1. Craig Roberts Physics Division Students Early-career scientists Published collaborations: 2010-present 1.Rocio BERMUDEZ (U Michoácan); 2.Chen CHEN (ANL, IIT, USTC); 3.Xiomara GUTIERREZ-GUERRERO (U Michoácan); 4.Trang NGUYEN (KSU); 5.Si-xue QIN (PKU); 6.Hannes ROBERTS (ANL, FZJ, UBerkeley); 7.Chien-Yeah SENG (UW-Mad) 8.Kun-lun WANG (PKU); 9.Lei CHANG (ANL, FZJ, PKU); 10.Huan CHEN (BIHEP); 11.Ian CLOËT (UAdelaide); 12.Bruno EL-BENNICH (São Paulo); 13.Mario PITSCHMANN (ANL & UW-Mad) 14.David WILSON (ANL); 15.Adnan BASHIR (U Michoácan); 16.Stan BRODSKY (SLAC); 17.Gastão KREIN (São Paulo) 18.Roy HOLT (ANL); 19.Mikhail IVANOV (Dubna); 20.Yu-xin LIU (PKU); 21.Michael RAMSEY-MUSOLF (UW-Mad) 22.Sebastian SCHMIDT (IAS-FZJ & JARA); 23.Robert SHROCK (Stony Brook); 24.Peter TANDY (KSU) 25.Shaolong WAN (USTC)

2. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 2

3. Confinement  Gluon and Quark Confinement –Empirical Fact: No coloured states have yet been observed to reach a detector Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 3 X 2.10.12: QCDNP2012-Matalascanas - 65  However –There is no agreed, theoretical definition of light-quark confinement –Static-quark confinement is irrelevant to real-world QCD There are no long-lived, very-massive quarks But light-quarks are ubiquitous  Flux tubes, linear potentials and string tensions play no role in relativistic quantum field theory with light degrees of freedom.

4. 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! 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 4 Phys.Rev. D 62 (2000) 016006Phys.Rev. D 62 (2000) 016006 [9 pages] 1993: "for elucidating the quantum structure of electroweak interactions in physics"

5. Confinement  QFT Paradigm: Confinement is expressed through a dramatic change in the analytic structure of propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator –Gribov (1978); Munczek (1983); Stingl (1984); Cahill (1989); Roberts, Williams & Krein (1992); Tandy (1994); … Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 5 complex-P 2 o Real-axis mass-pole splits, moving into pair(s) of complex conjugate poles or branch points, or more complicated nonanalyticities … o Spectral density no longer positive semidefinite & hence state cannot exist in observable spectrum Normal particle Confined particle 2.10.12: QCDNP2012-Matalascanas - 65 timelike axis: P 2 <0

6. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 6

7. Dynamical Chiral Symmetry Breaking  Whilst confinement is contentious …  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 is the most important mass generating mechanism for visible matter in the Universe. Responsible for approximately 98% of the proton’s mass. Higgs mechanism is ( almost ) irrelevant to light-quarks. Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 7 2.10.12: QCDNP2012-Matalascanas - 65

8. Frontiers of Nuclear Science: Theoretical Advances In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies. Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 8 DSE prediction of DCSB confirmed Mass from nothing! 2.10.12: QCDNP2012-Matalascanas - 65 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

9. Frontiers of Nuclear Science: Theoretical Advances In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies. Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 9 Hint of lattice-QCD support for DSE prediction of violation of reflection positivity 2.10.12: QCDNP2012-Matalascanas - 65 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

10. 12GeV The Future of JLab  Jlab 12GeV: This region scanned by 2<Q 2 <9 GeV 2 elastic & transition form factors. Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 10 2.10.12: QCDNP2012-Matalascanas - 65

11. The Future of Drell-Yan  Valence-quark PDFs and PDAs probe this critical and complementary region Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 11 2.10.12: QCDNP2012-Matalascanas - 65 π or K N

12.  Search for exotic hadrons  Exploit opportunities provided by new data on nucleon elastic and transition form factors  Precision experimental study of valence region, and theoretical computation of distribution functions and distribution amplitudes  Develop QCD as a probe for physics beyond the Standard Model 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 12

13. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 13  Search for exotic hadrons  Exploit opportunities provided by new data on nucleon elastic and transition form factors  Precision experimental study of valence region, and theoretical computation of distribution functions and distribution amplitudes  Develop QCD as a probe for physics beyond the Standard Model

14. Universal Truths  Spectrum of hadrons, and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron's characterising properties amongst its QCD constituents. Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 14 2.10.12: QCDNP2012-Matalascanas - 65 DDynamical Chiral Symmetry Breaking (DCSB) is most important mass generating mechanism for visible matter in the Universe. Higgs mechanism is ( almost ) irrelevant to light-quarks. RRunning of quark mass entails that calculations at even modest Q 2 require a Poincaré-covariant approach. Covariance requires existence of quark orbital angular momentum in hadron's rest-frame wave function. CConfinement is expressed through a violent change of the propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator. It is intimately connected with DCSB.

15. Universal Conventions  Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum)(http://en.wikipedia.org/wiki/QCD_vacuum) “The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non- perturbative vacuum state, characterized by many non- vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.” Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 15 2.10.12: QCDNP2012-Matalascanas - 65

16. Universal Misapprehensions  Since 1979, DCSB has commonly been associated literally with a spacetime- independent mass-dimension-three “vacuum condensate.”  Under this assumption, “condensates” couple directly to gravity in general relativity and make an enormous contribution to the cosmological constant  Experimentally, the answer is Ω cosm. const. = 0.76  This mismatch is a bit of a problem. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 16

17. New Paradigm “in-hadron condensates” 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 17

18. “Orthodox Vacuum”  Vacuum = “frothing sea”  Hadrons = bubbles in that “sea”, containing nothing but quarks & gluons interacting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped! 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 18 u u u d u u d d u

19. New Paradigm  Vacuum = hadronic fluctuations but no condensates  Hadrons = complex, interacting systems within which perturbative behaviour is restricted to just 2% of the interior 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 19 u u u d u u d d u

20. Some Relevant References  arXiv:1202.2376, Phys. Rev. C85, 065202 (2012) [9 pages] arXiv:1202.2376Phys. Rev. C85, 065202 (2012) [9 pages] Confinement contains condensates Stanley J. Brodsky, Craig D. Roberts, Robert Shrock, Peter C. Tandy  arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(RapCom), Expanding the concept of in-hadron condensates Lei Chang, Craig D. Roberts and Peter C. Tandy arXiv:1109.2903 [nucl-th]Phys. Rev. C85 (2012) 012201(RapCom)  arXiv:1005.4610 [nucl-th], Phys. Rev. C82 (2010) 022201(RapCom.) arXiv:1005.4610 [nucl-th]Phys. Rev. C82 (2010) 022201(RapCom.) New perspectives on the quark condensate, Brodsky, Roberts, Shrock, Tandy  arXiv:0905.1151 [hep-th], PNAS 108, 45 (2011) arXiv:0905.1151 [hep-th]PNAS 108, 45 (2011) Condensates in Quantum Chromodynamics and the Cosmological Constant, Brodsky and Shrock,  hep-th/0012253 hep-th/0012253 The Quantum vacuum and the cosmological constant problem, Svend Erik Rugh and Henrik Zinkernagel. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 20

21. Charting the interaction between light-quarks  Confinement can be related to the analytic properties of QCD's Schwinger functions.  Question of light-quark confinement is thereby translated into the challenge of charting the infrared behavior of QCD's universal β-function  Through QCD's DSEs, the pointwise behaviour of the β-function determines the pattern of chiral symmetry breaking.  DSEs connect β-function to experimental observables. Hence, comparison between computations and observations of o Hadron spectrum, Elastic & transition form factors, Parton distribution fns can be used to chart β-function’s long-range behaviour. Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 21 This is a well-posed problem whose solution is an elemental goal of modern hadron physics. The answer provides QCD’s running coupling. 2.10.12: QCDNP2012-Matalascanas - 65 Process-independent α S (Q 2 ) → unified description of observables

