1. Craig Roberts Physics Division

2. 1.Rocio BERMUDEZ (U Michoácan); 2.Chen CHEN (ANL, IIT, USTC); 3.Xiomara GUTIERREZ-GUERRERO (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.Lei CHANG (FZJ); 10.J. Javier COBOS-MARTINEZ (U.Sonora); 11.Ian CLOËT (ANL); 12.Bruno EL-BENNICH (São Paulo); 13.Mario PITSCHMANN (ANL & UW-Mad); 14.Si-xue QIN (U. Frankfurt am Main); 15.Jorge SEGOVIA (ANL); 16.David WILSON (ODU); Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 2 17.Adnan BASHIR (U Michoácan); 18.Stan BRODSKY (SLAC); 19.Gastão KREIN (São Paulo) 20.Roy HOLT (ANL); 21.Mikhail IVANOV (Dubna); 22.Yu-xin LIU (PKU); 23.Michael RAMSEY-MUSOLF (UW-Mad) 24.Alfredo RAYA (U Michoácan); 25.Sebastian SCHMIDT (IAS-FZJ & JARA); 26.Robert SHROCK (Stony Brook); 27.Peter TANDY (KSU); 28.Tony THOMAS (U.Adelaide) 29.Shaolong WAN (USTC) Students Postdocs Asst. Profs.

3. I.IntroductionIntroduction II.Pion valence-quark distributionPion valence-quark distribution III.Pion valence-quark parton distribution amplitudePion valence-quark parton distribution amplitude IV.Charged pion elastic form factorCharged pion elastic form factor V.Nucleon form factorsNucleon form factors VI.Nucleon structure functions at large-xNucleon structure functions at large-x VII.EpilogueEpilogue Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 3

4.  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 nucleon structure –Expose the facts or fallacies in modern descriptions of hadron structure Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 4

5.  Precision experimental study of 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 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 5

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7. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 7

8.  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 < 8000 GeV  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 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 8

9. Strong-interaction: QCD  Asymptotically free –Perturbation theory is valid and accurate tool at large-Q 2 –Hence chiral limit is defined  Essentially nonperturbative for Q 2 < 2 GeV 2 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 9  Nature’s only (now known) example of a truly nonperturbative, fundamental theory  A-priori, no idea as to what such a theory can produce

10. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 10

11. 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.” Hall-D Conceptual-DR(5) Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 11  Folklore “The color field lines between a quark and an anti-quark form flux tubes.

12. Light quarks & Confinement  Problem: 16 tonnes of force makes a lot of pions. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 12

13. Light quarks & Confinement  Problem: 16 tonnes of force makes a lot of pions. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 13

14. 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 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 14 G. Bali et al., PoS LAT2005 (2006) 308PoS LAT2005 (2006) 308

15.  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 Confinement Craig Roberts: Mapping Parton Structure and Correlations (62p) 15 complex-P 2 o Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities o State described by rapidly damped wave & hence state cannot exist in observable spectrum Normal particle Confined particle Hall-A Collaboration Meeting: 13-14 June 2013 timelike axis: P 2 <0 s ≈ 1/Im(m) ≈ 1/2Λ QCD ≈ ½fm

16. Light quarks & Confinement  In the study of hadrons, attention should turn from potential models toward the continuum bound-state problem in quantum field theory  Such approaches offer the possibility of posing simultaneously the questions –What is confinement? –What is dynamical chiral symmetry breaking? –How are they related? Is it possible that two phenomena, so critical in the Standard Model and tied to the dynamical generation of a mass-scale in QCD, can have different origins and fates? Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 16

17. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 17

18. 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 dynamics of gluons and quarks. –It’s the most important mass generating mechanism for visible matter in the Universe. Responsible for approximately 98% of the proton’s mass. Higgs mechanism is ( almost ) irrelevant to light- quarks. Craig Roberts: Mapping Parton Structure and Correlations (62p) 18 Hall-A Collaboration Meeting: 13-14 June 2013

19. DCSB Craig Roberts: Mapping Parton Structure and Correlations (62p) 19 Mass from nothing! Hall-A Collaboration Meeting: 13-14 June 2013 C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50Prog. Part. Nucl. Phys. 61 (2008) 50 M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227AIP Conf.Proc. 842 (2006) 225-227  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.

