Craig Roberts Physics Division

1. Prospects for the physics of cold, sparse hadrons Craig Roberts Physics Division

2. Certifying Quantum Chromodynamics at Jefferson Lab

3. Students, Postdocs Asst. Profs. Collaborators: 2012-Present • Lei Chang (U. Adelaide, PKU) • Ian Cloet (ANL) • Bruno El-Bennich(São Paulo); • Adnan BASHIR (U Michoácan); • Stan BRODSKY (SLAC); • Gastão KREIN (São Paulo) • Roy HOLT (ANL); • 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) • Hong-Shi ZONG (Nanjing U) Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons Rocio BERMUDEZ (U Michoácan); Shi CHAO (Nanjing U) Ming-hui DING (PKU); Fei GAO (PKU) 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); Shu-sheng XU (Nanjing U) Chen CHEN (USTC); J. JavierCOBOS-MARTINEZ (U.Sonora); Mario PITSCHMANN (Vienna); Si-xue QIN(U. Frankfurt am Main, PKU); Jorge SEGOVIA (ANL); David WILSON (ODU);

4. Selected Science Challenges for the coming decade Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • Search for exotic hadrons • Discovery would force dramatic reassessment of the distinction between the notions of matter fields and force fields • Exploit opportunities provided by new data on nucleon 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 contemporray descriptions of nucleon structure

5. Selected Science Challenges for the coming decade Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • 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 • Explore and exploit opportunities to use precision-QCD as a probe for physics beyond the Standard Model

6. Selected Science Challenges for the coming decade • Electron Ion Collider • 3D structure of the nucleon • Understanding the formation of nuclei • QCD at extremeparton densities • Testing the Standard Model at the Intensity Frontier Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

7. Overarching Science Challenges for the coming decade Discover meaning of confinement and its relationship to DCSB – the Origin of Visible Mass Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

8. What is QCD? Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

9. QCD is a Theory (not an effective theory) Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • 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 < 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) Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg-Landau theory of superconductivity

10. What is QCD? Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • Lagrangian of QCD • G = gluon fields • Ψ = quark fields • The key to complexity in QCD … gluon field strength tensor • Generates gluon self-interactions, whose consequences are extraordinary

11. cf.Quantum Electrodynamics Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons QED is the archetypal gauge field theory Perturbatively simple but nonperturbatively undefined Chracteristic feature: Light-by-light scattering; i.e., photon-photon interaction – leading-order contribution takes place at order α4. Extremely small probability because α4 ≈10-9 !

12. What is QCD? • Relativistic Quantum Gauge Field Theory: • Interactions mediated by vector boson exchange • Vector bosons are perturbatively-massless • Similar interaction in QED • Special feature of QCD – gluon self-interactions 3-gluon vertex 4-gluon vertex Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

13. Strong-interaction: QCD • Nature’sonly (now known) example of a truly nonperturbative, fundamental theory • A-priori, no idea as to what such a theory can produce Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • Asymptotically free • Perturbation theory is valid and accurate tool at large-Q2 • Hence chiral limit is defined • Essentiallynonperturbative for Q2 < 2 GeV2

14. What is Confinement? Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

15. 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: Prospects for the Physics of Cold, Sparse Hadrons 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.”

16. Light quarks & Confinement Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • Problem: 16 tonnes of force makes a lot of pions.

17. Light quarks & Confinement Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons Problem: 16 tonnes of force makes a lot of pions.

18. G. Bali et al., PoS LAT2005 (2006) 308 Light quarks & Confinement Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons 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

19. 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 • State described by rapidly damped wave & hence state cannot exist in observable spectrum Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • 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

20. Light quarks & Confinement Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • In the study of hadrons, attention should turn 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?

21. Dynamical ChiralSymmetry Breaking Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

22. Mass from Nothing Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

23. 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: Prospects for the Physics of Cold, Sparse Hadrons • DCSB is a fact in QCD • Dynamical, not spontaneous • Add nothing to QCD , no Higgs field, nothing! Effect achieved purely through 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.

24. 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: Prospects for the Physics of Cold, Sparse Hadrons

25. Where does the mass come from? αS23 Just one of the terms that are summed in a solution of the simplest, reasonable truncation of QCD’s gap equation Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons 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

26. Enigma of Mass Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

27. 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! B(k2) Miracle: two body problem solved, almost completely, once solution of one body problem is known Owing to DCSB & Exact in Chiral QCD Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • Pion’s Bethe-Salpeter amplitude Solution of the Bethe-Salpeter equation • Dressed-quark propagator • Axial-vector Ward-Takahashi identity entails

28. Enigma of mass fπ Eπ(p2) = B(p2) Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • 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.

29. In QCD, Gluons, too, become massive Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons Not just quarks … Gluons also have a gap equation … 1/k2behaviour signals essential singularity in the running coupling: Impossible to reach in perturbation theory

30. Valence quarks Parton structure of hadrons Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

31. Parton Structure of Hadrons Craig Roberts: Prospects for the Physics of Cold, Sparse 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

32. Deep inelastic scattering Probability that a quark/gluon within the target will carry a fraction x of the bound-state’s light-front momentum 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 Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • Quark discovery experiment at SLAC (1966-1978, Nobel Prize in 1990) • Completely different to elastic scattering • Blow the target to pieces instead of keeping only those events where it remains intact. • Cross-section is interpreted as a measurement of the momentum-fraction probability distribution for quarks and gluons within the target hadron: q(x), g(x)