22. Necessary Precondition  Experiment ↔ Theory comparison leads to an understanding of long-range behaviour of strong running-coupling  However, if one wants to draw reliable conclusions about Q 2 -dependence of QCD’s running coupling,  Then, approach must veraciously express Q 2 -dependence of QCD’s running masseS  True for ALL observables From spectrum … through elastic & transition form factors … to PDFs and GPDs … etc. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 22 Mass function exhibits inflexion point at Q IR ≈ m G ≈ 0.6GeV So … pQCD is definitely invalid for momenta Q<Q IR E.g., use of DGLAP equations cannot be justified in QCD at Q<Q IR =0.6GeV, irrespective of order. Distribution Functions of the Nucleon and Pion in the Valence Region, Roy J. Holt and Craig D. Roberts, arXiv:1002.4666 [nucl-th],arXiv:1002.4666 [nucl-th] Rev. Mod. Phys. 82 (2010) pp. 2991-3044 Essentially nonperturbative

23.  Goldstone’s theorem has a pointwise expression in QCD; Namely, in the chiral limit the wave-function for the two- body bound-state Goldstone mode is intimately connected with, and almost completely specified by, the fully-dressed one-body propagator of its characteristic constituent The one-body momentum is equated with the relative momentum of the two-body system Dichotomy of the pion Goldstone mode and bound-state 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 23

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25. Empirical status of the Pion’s valence-quark distributions  Owing to absence of pion targets, the pion’s valence-quark distribution functions are measured via the Drell-Yan process: π p → μ + μ − X  Three experiments: CERN (1983 & 1985) and FNAL (1989). No more recent experiments because theory couldn’t even explain these!  Problem Conway et al. Phys. Rev. D 39, 92 (1989)Phys. Rev. D 39, 92 (1989) Wijesooriya et al. Phys.Rev. C 72 (2005) 065203Phys.Rev. C 72 (2005) 065203 PDF behaviour at large-x inconsistent with pQCD; viz, expt. (1-x) 1+ε cf. QCD (1-x) 2+γ 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 25 Pion

26. Models of the Pion’s valence-quark distributions  (1−x) β with β=0 (i.e., a constant – any fraction is equally probable! ) –AdS/QCD models using light-front holography –Nambu–Jona-Lasinio models, when a translationally invariant regularization is used  (1−x) β with β=1 –Nambu–Jona-Lasinio NJL models with a hard cutoff –Duality arguments produced by some theorists  (1−x) β with 0<β<2 – Relativistic constituent-quark models, with power-law depending on the form of model wave function  (1−x) β with 1<β<2 –Instanton-based models, all of which have incorrect large-k 2 behaviour 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 26 Pion

27. Models of the Pion’s valence-quark distributions  (1−x) β with β=0 (i.e., a constant – any fraction is equally probable! ) –AdS/QCD models using light-front holography –Nambu–Jona-Lasinio models, when a translationally invariant regularization is used  (1−x) β with β=1 –Nambu–Jona-Lasinio NJL models with a hard cutoff –Duality arguments produced by some theorists  (1−x) β with 0<β<2 – Relativistic constituent-quark models, depending on the form of model wave function  (1−x) β with 1<β<2 –Instanton-based models 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 27 Pion

28. DSE prediction of the Pion’s valence-quark distributions  Consider a theory in which quarks scatter via a vector-boson exchange interaction whose k 2 >>m G 2 behaviour is (1/k 2 ) β,  Then at a resolving scale Q 0 u π (x;Q 0 ) ~ (1-x) 2β namely, the large-x behaviour of the quark distribution function is a direct measure of the momentum-dependence of the underlying interaction.  In QCD, β=1 and hence QCD u π (x;Q 0 ) ~ (1-x) 2 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 28 Pion

29.  Consider a theory in which quarks scatter via a vector-boson exchange interaction whose k 2 >m G 2 behaviour is (1/k 2 ) β,  Then at a resolving scale Q 0 u π (x;Q 0 ) ~ (1-x) 2β namely, the large-x behaviour of the quark distribution function is a direct measure of the momentum-dependence of the underlying interaction.  In QCD, β=1 and hence QCD u π (x;Q 0 ) ~ (1-x) 2 DSE prediciton of the Pion’s valence-quark distributions 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 29 Pion

30. “Model Scale”  At what scale Q 0 should the prediction be valid?  Hitherto, PDF analyses within models have used the resolving scale Q 0 as a parameter, to be chosen by requiring agreement between the model and low- moments of the PDF that are determined empirically. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 30 Pion  Modern DSE studies have exposed a natural value for the model scale; viz., the gluon mass Q 0 ≈ m G ≈ 0.6 GeV ≈ 1/0.33 fm which is the location of the inflexion point in the chiral-limit dressed-quark mass function Essentially nonperturbative domain

31. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 31

32. Reanalysis of q v π (x)  After first DSE computation, the “Conway et al.” data were reanalysed, this time at next-to-leading-order ( Wijesooriya et al. Phys.Rev. C 72 (2005) 065203 )Phys.Rev. C 72 (2005) 065203  The new analysis produced a much larger exponent than initially obtained; viz., β=1.87, but now it disagreed equally with model results and the DSE prediction NB. Within pQCD, one can readily understand why adding a higher-order correction leads to a suppression of q v π (x) at large-x. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 32 Hecht, Roberts, Schmidt Phys.Rev. C 63 (2001) 025213  New experiments were proposed … for accelerators that do not yet exist but the situation remained otherwise unchanged  Until the publication of Distribution Functions of the Nucleon and Pion in the Valence Region, Roy J. Holt and Craig D. Roberts, arXiv:1002.4666 [nucl-th], Rev. Mod. Phys. 82 (2010) pp. 2991-3044 arXiv:1002.4666 [nucl-th]Rev. Mod. Phys. 82 (2010) pp. 2991-3044

33. Reanalysis of q v π (x)  This article emphasised and explained the importance of the persistent discrepancy between the DSE result and experiment as a challenge to QCD  It prompted another reanalysis of the data, which accounted for a long-overlooked effect: viz., “soft-gluon resummation,” –Compared to previous analyses, we include next-to-leading- logarithmic threshold resummation effects in the calculation of the Drell-Yan cross section. As a result of these, we find a considerably softer valence distribution at high momentum fractions x than obtained in previous next-to-leading-order analyses, in line with expectations based on perturbative-QCD counting rules or Dyson- Schwinger equations. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 33 Distribution Functions of the Nucleon and Pion in the Valence Region, Roy J. Holt and Craig D. Roberts, arXiv:1002.4666 [nucl-th], Rev. Mod. Phys. 82 (2010) pp. 2991-3044 arXiv:1002.4666 [nucl-th]Rev. Mod. Phys. 82 (2010) pp. 2991-3044 Aicher, Schäfer, Vogelsang, “Soft-Gluon Resummation and the Valence Parton Distribution Function of the Pion,” Phys. Rev. Lett. 105 (2010) 252003 Phys. Rev. Lett. 105 (2010) 252003

34. Current status of q v π (x)  Data as reported byE615  DSE prediction (2001) 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 34 Trang, Bashir, Roberts & Tandy, “Pion and kaon valence- quark parton distribution functions,” arXiv:1102.2448 [nucl-th], Phys. Rev. C 83, 062201(R) (2011) [5 pages]arXiv:1102.2448 [nucl-th],Phys. Rev. C 83, 062201(R) (2011) [5 pages]

35. Current status of q v π (x)  Data after inclusion of soft-gluon resummation  DSE prediction and modern representation of the data are indistinguishable on the valence-quark domain  Emphasises the value of using a single internally- consistent, well- constrained framework to correlate and unify the description of hadron observables 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 35 Trang, Bashir, Roberts & Tandy, “Pion and kaon valence- quark parton distribution functions,” arXiv:1102.2448 [nucl-th], Phys. Rev. C 83, 062201(R) (2011) [5 pages]arXiv:1102.2448 [nucl-th],Phys. Rev. C 83, 062201(R) (2011) [5 pages]

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37.  Reconstruct φ π (x) from moments: 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 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 37 Pion’s Bethe-Salpeter wave function Work now underway with sophisticated rainbow-ladder interaction: Chang, Cloët, Roberts, Schmidt & Tandy Expression exact in QCD – no corrections Expose DCSB in a quantum mechanical wave function

38. Pion’s valence-quark Distribution Amplitude  Using simple parametrisations of solutions to the gap and Bethe-Salpeter equations, rapid and semiquantitatively reliable estimates can be made for φ π (x) –(1/k 2 ) ν=0 –(1/k 2 ) ν =½ –(1/k 2 ) ν =1  Again, unambiguous and direct mapping between behaviour of interaction and behaviour of distribution amplitude 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 38 Leading pQCD φ π (x)=6 x (1-x)

