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 for Ian Cloët: Images of the Origin of Mass (66p) 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, ANL); J. JavierCOBOS-MARTINEZ (U.Sonora); Mario PITSCHMANN (Vienna); Si-xue QIN(PKU, U. Frankfurt am Main); Jorge SEGOVIA (ANL); David WILSON (ODU); Lei CHANG (PKU, U.Adelaide); Ian CLOËT (ANL); Bruno EL-BENNICH (São Paulo);

3. Pretend from now on that I am a vegetarian with a pony-tail, who was born in Australia and enjoys Belgian beer. Ian Cloët Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

4. Overarching Science Challenges for the coming decade: 2013-2022 Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 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.

5. Immediate Science Challenges for the coming decade: 2013-2022 Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • 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

6. What is QCD? Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

7. QCD is a Theory (not an effective theory) Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • 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

8. Contrast: so-called Effective Field Theories Can Cannot • QCD appears valid at all energy scales that have been tested so far: no breakdown below • E ≈ 60000 mπ • Cannot be used to test QCD • Any mismatch between • EF-Theory and experiment owes to an error in the formulation of one or conduct of the other Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) EFTs applicable over a very restricted energy domain; e.g., ChPT known to breakdown for E > 2mπ Can be used to help explore how features of QCD influence observables

9. What is Confinement? Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

10. 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 for Ian Cloët: Images of the Origin of Mass (66p) 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.”

11. Light quarks & Confinement Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • Problem: 16 tonnes of force makes a lot of pions.

12. Light quarks & Confinement Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) Problem: 16 tonnes of force makes a lot of pions.

13. G. Bali et al., PoS LAT2005 (2006) 308 Light quarks & Confinement Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 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

14. 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 for Ian Cloët: Images of the Origin of Mass (66p) • 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

15. Dynamical ChiralSymmetry Breaking Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

16. Mass from Nothing Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

17. 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 for Ian Cloët: Images of the Origin of Mass (66p) • 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.

18. 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 for Ian Cloët: Images of the Origin of Mass (66p)

19. Where does the mass come from? αS23 Just one of the terms that are summed in a solution of the rainbow-ladder gap equation Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) Deceptively simply picture Corresponds to the sum of a countable infinity of diagrams. NB. QED has 12,672 α5 diagrams Impossible to compute this in perturbation theory. The standard algebraic manipulation tools are just inadequate

20. Enigma of Mass Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

21. Bound-states in Quantum Field Theory Sketching the Bethe-Salpeter kernel, Lei Chang and Craig D. Roberts, arXiv:0903.5461 [nucl-th], Phys. Rev. Lett. 103 (2009) 081601 (4 pages) Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • Mass and “Wave Function” are obtained from a Bethe-Salpeter equation • Generalisation of the Lippmann-Schwinger equation • The pion … Nature’s strong-interaction messenger … is a critical example

22. Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273  Pion’s Goldberger-Treiman relation Pseudovector components necessarily nonzero. Cannot be ignored! Miracle: two body problem solved, almost completely, once solution of one body problem is known Exact in Chiral QCD Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • Pion’s Bethe-Salpeter amplitude Solution of the Bethe-Salpeter equation • Dressed-quark propagator • Axial-vector Ward-Takahashi identity entails

23. Dichotomy of the pionGoldstone mode and bound-state fπ Eπ(p2) = B(p2) Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • 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

24. Enigma of mass fπ Eπ(p2) = B(p2) Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • The quark level Goldberger-Treiman relation shows that DCSB has a very deep and far reaching impact on physics within the strong interaction sector of the Standard Model; viz., Goldstone's theorem is fundamentally an expression of equivalence between the one-body problem and the two-body problem in the pseudoscalar channel.  • This emphasises that Goldstone's theorem has a pointwise expression in QCD • Hence, pion properties are an almost direct measure of the dressed-quark mass function.  • Thus, enigmatically, the properties of the masslesspion are the cleanest expression of the mechanism that is responsible for almost all the visible mass in the universe.