33. All along the light-front Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

34. Parton Structure of Hadrons Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • Light front provides a link with quantum mechanics • If a probability interpretation is ever valid, then it’s in the infinite-momentum frame • Enormous amount of intuitively expressive information about hadrons & processes involving them is encoded in • Parton distribution functions • Generalisedparton 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

35. Parton Structure of Hadrons Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • Need for calculation is emphasised by Saga of pion’s valence-quark distribution: • 1989 (E615): uvπ ~ (1-x)1 – inferred from LO-Drell-Yan Disagrees with QCD • “Predictions” from numerous models “explained” data and described it as challenge to QCD • 2001: DSE- QCD predicts uvπ ~ (1-x)2 argues that distribution inferred from data can’t be correct

36. Parton Structure of Hadrons Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • Need for calculation is emphasised by Saga of pion’s valence-quark distribution: • 1989 (E615): 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

37. fπ Eπ(p2) = B(p2) Enigma of mass Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons The properties of the almostmasslesspion are the cleanest expression of the mechanism that is responsible for almost all the visible mass in the universe. Pion properties are an (almost) direct measure of the dressed-quark mass function.  Possible to obtain robust theoretical predictions for pion distribution amplitudes and functions

38. Pion’s Wave Function Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons

39. Pion’s Bethe-Salpeter Wave Function Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • The pion’s total momentum “q” defines the light-front, so that • n⋅q = q+ , qperp = 0, n⋅x = 0 • Associated with this x+ = 0, so that x.q = x-q+ and x2 = xperp2 • There are two light-front wave functions • φπ(u,x2=xperp2), ψπ(u,x2=xperp2) • “u=k+/q+”measures the light-front fraction of the pion’s momentum carried by the valence-quark and “xperp2”measures the extent of the wave function in the direction perpendicular to the light-front

40. Pion’s Bethe-Salpeter Wave Function Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons Using n⋅x = 0, then and one recovers the direct connection between the light-front wave function & the pion’s covariant Bethe-Salpeter amplitude

41. “Twist” expansion Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • There is a rigorous definition • Related to the mass-dimension and angular momentum associated with an operator • For our purposes, however, it is enough to consider that φπ(u,xperp2) = φπ(2)(u,xperp2=0) … leading twist = 2 + xperp2φπ(4)(u,xperp2=0) … twist 4 + xperp4φπ(6)(u,xperp2=0) … twist 6 + … This is an expansion about the “light-cone” x2=0 . Each order in xperp2 relates to a given order in 1/[kperp2] • Some nonperturbative approaches; e.g., lattice-QCD and QCD sum rules, can only provide the first few elements which appear in this twist expansion They can’t provide direct access to the full xperp2 dependence

42. Parton Distribution AmplitudeLeading twist: φπ(2)(u,xperp2=0) • αS(Q2) is the strong running coupling, • φπ(u) is the meson’s twist-two valence-quark PDA • fP is the meson's leptonic decay constant Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons φπ(2)(u) is the amplitude associated with the probability that a given (dressed) valence quark will carry a fraction “u” of the hadron’s light-front momentum In the theory of strong interactions, the cross-sections for many hard exclusive hadronic reactions can be expressed in terms of the PDAs of the hadrons involved Example: pseudoscalar-meson elastic electromagnetic form factor

43. Pion’s valence-quark Distribution Amplitude Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons The distribution amplitude φπ(x) is actually dependent on the momentum-scale at which a particular interaction takes place; viz., φπ(x)= φπ(x,Q) Owing to conformal invariance of QCD, on some domain of asymptotic momenta, φπ(x) necessarily 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 φπ(x)=φπ(1-x) Evolution, analogous to that of the parton distribution functions, is encoded in the coefficients an(Q): these coefficients vanish as Q → ∞

44. Conformal QCD Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • an(Q) → 0 as Q→ ∞ Hence: φasy(x)= 6 x (1-x) = φconformal(x) • Question … thirty-plus years standing: When, if ever, can φasy(x) provide an empirically useful representation of hard exclusive processes involving the pion? • Only a reliable nonperturbative computation within QCD can answer that question.

45. Moments of the amplitudes Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • Typically, nonperturbative approaches can only provide access to moments of the distributions • If one has all the moments, then the distribution can be recovered exactly via standard mathematical methods (Inverse Mellin transform) • However, lattice-QCD breaks O(4) invariance • Hence, contemporary simulations can only produce m=0, 1, 2 • Sum rules, too, can only produce low-order moments • Because they don’t compute Bethe-Salpeter amplitudes • QCD’s Dyson-Schwinger equations • All moments can be computed • Associated distribution can be reconstructed precisely

46. 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 Pion’s Bethe-Salpeter wave function Whenever a nonrelativistic limit is realistic, this would correspond to the Schroedinger wave function. Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons • 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=0.5

47. 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: Prospects for the Physics of Cold, Sparse Hadrons Both kernels agree: marked broadening of φπ(x), which owes to DCSB

48. 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 First clear image of DCSB on the light-front; i.e., in the infinite momentum frame. Asymptotic DB RL Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons Both kernels agree: marked broadening of φπ(x), which owes to DCSB

49. 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: Prospects for the Physics of Cold, Sparse Hadrons

50. Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. Roberts, arXiv:1310.2651 [nucl-th], Prog. Part. Nucl. Phys. in press When is asymptotic PDA valid? Q2=27 GeV2 This is not δ(x)! Craig Roberts: Prospects for the Physics of Cold, Sparse Hadrons 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. (See Nobel-winning papers of Politzer, and Gross & Wilczek) This is far from valid at currently accessible scales