39. Pion’s valence-quark Distribution Amplitude  Preliminary results: rainbow-ladder QCD analyses of renormalisation-group-improved (1/k 2 ) ν =1 interaction – humped disfavoured but modest flattening 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 39  Such behaviour is only obtained with (1) Running mass in dressed-quark propagators (2) Pointwise expression of Goldstone’s theorem Chang, Cloët, Roberts, Schmidt & Tandy, in progress; Si-xue Qin, Lei Chang, Yu-xin Liu, Craig Roberts and David Wilson, arXiv:1108.0603 [nucl-th], Phys. Rev. C 84 042202(R) (2011) arXiv:1108.0603 [nucl-th]Phys. Rev. C 84 042202(R) (2011) Leading pQCD φ π (x)=6 x (1-x) Reconstructed from 100 moments E π (k 2 ) but constant mass quark a 2 <0 a 2 >0

40. Pion’s valence-quark Distribution Amplitude  x ≈ 0 & x ≈ 1 correspond to maximum relative momentum within bound-state –expose pQCD physics  x ≈ ½ corresponds to minimum possible relative momentum –behaviour of distribution around midpoint is strongly influence by DCSB 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 40 Leading pQCD φ π (x)=6 x (1-x)  Preliminary results, rainbow-ladder QCD analyses of (1/k 2 ) ν =1 interaction humped disfavoured but modest flattening

41. Pion’s valence-quark Distribution Amplitude  x ≈ 0 & x ≈ 1 correspond to maximum relative momentum within bound-state –expose pQCD physics  x ≈ ½ corresponds to minimum possible relative momentum –behaviour of distribution around midpoint is strongly influence by DCSB 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 41 Leading pQCD φ π (x)=6 x (1-x)  Preliminary results, rainbow-ladder QCD analyses of (1/k 2 ) ν =1 interaction humped disfavoured but modest flattening

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43. Unification of Meson & Baryon Properties  Correlate the properties of meson and baryon ground- and excited-states within a single, symmetry-preserving framework  Symmetry-preserving means: Poincaré-covariant Guarantee Ward-Takahashi identities Express accurately the pattern by which symmetries are broken Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 43 2.10.12: QCDNP2012-Matalascanas - 65

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...  Both have “correct” parity and “right” masses  In Nucleon’s Rest Frame Amplitude has s−, p− & d−wave correlations Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 44 diquark quark quark exchange ensures Pauli statistics composed of strongly- dressed quarks bound by dressed-gluons 2.10.12: QCDNP2012-Matalascanas - 65 R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145

45. Contact Interaction 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 45  Symmetry-preserving treatment of vector×vector contact interaction is useful tool for the study of phenomena characterised by probe momenta less-than the dressed-quark mass, M. Because: For experimental observables determined by probe momenta Q 2 <M 2, contact interaction results are not realistically distinguishable from those produced by the most sophisticated renormalisation-group-improved kernels.  Symmetry-preserving regularisation of the contact interaction serves as a useful surrogate, opening domains which analyses using interactions that more closely resemble those of QCD are as yet unable to enter.  They’re critical in attempts to use data as tool for charting nature of the quark-quark interaction at long-range; i.e., identifying signals of the running of couplings and masses in QCD.

46. Contact Interaction  arXiv:1204.2553 [nucl-th] arXiv:1204.2553 [nucl-th] Spectrum of hadrons with strangeness Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson  arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages] arXiv:1112.2212 [nucl-th]Phys. Rev. C85 (2012) 025205 [21 pages] Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts  arXiv:1102.4376 [nucl-th], Phys. Rev. C 83, 065206 (2011) [12 pages], arXiv:1102.4376 [nucl-th]Phys. Rev. C 83, 065206 (2011) [12 pages] π- and ρ-mesons, and their diquark partners, from a contact interaction, H.L.L. Roberts, A. Bashir, L.X. Gutierrez-Guerrero, C.D. Roberts and David J. Wilson  arXiv:1101.4244 [nucl-th], Few Body Syst. 51 (2011) pp. 1-25 arXiv:1101.4244 [nucl-th]Few Body Syst. 51 (2011) pp. 1-25 Masses of ground and excited-state hadrons H.L.L. Roberts, Lei Chang, Ian C. Cloët and Craig D. Roberts  arXiv:1009.0067 [nucl-th], Phys. Rev. C82 (2010) 065202 [10 pages] arXiv:1009.0067 [nucl-th]Phys. Rev. C82 (2010) 065202 [10 pages] Abelian anomaly and neutral pion production Hannes L.L. Roberts, C.D. Roberts, A. Bashir, L. X. Gutiérrez-Guerrero & P. C. Tandy  arXiv:1002.1968 [nucl-th], Phys. Rev. C 81 (2010) 065202 (5 pages) arXiv:1002.1968 [nucl-th]Phys. Rev. C 81 (2010) 065202 (5 pages) Pion form factor from a contact interaction L. Xiomara Gutiérrez-Guerrero, Adnan Bashir, Ian C. Cloët and C. D. Roberts 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 46 Symmetry-preserving treatment of vector- vector contact-interaction: series of papers establishes strengths & limitations.

