Craig Roberts Physics Division

1. Images of the Origin of Mass Craig Roberts Physics Division

2. Students Postdocs Asst. Profs. Collaborators: 2011-Present • Adnan BASHIR (U Michoácan); • Stan BRODSKY (SLAC); • Gastão KREIN (São Paulo) • Roy HOLT (ANL); • Mikhail IVANOV (Dubna); • Yu-xin LIU (PKU); • Michael RAMSEY-MUSOLF (UW-Mad) • Alfredo RAYA (U Michoácan); • Sebastian SCHMIDT (IAS-FZJ & JARA); • Robert SHROCK (Stony Brook); • Peter TANDY (KSU); • Tony THOMAS (U.Adelaide) • Shaolong WAN (USTC) Craig Roberts: Images of the Origin of Mass (44p) Rocio BERMUDEZ (U Michoácan); Xiomara GUTIERREZ-GUERRERO (U Michoácan); S. HERNÁNDEZ(U Michoácan); Trang NGUYEN (KSU); Khépani RAYA (U Michoácan); Hannes ROBERTS (ANL, FZJ, UBerkeley); Chien-Yeah SENG (UW-Mad) Kun-lun WANG (PKU); Chen CHEN (USTC); J. JavierCOBOS-MARTINEZ (U.Sonora); Mario PITSCHMANN (ANL & UW-Mad); Si-xue QIN(U. Frankfurt am Main); Jorge SEGOVIA (ANL); David WILSON (ODU); Lei CHANG (U.Adelaide); Ian CLOËT (ANL); Bruno EL-BENNICH (São Paulo);

3. Overarching Science Challenges for the coming decade: 2013-2022 Craig Roberts: Images of the Origin of Mass (44p) Discover the meaning of confinement Determine its connection with DCSB (dynamical chiral symmetry breaking) Elucidate their signals in observables … so experiment and theory together can map the nonperturbativebehaviour of the strong interaction In my view, it is unlikely that two phenomena, so critical in the Standard Model and tied to the dynamical generation of a single mass-scale, can have different origins and fates.

4. Immediate Science Challenges for the coming decade: 2013-2022 Craig Roberts: Images of the Origin of Mass (44p) • 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

5. What is QCD? Craig Roberts: Images of the Origin of Mass (44p)

6. QCD is a Theory (not an effective theory) Craig Roberts: Images of the Origin of Mass (44p) • Very likely a self-contained, nonperturbativelyrenormalisable 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) Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg-Landau theory of superconductivity

7. What is Confinement? Craig Roberts: Images of the Origin of Mass (44p)

8. Light quarks & Confinement • Folklore … Hall-DConceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes. Craig Roberts: Images of the Origin of Mass (44p) 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.”

9. Light quarks & Confinement Craig Roberts: Images of the Origin of Mass (44p) • Problem: 16 tonnes of force makes a lot of pions.

10. Light quarks & Confinement Craig Roberts: Images of the Origin of Mass (44p) Problem: 16 tonnes of force makes a lot of pions.

11. G. Bali et al., PoS LAT2005 (2006) 308 Light quarks & Confinement Craig Roberts: Images of the Origin of Mass (44p) 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

12. Confinement Confined particle Normal particle complex-P2 complex-P2 timelike axis: P2<0 s ≈ 1/Im(m) ≈ 1/2ΛQCD≈ ½fm • 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) • State described by rapidly damped wave & hence state cannot exist in observable spectrum Craig Roberts: Images of the Origin of Mass (44p) • 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

13. Dynamical ChiralSymmetry Breaking Craig Roberts: Images of the Origin of Mass (44p)

14. Dynamical Chiral Symmetry Breaking Confinement contains condensates, S.J. Brodsky, C.D. Roberts, R. Shrock and P.C. Tandy, arXiv:1202.2376 [nucl-th], Phys. Rev. C85 (2012) 065202 Craig Roberts: Images of the Origin of Mass (44p) • 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.