20. 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 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 20

21. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 21 Valence quarks

22. Parton Structure of Hadrons  Valence-quark structure of hadrons –Definitive of a hadron – it’s how we tell 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?  Any nontrivial answers are essentially nonperturbative features of QCD Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 22

23. Parton Structure of Hadrons  Light front provides a link with quantum mechanics –If a probability interpretation is ever valid, it’s in the infinite-momentum frame  Enormous amount of intuitively expressive information about hadrons & processes involving them is encoded in –Parton distribution functions –Generalised parton distribution functions –Transverse-momentum-dependent parton distribution functions  Information will be revealed by the measurement of these functions – so long as they can be calculated Success of programme demands very close collaboration between experiment and theory Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 23

24. 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; Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 24

25. 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 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 25

26.  Exact expression in QCD for the pion’s valence-quark parton distribution amplitude  Expression is Poincaré invariant but a probability interpretation is only valid in the light-front frame because only therein does one have particle-number conservation.  Probability that a valence-quark or antiquark carries a fraction x=k + / P + of the pion’s light-front momentum { n 2 =0, n.P = -m π } Pion’s valence-quark Distribution Amplitude Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 26 Pion’s Bethe-Salpeter wave function Whenever a nonrelativistic limit is realistic, this would correspond to the Schroedinger wave function.

27.  Moments method is ideal for φ π (x): entails  Contact interaction (1/k 2 ) ν, ν=0 Straightforward exercise to show ∫ 0 1 dx x m φ π (x) = f π 1/(1+m), hence φ π (x)= f π Θ(x)Θ(1-x) Pion’s valence-quark Distribution Amplitude Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 27 Pion’s Bethe-Salpeter wave function

28. Pion’s valence-quark Distribution Amplitude  The distribution amplitude φ π (x) is actually dependent on the momentum-scale at which a particular interaction takes place; viz., φ π (x)= φ π (x,Q)  One may show in general that φ π (x) has an expansion in terms of Gegenbauer–α=3/2 polynomials: Only even terms contribute because the neutral pion is an eigenstate of charge conjugation, so φ π (x)=φ π (1-x)  Evolution, analogous to that of the parton distribution functions, is encoded in the coefficients a n (Q) Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 28

29. Pion’s valence-quark Distribution Amplitude  However, practically, in reconstructing φ π (x) from its moments, it is better to use Gegenbauer–α polynomials and then rebuild the Gegenbauer–α=3/2 expansion from that. –Better means – far more rapid convergence because Gegenbauer–α=3/2 is only accurate near Λ QCD /Q=0. –One nontrivial Gegenbauer–α polynomial provides converged reconstruction cf. more than SEVEN Gegenbauer–α=3/2 polynomials  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 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 29 Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]

30. Pion’s valence-quark Distribution Amplitude  Both kernels agree: marked broadening of φ π (x), which owes to DCSB Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 30 Asymptotic RL DB  This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB.  Difference between RL and DB results is readily understood: B(p 2 ) is more slowly varying with DB kernel and hence a more balanced result Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]

31. Pion’s valence-quark Distribution Amplitude  Both kernels agree: marked broadening of φ π (x), which owes to DCSB Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 31 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(p2) is more slowly varying with DB kernel and hence a more balanced result Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]

32. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 32  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: E12-06-10E12-06-10 Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages] Pion’s valence-quark Distribution Amplitude

33. Lattice comparison Pion’s valence-quark PDA  Employ the generalised-Gegenbauer method described previously (and in Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages] ). Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages] Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 33  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=0.35 +0.32 = 0.67 - 0.24 = 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) 074501 Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th]arXiv:1306.2645 [nucl-th]

34. Lattice comparison Pion’s valence-quark PDA  Establishes that contemporary DSE- and lattice-QCD computations, at the same scale, agree on the pointwise form of the pion's PDA, φ π (x).  This unification of DSE- and lattice-QCD results expresses a deeper equivalence between them, expressed, in particular, via the common behaviour they predict for the dressed-quark mass-function, which is both –a definitive signature of dynamical chiral symmetry breaking –and the origin of the distribution amplitude's dilation. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 34 Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th]arXiv:1306.2645 [nucl-th]

35. 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. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 35  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 2 100 GeV 2 Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th]arXiv:1306.2645 [nucl-th]

36. When is asymptotic PDA valid?  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 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 36 Q 2 =27 GeV 2 This is not δ(x)! Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th]arXiv:1306.2645 [nucl-th]

37. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 37  P. Maris & P.C. Tandy, Phys.Rev. C62 (2000) 055204: numerical procedure is practically useless for Q 2 >4GeV 2, so prediction ends!Phys.Rev. C62 (2000) 055204  Algorithm developed for pion PDA overcomes this obstacle  Solves the practical problem of continuing from Euclidean metric formulation to Minkowski space Pion electromagnetic form factor at spacelike momenta, Lei Chang et al. (in progress)

38. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 38  Improved DSE interaction kernel, based on DSE and lattice-QCD studies of gluon sector S.-x. Qin, L. Chang et al. Phys.Rev. C84 (2011) 042202(R) Phys.Rev. C84 (2011) 042202(R)  New prediction in better agreement with available data than old DSE result  Prediction extends from Q 2 =0 to arbitrarily large Q 2, without interruption, unifying both domains Pion electromagnetic form factor at spacelike momenta, Lei Chang et al. (in progress) DSE 2000 … Breakdown here

39. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 39  Unlimited domain of validity emphasised in this figure  Depict prediction on domain 0<Q 2 <20GeV 2 but have computed the result to Q 2 =100GeV 2.  If it were necessary, reliable results could readily be obtained at even higher values. Pion electromagnetic form factor at spacelike momenta, Lei Chang et al. (in progress) DSE 2013

40. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 40  Predict a maximum at 6-GeV 2, which lies within domain that is accessible to JLab12  Difficult, however, to distinguish DSE prediction from Amendolia-1986 monopole  What about comparison with perturbative QCD? Pion electromagnetic form factor at spacelike momenta, Lei Chang et al. (in progress) Amendolia et al. DSE 2013 ρ-meson pole VMD maximum A-rated: E12-06-10E12-06-10

41. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 41  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  Near agreement between the pertinent perturbative QCD prediction and DSE- 2013 prediction is striking. Pion electromagnetic form factor at spacelike momenta, Lei Chang et al. (in progress) 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%  Single DSE interaction kernel, determined fully by just one parameter and preserving the one-loop renormalisation group behaviour of QCD, has unified the F π (Q 2 ) and φ π (x) (and numerous other quantities)

42. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 42  Leading-order, leading-twist QCD prediction, obtained with φ π (x) evaluated at a scale appropriate to the experiment underestimates DSE-2013 prediction by merely an approximately uniform 15%.  Small mismatch is explained by a combination of higher- order, higher-twist corrections & and shortcomings in the rainbow-ladder truncation. Pion electromagnetic form factor at spacelike momenta, Lei Chang et al. (in progress) DSE 2013 pQCD obtained with φ π asy (x) pQCD obtained φ π (x;2GeV), i.e., the PDA appropriate to the scale of the experiment 15%  Hence, one should expect dominance of hard contributions to the pion form factor for Q 2 >8GeV 2.  Nevertheless, the normalisation of the form factor is fixed by a pion wave- function whose dilation with respect to φ π asy (x) is a definitive signature of DCSB

43. Structure of Hadrons  Dynamical chiral symmetry breaking (DCSB) – has enormous impact on meson properties.  Must be included in description and prediction of baryon properties.  DCSB is essentially a quantum field theoretical effect. In quantum field theory  Meson appears as pole in four-point quark-antiquark Green function → Bethe-Salpeter Equation  Nucleon appears as a pole in a six-point quark Green function → Faddeev Equation.  Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarks  Tractable equation is based on the observation that an interaction which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channel Craig Roberts: Mapping Parton Structure and Correlations (62p) 43 R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145 Hall-A Collaboration Meeting: 13-14 June 2013 SU c (3):

44. Faddeev Equation  Linear, Homogeneous Matrix equation  Yields wave function (Poincaré Covariant Faddeev Amplitude) that describes quark-diquark relative motion within the nucleon  Scalar and Axial-Vector Diquarks...  For nucleon, both have “correct” parity and “right” masses  In Nucleon’s Rest Frame Amplitude has s−, p− & d−wave correlations Craig Roberts: Mapping Parton Structure and Correlations (62p) 44 diquark quark quark exchange ensures Pauli statistics composed of strongly- dressed quarks bound by dressed-gluons Hall-A Collaboration Meeting: 13-14 June 2013 R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145

45. Structure of Hadrons 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 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 45 SU(2) isospin symmetry of hadrons might emerge from mixing half-integer spin particles with their antiparticles.

46. 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. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 46

47. Photon-nucleon current  Composite nucleon must interact with photon via nontrivial current constrained by Ward-Green-Takahashi identities  DSE → BSE → Faddeev equation plus current → nucleon form factors Craig Roberts: Mapping Parton Structure and Correlations (62p) 47 Vertex must contain the dressed-quark anomalous magnetic moment Oettel, Pichowsky, Smekal Eur.Phys.J. A8 (2000) 251-281 Hall-A Collaboration Meeting: 13-14 June 2013 L. Chang, Y. –X. Liu and C.D. Roberts arXiv:1009.3458 [nucl-th] arXiv:1009.3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001  In a realistic calculation, the last three diagrams represent 8-dimensional integrals, which can be evaluated using Monte-Carlo techniques

48. Craig Roberts: Mapping Parton Structure and Correlations (62p) 48 I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th]  Highlights again the critical importance of DCSB in explanation of real-world observables.  DSE result Dec 08 DDSE result – including the anomalous magnetic moment distribution Hall-A Collaboration Meeting: 13-14 June 2013 L. Chang, Y. –X. Liu and C.D. Roberts arXiv:1009.3458 [nucl-th] arXiv:1009.3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001

