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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); 10.J. Javier COBOS-MARTINEZ (U.Sonora); 11.Mario PITSCHMANN (ANL & UW-Mad); 12.Si-xue QIN (U. Frankfurt am Main); 13.Jorge SEGOVIA (ANL); 14.David WILSON (ODU); 15.Lei CHANG (U.Adelaide); 16.Ian CLOËT (ANL); 17.Bruno EL-BENNICH (São Paulo); MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 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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Exploit opportunities provided by new data on hadron elastic and transition form factors –Chart infrared evolution of QCDs 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 4

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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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 6

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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. MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 8 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. MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 9

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Light quarks & Confinement Problem: 16 tonnes of force makes a lot of pions. MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 10

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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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 11 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 12 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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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. –Its the most important mass generating mechanism for visible matter in the Universe. Responsible for 98% of the protons 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. MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 14 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 15 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 quarks 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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MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 16 Valence quarks

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Parton Structure of Hadrons Valence-quark structure of hadrons –Definitive of a hadron. After all, its 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 17

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Parton Structure of Hadrons Need for calculation is emphasised by Saga of pions 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 cant be correct; MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 18 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 pions 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 cant be correct; o 2010: NLO reanalysis including soft-gluon resummation, inferred distribution agrees with DSE and QCD MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 19 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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Pions valence-quark Distribution Amplitude Same methods can be used to compute φ π (x) = projection of the pions 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 20 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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Pions valence-quark Distribution Amplitude Both kernels agree: marked broadening of φ π (x), which owes to DCSB MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 21 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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Pions valence-quark Distribution Amplitude Both kernels agree: marked broadening of φ π (x), which owes to DCSB MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 22 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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Pions valence-quark Distribution Amplitude MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 23 Established a one-to-one connection between DCSB and the pointwise form of the pions 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 pions wave function is measurable in pions 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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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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 24 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? MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 25 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? MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 26 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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MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 27 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) New Algorithm Pion electromagnetic form factor at spacelike momenta, Lei Chang et al. arXiv: [nucl-th],arXiv: [nucl-th] Phys. Rev. Lett. in press 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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MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 28 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. in press 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 29 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 30 SU(2) isospin symmetry of hadrons might emerge from mixing half-integer spin particles with their antiparticles. Faddeev Equation

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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. MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 31

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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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 32 Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 (2011) Q 4 F 2 q / 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 33 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

34 Visible Impacts of DCSB MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 34 Apparently small changes in M(p) within the domain 1

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Visible Impacts of DCSB MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 35 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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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 x1 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. MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 37 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. MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 38 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 39 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 neutrons 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 40 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 neutrons 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 41 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 42 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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Lattice comparison Pions 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] MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 46 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]arXiv: [nucl-th]

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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. MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 47 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], arXiv: [nucl-th] Phys. Rev. Lett. 111 (2013) [5 pages]

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Flavor separation of proton form factors Visible Impacts of DCSB MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 48 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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Orthodox Vacuum Vacuum = frothing sea Hadrons = bubbles in that sea, containing nothing but quarks & gluons interacting perturbatively, unless theyre near the bubbles boundary, whereat they feel theyre trapped! MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 50 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 MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 51 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! MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 52 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? MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 53 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: , MENU 2013: 30/09- 04/10 54 Craig Roberts: Images of the Origin of Mass (44p)

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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: , MENU 2013: 30/09-04/10 55 Craig Roberts: Images of the Origin of Mass (44p)

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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? MENU 2013: 30/09-04/10 Craig Roberts: Images of the Origin of Mass (44p) 56

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