15. DCSB C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50 M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227 • 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 Mass from nothing! • 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. Craig Roberts: Images of the Origin of Mass (44p)

16. Valence quarks Parton structure of hadrons Craig Roberts: Images of the Origin of Mass (44p)

17. Parton Structure of Hadrons Craig Roberts: Images of the Origin of Mass (44p) • 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

18. Valence quark distributions in the pion, M.B. Hecht, Craig D. Roberts, S.M. Schmidt, nucl-th/0008049, Phys.Rev. C63 (2001) 025213 . Parton Structure of Hadrons Craig Roberts: Images of the Origin of Mass (44p) • Need for calculation is emphasised by Saga of pion’s valence-quark distribution: • 1989: uvπ ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD; • 2001: DSE- QCD predicts uvπ ~ (1-x)2 argues that distribution inferred from data can’t be correct;

19. Valence quark distributions in the pion, M.B. Hecht, Craig D. Roberts, S.M. Schmidt, nucl-th/0008049, Phys.Rev. C63 (2001) 025213 . Parton Structure of Hadrons Soft-gluon resummation and the valence parton distribution function of the pion, M. Aicher, A. Schafer, W. Vogelsang, Phys.Rev.Lett. 105 (2010) 252003, arXiv:1009.2481 [hep-ph] Craig Roberts: Images of the Origin of Mass (44p) • Need for calculation is emphasised by Saga of pion’s valence-quark distribution: • 1989: uvπ ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD; • 2001: DSE- QCD predicts uvπ ~ (1-x)2 argues that distribution inferred from data can’t be correct; • 2010: NLO reanalysis including soft-gluon resummation, inferred distribution agrees with DSE and QCD

20. Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude Craig Roberts: Images of the Origin of Mass (44p) • Same methods can be used to compute φπ(x) = projection of the pion’sPoincaré-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. xα (1-x)α, with α=0.3

21. Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude • 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(p2) is more slowly varying with DB kernel and hence a more balanced result Asymptotic DB RL Craig Roberts: Images of the Origin of Mass (44p) Both kernels agree: marked broadening of φπ(x), which owes to DCSB

22. Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude These computations are the first to directly expose DCSB – pointwise – on the light-front; i.e., in the infinite momentum frame. • 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(p2) is more slowly varying with DB kernel and hence a more balanced result Asymptotic DB RL Craig Roberts: Images of the Origin of Mass (44p) Both kernels agree: marked broadening of φπ(x), which owes to DCSB

23. Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50 Dilation of pion’s wave function is measurable in pion’s electromagnetic form factor at JLab12 A-rated:E12-06-10 • 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 Craig Roberts: Images of the Origin of Mass (44p)

24. Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. Roberts When is asymptotic PDA valid? Q2=27 GeV2 This is not δ(x)! Craig Roberts: Images of the Origin of Mass (44p) PDA is a wave function not directly observable but PDF is. φπasy(x) can only be a good approximation to the pion's PDA when it is accurate to write uvπ (x) ≈ δ(x) for the pion's valence-quark distribution function. This is far from valid at currently accessible scales

25. Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. Roberts When is asymptotic PDA valid? JLab 2GeV LHC: 16TeV Evolution in QCD is LOGARITHMIC • NLO evolution of PDF, computation of <x>. • Even at LHC energies, light-front fraction of the π momentum: • <x>dressed valence-quarks = 25% • <x>glue = 54%, <x>sea-quarks = 21% Craig Roberts: Images of the Origin of Mass (44p) When is asymptopia reached? If uvπ(x) ≈ δ(x), then <x> = ∫01dx x uvπ(x) = 0; i.e., the light-front momentumfraction carried by valence-quarks is ZERO  Asymptopia is reached when <x> is “small” As usual, the computed valence-quark distribution produces (π = u+dbar) 2<x>2GeV = 44% When is <x> small?

26. Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. Roberts When is asymptotic PDA valid? JLab 2GeV LHC: 16TeV Even at LHC energy scales, nonperturbative effects, such as DCSB, are playing a crucial role in setting the scales in PDAs and PDFs. Evolution in QCD is LOGARITHMIC • NLO evolution of PDF, computation of <x>. • Even at LHC energies, light-front fraction of the π momentum: • <x>dressed valence-quarks = 25% • <x>glue = 54%, <x>sea-quarks = 21% Craig Roberts: Images of the Origin of Mass (44p) When is asymptopia reached? If uvπ(x) ≈ δ(x), then <x> = ∫01dx x uvπ(x) = 0; i.e., the light-front momentumfraction carried by valence-quarks is ZERO  Asymptopia is reached when <x> is “small” As usual, the computed valence-quark distribution produces (π = u+dbar) 2<x>2GeV = 44% When is <x> small?