49. Visible Impacts of DCSB Craig Roberts: Mapping Parton Structure and Correlations (62p) 49 Hall-A Collaboration Meeting: 13-14 June 2013  Apparently small changes in M(p) within the domain 1<p(GeV)<3 have striking effect on the proton’s electric form factor  The possible existence and location of the zero is determined by behaviour of Q 2 F 2 p (Q 2 )  Like the pion’s PDA, Q 2 F 2 p (Q 2 ) measures the rate at which dress-ed- quarks become parton-like: F 2 p =0 for bare quark-partons Therefore, G E p can’t be zero on the bare-parton domain I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed- quarks via the proton's charge distribution, arXiv: 1304.0855 [nucl-th]arXiv: 1304.0855 [nucl-th]

50. Visible Impacts of DCSB Craig Roberts: Mapping Parton Structure and Correlations (62p) 50 Hall-A Collaboration Meeting: 13-14 June 2013  Follows that the possible existence and location of a zero in the ratio of proton elastic form factors [μ p G Ep (Q 2 )/G Mp (Q 2 )] are a direct measure of the nature of the quark-quark interaction in the Standard Model. I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed- quarks via the proton's charge distribution, arXiv: 1304.0855 [nucl-th]arXiv: 1304.0855 [nucl-th]

51. Flavor separation of proton form factors Visible Impacts of DCSB Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 51  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

52. Flavor separation of proton form factors  Very different behavior for u & d quarks Means apparent scaling in proton F2/F1 is purely accidental Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 52 Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 (2011) 252003 Q4F2q/Q4F2q/ Q 4 F 1 q

53. 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 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 53 Cloët, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36 Wilson, Cloët, Chang, Roberts, PRC 85 (2012) 045205  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

54. 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. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 54 I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th]arXiv:0812.0416 [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:1112.2212 [nucl-th]arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]Phys. Rev. C85 (2012) 025205 [21 pages] Measures relative strength of axial-vector/scalar diquarks in proton

55. Craig Roberts: Mapping Parton Structure and Correlations (62p) 55 Neutron Structure Function at high-x SU(6) symmetry pQCD, uncorrelated Ψ 0 + qq only 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) DSE: “realistic” Distribution of neutron’s momentum amongst quarks on the valence-quark domain Hall-A Collaboration Meeting: 13-14 June 2013 DSE: “contact” Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) 117501 x>0.9 Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) 252001 I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th]arXiv:0812.0416 [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:1112.2212 [nucl-th]arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]Phys. Rev. C85 (2012) 025205 [21 pages]

56. Craig Roberts: Mapping Parton Structure and Correlations (62p) 56 Neutron Structure Function at high-x SU(6) symmetry pQCD, uncorrelated Ψ 0 + qq only 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) DSE: “realistic” Distribution of neutron’s momentum amongst quarks on the valence-quark domain Hall-A Collaboration Meeting: 13-14 June 2013 DSE: “contact” Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) 117501 x>0.9 Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) 252001 I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th]arXiv:0812.0416 [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:1112.2212 [nucl-th]arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]Phys. Rev. C85 (2012) 025205 [21 pages]

57. 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) 054512>  Current knowledge of transversity: SIDIS @HERMES, 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 E12-09-018-SIDIS; CLAS12; and SoLID) Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 57 Direction of motion

58. Tensor Charge: σ μν current 1.Anselmino et al., NPhysProcSupp (2009)NPhysProcSupp (2009) 2.Pitschmann et al. (DSE) (2013) [including axial-vector diquarks but contact interaction] 3.Hecht et al. (DSE), PRC64 (2001) 025204 [only scalar diquarks] PRC64 (2001) 025204 4.Cloët et al., PLB659 (2008) 214PLB659 (2008) 214 5.Pasquini et al., PRD76 (2007) 034020PRD76 (2007) 034020 6.Wakamatsu, PLB653 (2007) 398PLB653 (2007) 398 7.Gockeler et al., PLB627 (2005) 113PLB627 (2005) 113 8.Gamberg et al., PRL 87 (2001) 242001PRL 87 (2001) 242001 9.He et al., PRD52 (1995) 2960PRD52 (1995) 2960 10.Bacchetta et al., JHEP 1303 (2013) 119JHEP 1303 (2013) 119 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 58 Direction of motion Big shift from including axial- vector diquark correlations? d-quark can now be unpaired and u-quark “locked away.” Figure inspired by: A. Prokhudin arXiv:1304.0469arXiv:1304.0469

59. 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 Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 59

60. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 60

61. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 61

62. Hall-A Collaboration Meeting: 13-14 June 2013 Craig Roberts: Mapping Parton Structure and Correlations (62p) 62