25. Interaction model for the gap equationSi-xue Qin, Lei Chang, Y.-x.Liu, C.D. Roberts and D.J. WilsonarXiv:1108.0603 [nucl-th],  Phys. Rev. C 84 (2011) 042202(R) [5 pages] In QCD, Gluons, too, become massive Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) Not just quarks … Gluons also have a gap equation … 1/k2behaviour signals essential singularity in the running coupling: Impossible to reach in perturbation theory

26. Valence quarks Parton structure of hadrons Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

27. Parton Structure of Hadrons Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • 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

28. 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 for Ian Cloët: Images of the Origin of Mass (66p) • 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;

29. 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 for Ian Cloët: Images of the Origin of Mass (66p) • 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

30. DCSB on the light-front Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

31. Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • Developed DSE methods 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

32. 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 for Ian Cloët: Images of the Origin of Mass (66p) Both kernels agree: marked broadening of φπ(x), which owes to DCSB

33. 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 for Ian Cloët: Images of the Origin of Mass (66p) Both kernels agree: marked broadening of φπ(x), which owes to DCSB

34. 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 for Ian Cloët: Images of the Origin of Mass (66p)

35. Extracting information from lattice-QCD today Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

36. Valence-quark Distribution Amplitudes of light-quark mesons from lattice-QCD R. Arthur et al., Phys.Rev. D83 (2011) 07450 Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) PDA Moments from lattice-QCD Best available results show no distinction between pseudoscalar and vector, nor between light-front parallel and perpendicular polarisations DSE studies underway: Shi-chao, Peter Tandy et al.

37. Lei Chang et al. In progress. Valence-quark Distribution Amplitudes of light-quark mesons from lattice-QCD φπ~ xα (1-x)α α=0.35 φπ~ xα (1-x)β α=0.39±0.10 β=0.47 -/+ 0.16 +0.32 = 0.67 - 0.24 = 0.11 • Reconstruct PDAs using method described in Pion distribution amplitude from lattice-QCD, I. C. Cloët, L. Chang, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1306.2645 [nucl-th], Phys. Rev. Lett. 111 (2013) 092001 [5 pages] • SU(3) breaking is measured by shift in peak: ratio =1.09 • xmax=0.545 for φK(xmax) cf.xmax=φπ(½) for φπ (x) • cf. ratio of 1.15 for peak of [x svK(xmax)]/[x uvK(xmax)] Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

38. 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 for Ian Cloët: Images of the Origin of Mass (66p) 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

39. 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 for Ian Cloët: Images of the Origin of Mass (66p) 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?

40. 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 for Ian Cloët: Images of the Origin of Mass (66p) 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?

41. Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. Roberts At the “Planck scale” Evolution in QCD is LOGARITHMIC Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) In the truly asymptotic domain, way, way beyond LHC energy scales, gluons and sea-quarks share the momentum of a hadron, each with roughly 50% of the momentum

42. e(p) + H(q) → e(p’) + H(q’) Elastic Scattering Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

43. Peter Tandy can now die a happy man Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

44. 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) • However, using brute-force numerical techniques it was impossible to proceed reliably beyond Q2=4GeV2 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 for Ian Cloët: Images of the Origin of Mass (66p)

45. New Algorithm Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

46. Pion electromagnetic form factor at spacelikemomenta, Lei Changet al. arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111 (2013) 141802 [5 pages] 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 for Ian Cloët: Images of the Origin of Mass (66p)

47. R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145 BaryonStructure SUc(3): Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • 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

48. Faddeev Equation Baryon Structure SU(2)isospin symmetry of hadrons might emerge from mixing half-integer spin particles with their antiparticles. Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) 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

49. Nucleon StructureProbed in scattering experiments Structurelessfermion, or simply structured fermion, F1=1 & F2=0, so that GE=GM and hence distribution of charge and magnetisation within this fermion are identical F1 = Dirac form factor F2 = Pauli form factor GM = Sachs Magntic form factor If a nonrelativistic limit exists, this relates to the magnetisation density GE = Sachs Electric form factor If a nonrelativistic limit exists, this relates to the charge density Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) Electron is a good probe because it is structureless Electron’s relativistic current is Proton’s electromagnetic current

50. Structure of Hadrons Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p) • 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.