27. Pion electromagnetic form factor at spacelikemomenta, Lei Changet al. arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. in press Charged pionelastic form factor • Single interaction kernel, determined by just 1 parameter and preserving the one-loop RG-behaviour of QCD, had unified Fπ(Q2) and φπ(x) (and many other quantities) • New Algorithm DSE 2000 DSE 2013 15% pQCD obtained with φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment pQCD obtained withφπasy(x) Craig Roberts: Images of the Origin of Mass (44p)

28. Pion electromagnetic form factor at spacelikemomenta, Lei Changet al. arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. in press Charged pionelastic form factor • Single interaction kernel, determined by just 1 parameter and preserving the one-loop RG-behaviour of QCD, has unified Fπ(Q2) and φπ(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 DSE 2013 15% pQCD obtained with φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment pQCD obtained withφπasy(x) • Near agreement between the pertinent perturbative QCD prediction and DSE-2013 prediction is striking. • Dominance of hard contributions to the pion form factor for Q2>8GeV2. • Normalisation is fixed by a pion wave-function whose dilation with respect to φπasy(x) is a definitive signature of DCSB Craig Roberts: Images of the Origin of Mass (44p)

29. R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145 BaryonStructure SUc(3): Craig Roberts: Images of the Origin of Mass (44p) • 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

30. Faddeev Equation Baryon Structure SU(2)isospin symmetry of hadrons might emerge from mixing half-integer spin particles with their antiparticles. Craig Roberts: Images of the Origin of Mass (44p) 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 masslesspion 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, r0+ ~ rπ & r1+ ~ rρ(actually 10% larger) • They have soft form factors

31. Structure of Hadrons Craig Roberts: Images of the Origin of Mass (44p) • 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 nonpointlikediquark correlations • scale at which p-QCD effects become evident • strangeness content • meson-cloud effects • etc.

32. Flavor separation of proton form factors Q4F2q/k Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 (2011) 252003 Q4 F1q Craig Roberts: Images of the Origin of Mass (44p) Very different behavior for u & d quarks Means apparent scaling in proton F2/F1 is purely accidental

33. Cloët, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36 Wilson, Cloët, Chang, Roberts, PRC 85 (2012) 045205 Diquark correlations! u d =Q2/M2 • 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 Craig Roberts: Images of the Origin of Mass (44p) • 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

34. I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution,arXiv:1304.0855 [nucl-th], Phys. Rev. Lett. 111 (2013) 101803 Visible Impacts of DCSB • Apparently small changes in M(p) within the domain 1<p(GeV)<3 • have striking effect on the proton’s electric form factor • The possible existence and location of the zero is determined by behaviour of Q2F2p(Q2) • Like the pion’s PDA, Q2F2p(Q2) measures the rate at which dressed-quarks become parton-like: • F2p=0 for bare quark-partons • Therefore, GEp can’t be zero on the bare-parton domain 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:1304.0855 [nucl-th], Phys. Rev. Lett. 111 (2013) 101803 Visible Impacts of DCSB • Follows that the • possible existence • and location • of a zero in the ratio of proton elastic form factors • [μpGEp(Q2)/GMp(Q2)] • are a direct measure of the nature of the quark-quark interaction in the Standard Model. Leads to Prediction neutron:proton GEn(Q2) > GEp(Q2) at Q2 > 4GeV2 Craig Roberts: Images of the Origin of Mass (44p)

36. Far valence domain x≃1 Craig Roberts: Images of the Origin of Mass (44p)

37. Nucleon spin structure at very high-xCraig D. Roberts, Roy J. Holt and Sebastian M. SchmidtarXiv:1308.1236 [nucl-th], Phys. Lett. B in press Far valence domain x≃1 Craig Roberts: Images of the Origin of Mass (44p) • 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., • limx→1dv(x)/uv(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.

38. I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36 D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages] Neutron Structure Function at high-x Measures relative strength of axial-vector/scalar diquarks in proton Craig Roberts: Images of the Origin of Mass (44p) • Valence-quark distributions at x=1 • Fixed point under DGLAP evolution • Strong discriminator between theories • Algebraic formula • P1p,s= contribution to the proton's charge arising from diagrams with a scalar diquark component in both the initial and final state • P1p,a = kindred axial-vector diquark contribution • P1p,m = contribution to the proton's charge arising from diagrams with a different diquark component in the initial and final state.