47. Spectrum of Hadrons with Strangeness  Solve gap equation for u & s-quarks  Input ratio m s /m u = 24 is consistent with modern estimates  Output ratio M s /M u = 1.43 shows dramatic impact of DCSB, even on the s-quark: M s -m s = 0.36 GeV = M 0 … This is typical of all DSE and lattice studies  κ = in-hadron condensate rises slowly with mass of hadron 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 47 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson

48. Spectrum of Mesons with Strangeness  Solve Bethe-Salpeter equations for mesons and diquarks 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 48 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson

49. Spectrum of Mesons with Strangeness  Solve Bethe-Salpeter equations for mesons and diquarks 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 49 Computed values for ground-states are greater than the empirical masses, where they are known. Typical of DCSB-corrected kernels that omit resonant contributions; i.e., do not contain effects that may phenomenologically be associated with a meson cloud. Perhaps underestimate radial- ground splitting by 0.2GeV arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson

50. Spectrum of Diquarks with Strangeness  Solve Bethe-Salpeter equations for mesons and diquarks 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 50 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson

51. Spectrum of Diquarks with Strangeness  Solve Bethe-Salpeter equations for mesons and diquarks 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 51 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson Level ordering of diquark correlations is same as that for mesons. In all diquark channels, except scalar, mass of diquark’s partner meson is a fair guide to the diquark’s mass: o Meson mass bounds the diquark’s mass from below; o Splitting always less than 0.13GeV and decreases with increasing meson mass Scalar channel “special” owing to DCSB

52. Bethe-Salpeter amplitudes  Bethe-Salpeter amplitudes are couplings in Faddeev Equation  Magnitudes for diquarks follow precisely the meson pattern 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 52 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson Owing to DCSB, FE couplings in ½ - channels are 25-times weaker than in ½ + !

53. Spectrum of Baryons with Strangeness  Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 53 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson

54. Spectrum of Baryons with Strangeness  Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 54 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson  As with mesons, computed baryon masses lie uniformly above the empirical values.  Success because our results are those for the baryons’ dressed- quark cores, whereas empirical values include effects associated with meson-cloud, which typically produce sizable reductions. Jülich EBAC

55. Spectrum of Baryons with Strangeness  Updated comparison with bare masses from ANL-Osaka Coupled Channels Collaboration Searched for best fit, including (CC BARE -DSE) 2 ANL-Osaka bare masses provide excellent description of enormous amount of data  rms |Rel. Err.| = 9.4 ± 5.7 % This is remarkable, given that the DSE results have neither been optimised nor tuned in any way. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 55 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson & Toru Sato, private communication. P 11 S 11 P 33 D 33 ANL-Osaka1.832.042.611.282.162.13 DSE1.832.302.351.391.842.33 |Rel. Err.|011.3%11.1%7.9%17.4%8.6%

56. Structure of Baryons with Strangeness  Baryon structure is flavour-blind 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 56 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson Diquark content

57. Structure of Baryons with Strangeness  Baryon structure is flavour-blind 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 57 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, Chang, Roberts, Wan and Wilson & Nucleon and Roper em elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts, arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]arXiv:1112.2212 [nucl-th]Phys. Rev. C85 (2012) 025205 [21 pages] Diquark content  J qq =0 content of J= ½ baryons is almost independent of their flavour structure  Radial excitation of ground-state octet possess zero scalar diquark content!  This is a consequence of DCSB  Ground-state (1/2) + possess unnaturally large scalar diquark content  Orthogonality forces radial excitations to possess (almost) none at all! 80% 50% 0%

