12 (Hall-A E SIDIS; CLAS12; and SoLID) 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 62 Direction of motion

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Tensor Charge: σ μν current 1.Jlab 12 Projection 2.Anselmino et al., [hep-ph] [hep-ph] 3.Pitschmann et al. (DSE) (2013) [including axial-vector diquarks but contact interaction] 4.Hecht et al. (DSE), PRC64 (2001) [only scalar diquarks] PRC64 (2001) Cloët et al., PLB659 (2008) 214PLB659 (2008) Pasquini et al., PRD76 (2007) PRD76 (2007) Wakamatsu, PLB653 (2007) 398PLB653 (2007) Gockeler et al., PLB627 (2005) 113PLB627 (2005) Gamberg et al., PRL 87 (2001) PRL 87 (2001) He et al., PRD52 (1995) 2960PRD52 (1995) Bacchetta et al., JHEP 1303 (2013) 119JHEP 1303 (2013) 119 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 63 Direction of motion Big shift from including axial- vector diquark correlations? d-quark can now be unpaired.

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Theory Lattice-QCD –Significant progress in the last five years –This must continue Bound-state problem in continuum quantum field theory –Significant progress, too –This must continue First Sino-Americas School & Workshop on the Continuum Bound-State Problem, Hefei, China. First Sino-Americas School & Workshop on the Continuum Bound-State Problem 22-26/Oct./2013 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 64

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 65

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 66

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 67

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Lattice comparison Pion’s valence-quark PDA Employ the generalised-Gegenbauer method described previously (and in Phys. Rev. Lett. 110 (2013) (2013) [5 pages] ). Phys. Rev. Lett. 110 (2013) (2013) [5 pages] 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 68 Lattice-QCD => one nontrivial moment: = 0.27 ± 0.04 Legend Solid = DB (Best) DSE Dashed = RL DSE Dotted (black) = 6 x (1-x) Dot-dashed = midpoint lattice; and the yellow shading exhibits band allowed by lattice errors φ π ~ x α (1-x) α α= = = 0.11 DB α=0.31 but 10% a 2 <0 RL α=0.29 and 0% a 2 V. Braun et al., PRD 74 (2006) Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv: [nucl-th], Phys. Rev. Lett. 111 (2013) [5 pages]arXiv: [nucl-th]Phys. Rev. Lett. 111 (2013) [5 pages]

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When is asymptotic PDA valid? Under leading-order evolution, the PDA remains broad to Q 2 >100 GeV 2 Feature signals persistence of the influence of dynamical chiral symmetry breaking. 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 69 Consequently, the asymptotic distribution, φ π asy (x), is a poor approximation to the pion's PDA at all such scales that are either currently accessible or foreseeable in experiments on pion elastic and transition form factors. Thus, related expectations based on φ π asy (x) should be revised. asymptotic 4 GeV GeV 2 Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv: [nucl-th], Phys. Rev. Lett. 111 (2013) [5 pages]arXiv: [nucl-th]Phys. Rev. Lett. 111 (2013) [5 pages]

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Flavor separation of proton form factors Visible Impacts of DCSB 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 70 Effect driven primarily by electric form factor of doubly-represented u-quark u-quark is 4-times more likely than d-quark to be involved in hard interaction So … G Ep u ≈ G Ep Singly-represented d-quark is usually sequestered inside a soft diquark correlation So, although it also becomes parton-like more quickly as α increases, that is hidden from view d-quark u-quark I.C. Cloët & C.D. Roberts … continuing

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1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 71

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“Orthodox Vacuum” Vacuum = “frothing sea” Hadrons = bubbles in that “sea”, containing nothing but quarks & gluons interacting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped! 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 72 u u u d u u d d u

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New Paradigm Vacuum = hadronic fluctuations but no condensates Hadrons = complex, interacting systems within which perturbative behaviour is restricted to just 2% of the interior 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 73 u u u d u u d d u

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Regge Trajectories? Martinus Veltmann, “Facts and Mysteries in Elementary Particle Physics” (World Scientific, Singapore, 2003): In time the Regge trajectories thus became the cradle of string theory. Nowadays the Regge trajectories have largely disappeared, not in the least because these higher spin bound states are hard to find experimentally. At the peak of the Regge fashion (around 1970) theoretical physics produced many papers containing families of Regge trajectories, with the various (hypothetically straight) lines based on one or two points only! 1st Sino-Americas Workshop and School on the Bound- State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 74 Phys.Rev. D 62 (2000) Phys.Rev. D 62 (2000) [9 pages] 1993: "for elucidating the quantum structure of electroweak interactions in physics" Systematics of radial and angular-momentum Regge trajectories of light non-strange qqbar- states“ P. Masjuan, E. Ruiz Arriola, W. Broniowski. arXiv: [hep-ph]arXiv: [hep-ph]

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Hybrid Hadrons & Lattice QCD – Robert Edwards, Baryons13 Heavy pions … so, naturally, constituent-quark like spectra To which potential does it correspond? 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 75 arXiv: ,

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Hybrid meson models – Robert Edwards, Baryons13 With minimal quark content,, gluonic field can in a color singlet or octet `constituent’ gluon in S-wave `constituent’ gluon in P-wave bag model flux-tube model arXiv: , st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct 76 Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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Hybrid baryon models – Robert Edwards, Baryons13 Minimal quark content,, gluonic field can be in color singlet, octet or decuplet bag model flux-tube model Now must take into account permutation symmetry of quarks and gluonic field arXiv: , st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct 77 Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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I.IntroductionIntroduction II.Pion valence-quark distributionPion valence-quark distribution III.Pion valence-quark parton distribution amplitudePion valence-quark parton distribution amplitude IV.When is the asymptotic PDA a good approximation?When is the asymptotic PDA a good approximation? V.Charged pion elastic form factorCharged pion elastic form factor VI.Nucleon form factorsNucleon form factors VII.Nucleon structure functions at large-xNucleon structure functions at large-x VIII.EpilogueEpilogue A.DSE cf. Lattice PDA & PDA evolutionDSE cf. Lattice PDAPDA evolution B.GE/GM flavour separationGE/GM flavour separation C.Confinement contains condensatesConfinement contains condensates D.Regge Trajectories?Regge Trajectories? 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 78

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