39. I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36 D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages] Neutron StructureFunction at high-x x>0.9 d/u=1/2 SU(6) symmetry • 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” pQCD, uncorrelated Ψ DSE: “contact” d/u=0.18 0+qq only, d/u=0 Melnitchouk, Accardiet al. Phys.Rev. D84 (2011) 117501 Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) 252001 Distribution of neutron’s momentum amongst quarks on the valence-quark domain Craig Roberts: Images of the Origin of Mass (44p)

40. I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36 D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages] Neutron StructureFunction at high-x NB. d/u|x=1= 0 means there are no valence d-quarks in the proton! JLab12 can solve this enigma x>0.9 d/u=1/2 SU(6) symmetry • 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” pQCD, uncorrelated Ψ DSE: “contact” d/u=0.18 0+qq only, d/u=0 Melnitchouk, Accardiet al. Phys.Rev. D84 (2011) 117501 Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) 252001 Distribution of neutron’s momentum amongst quarks on the valence-quark domain 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) 052301, arXiv:1009.5666 [hep-ph] Neutron StructureFunction at high-x Observation: EMC effect measured in electron DIS at 0.35 < xB < 0.7, is linearly related to the Short Range Correlation (SRC) scale factor obtained from electron inclusive scattering at xB > 1. • “While it is quite hazardous to extrapolate from our limited xB range all the way to xB = 1, these results appear to disfavor models of the proton with d/u=0 at xB = 1” Figure courtesy of D.W. Higinbotham Craig Roberts: Images of the Origin of Mass (44p)

42. Nucleon spin structure at very high-xCraig D. Roberts, Roy J. Holt and Sebastian M. SchmidtarXiv:1308.1236 [nucl-th], Phys. Lett. B in press Nucleon spin structure at very high x • 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. Craig Roberts: Images of the Origin of Mass (44p)

43. Epilogue Craig Roberts: Images of the Origin of Mass (44p)

44. Epilogue Craig Roberts: Images of the Origin of Mass (44p) • The Physics of Hadrons is Unique: • Confronting a fundamental theory in which the elementary degrees-of-freedom are intangible and only composites reach detectors • Confinement in real-world is NOT understood • But DCSB is understood, and is crucial to any understanding of hadron phenomena • They must have a common origin • Experimental and theoretical study of the Bound-state problem in continuum QCD promises to provide many more predictions, insights and answers.

45. This is not the end Craig Roberts: Images of the Origin of Mass (44p)

46. Pion distribution amplitude from lattice-QCD, I.C. Cloëtet al. arXiv:1306.2645 [nucl-th] Lattice comparisonPion’s valence-quark PDA V. Braun et al., PRD 74 (2006) 074501 • Lattice-QCD • => one nontrivial moment: • <(2x-1)2> = 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 • DBα=0.31 but 10% a2<0 • RL α=0.29 and 0% a2 φπ~ xα (1-x)α α=0.35 +0.32 = 0.67 - 0.24 = 0.11 Craig Roberts: Images of the Origin of Mass (44p) Employ the generalised-Gegenbauer method described previously (and in Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]).

47. Pion distribution amplitude from lattice-QCD, I.C. Cloëtet al. arXiv:1306.2645 [nucl-th],  Phys. Rev. Lett. 111 (2013) 092001 [5 pages] When is asymptotic PDA valid? asymptotic 4 GeV2 100 GeV2 • Consequently, the asymptotic distribution, • φπasy(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 φπasy(x) should be revised. Craig Roberts: Images of the Origin of Mass (44p) Under leading-order evolution, the PDA remains broad to Q2>100 GeV2 Feature signals persistence of the influence of dynamical chiral symmetry breaking.

48. I.C. Cloët & C.D. Roberts … continuing Flavor separation of proton form factorsVisible Impacts of DCSB • 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 … GEpu ≈ GEp u-quark d-quark • 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 Craig Roberts: Images of the Origin of Mass (44p)

49. Confinement contains condensates Craig Roberts: Images of the Origin of Mass (44p)

50. “Orthodox Vacuum” u d u u d u u u d Craig Roberts: Images of the Origin of Mass (44p) 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!