58. Spectrum of Hadrons with Strangeness  Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 58 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson (1/2)+ (1/2)-

59. Spectrum of Hadrons with Strangeness  Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 59 arXiv:1204.2553 [nucl-th], arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson (1/2)+ (1/2)-  This level ordering has long been a problem in CQMs with linear or HO confinement potentials  Correct ordering owes to DCSB  Positive parity diquarks have Faddeev equation couplings 25- times greater than negative parity diquarks  Explains why approaches within which DCSB cannot be realised (CQMs) or simulations whose parameters suppress DCSB will both have difficulty reproducing experimental ordering

60. Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 60 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” I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th] 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] Distribution of neutron’s momentum amongst quarks on the valence-quark domain 2.10.12: QCDNP2012-Matalascanas - 65 DSE: “contact” Melnitchouk et al. Phys.Rev. D84 (2011) 117501 x=1 means Q 2 +2p.q=0 “elastic scattering” Means d v /u v = (P d /P u ) elastic Obtained from Q 2 =0 flavour- separated Dirac form factor

61. Nucleon to Roper Transition Form Factors  Extensive CLAS @ JLab Programme has produced the first measurements of nucleon-to-resonance transition form factors  Theory challenge is to explain the measurements  Notable result is zero in F 2 p→N *, explanation of which is a real challenge to theory.  First observation of a zero in a form factor 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 61 I. Aznauryan et al., Results of the N* Program at JLab arXiv:1102.0597 [nucl-ex]

62. Nucleon to Roper Transition Form Factors  Extensive CLAS @ JLab Programme has produced the first measurements of nucleon-to-resonance transition form factors  Theory challenge is to explain the measurements  Notable result is zero in F 2 p→N *, explanation of which is a real challenge to theory.  DSE study connects appearance of zero in F 2 p→N * with axial-vector-diquark dominance in Roper resonance and structure of form factors of J=1 state 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 62 I. Aznauryan et al., Results of the N* Program at JLab arXiv:1102.0597 [nucl-ex] Γ μ,αβ Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts, Phys. Rev. C85 (2012) 025205 [21 pages]Phys. Rev. C85 (2012) 025205 [21 pages] Solid – DSE Dashed – EBAC Quark Core Near match supports picture of Roper as quark core plus meson cloud

63. Nucleon to Roper Transition Form Factors  Tiator and Vanderhaeghen – in progress –Empirically-inferred light-front-transverse charge density –Positive core plus negative annulus  Readily explained by dominance of axial-vector diquark configuration in Roper –Considering isospin and charge Negative d-quark twice as likely to be delocalised from the always-positive core than the positive u-quark 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 63 {uu} d 2 {ud} u 1+

64. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 64

65.  Confinement with light-quarks is not connected in any known way with a linear potential; not with a potential of any kind.  Confinement with light-quarks is associated with a dramatic change in the infrared structure of the parton propagators.  Dynamical chiral symmetry breaking, the origin of 98% of visible matter in universe, is manifested unambiguously and fundamentally in an equivalence between the one- and two- body problem in QCD  Working together to chart the behaviour of the running masses in QCD, experiment and theory can potentially answer the questions of confinement and dynamical chiral symmetry breaking; a task that currently each alone find hopeless. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 65 QCD is the most interesting part of the standard model - Nature’s only example of an essentially nonperturbative fundamental theory,

66. 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 66

67. Contents  ConfinementConfinement  Dynamical chiral symmetry breaking Dynamical chiral symmetry breaking  New Paradigm “in-hadron condensates” New Paradigm “in-hadron condensates”  Dichotomy of the pion Dichotomy of the pion  Pion valence-quark distribution Pion valence-quark distribution  Pion’s Distribution Amplitude Pion’s Distribution Amplitude  Grand Unification - Mesons and Baryons Grand Unification - Mesons and Baryons  Neutron Structure Function at high x Neutron Structure Function at high x  Nucleon to Roper Transition Form Factors Nucleon to Roper Transition Form Factors  Epilogue Epilogue 2.10.12: QCDNP2012-Matalascanas - 65 Craig Roberts: Deconstructing Hadrons in Continuum Strong QCD 67