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Craig Roberts, Physics Division

Strong coupling QCD – the ins and outs of bound-states. Craig Roberts, Physics Division. Students, Postdocs , Asst. Profs. Collaborators: 2012-Present. Lei Chang (U. Adelaide ) ; Ian Cloet (ANL) ; Bruno El- Bennich (São Paulo);. Adnan BASHIR ( U Michoácan ); Stan BRODSKY (SLAC);

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Craig Roberts, Physics Division

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  1. Strong coupling QCD – the ins and outs of bound-states Craig Roberts, Physics Division

  2. Students, Postdocs, Asst. Profs. Collaborators: 2012-Present • Lei Chang (U. Adelaide) ; • 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); • HervéMoutarde (CEA, Saclay) ; • Michael RAMSEY-MUSOLF (UM-Amherst) ; • Alfredo RAYA (U Michoácan); • Jose RodriguezQintero (U. Huelva) ; • 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: Strong-coupling QCD and the ins and outs of bound-states Rocio BERMUDEZ (U Michoácan); Shi CHAO (Nanjing U) ; Ming-hui DING (PKU); Fei GAO (PKU) ; S. HERNÁNDEZ(U Michoácan); Cédric MEZRAG (CEA, Saclay) ; Trang NGUYEN (KSU); Khépani RAYA (U Michoácan); Hannes ROBERTS (ANL, FZJ, UBerkeley); Chien-Yeah SENG (UM-Amherst) ; 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);

  3. Physics is an empirical science Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  4. It’s not physics unless it can be tested empirically. Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  5. It’s not proven unless it’s verified experimentally. Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  6. Top Open Questions in Physics Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  7. Understand the 4% of material that we know exists Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  8. Key Questions for the Future Examples of Emergent Phenomena in QCD, the strong-interaction sector of the Standard Model Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states What is confinement? Where is the mass of the nucleon? Where is the nucleon's magnetic moment? What is the nucleon? What is a hadron? …

  9. Key Questions for the Future One cannot properly know what lies beyond the Standard Model unless one first knows what is in the Standard Model Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states What is confinement? Where is the mass of the nucleon? Where is the nucleon's magnetic moment? What is the nucleon? What is a hadron? …

  10. Jefferson Lab Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  11. Thomas Jefferson National Accelerator Facility (JLab) e.g. S. J. Brodsky and G. R. Farrar, Phys. Rev. Lett. 31, 1153 (1973) QCD scaling violations Parton model scaling Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states One of the primary reasons for building CEBAF/JLab Prediction: at energy-scales greater than some a priori unknown minimum value, Λ, cross-sections and form factors will behave as power = ( number valence-quarks– 1 +Δλ) Δλ=0,1, depending on whether helicity is conserved or flipped … prediction of 1/k2 vector-boson exchange logarithm = distinctive feature & concrete prediction of QCD Initially imagined that Λ = 1GeV! So, JLab was initially built to reach 4GeV.

  12. Thomas Jefferson National Accelerator Facility (JLab) Particle physics paradigm Particle physics paradigm Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states • 1994 – 2004 • An enormous number of fascinating experimental results • Including an empirical demonstration that the distribution of charge and magnetisation within the proton are completely different, • Suggesting that quark-quark correlations play a crucial role in nucleon structure • But no sign of parton model scaling and certainly not of scaling violations

  13. Thomas Jefferson National Accelerator Facility (JLab) Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states 2004 … Mission Need Agreed on upgrade of CEBAF (JLab's accelerator) to 12GeV 2014 … 12GeV commissioning beams now being delivered to the experimental halls Final cost of upgrade is approximately $370-Million Physics of JLab at 12GeV arXiv:1208.1244 [hep-ex]

  14. Critical Theory Needs for JLab12 Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states • Experiment – Goal: accurate measurement of pion form factor to 6 GeV2; and it can produce a 10% measurement at 9 GeV2 • Experiment – Goal: Accurate measurement of nucleon elastic and transition form factors to 15 GeV2 • Experiment – Goal: Hadron tomography in momentum and configuration space • Critical need for success of Laboratory’s programme • Insightful computational framework • Capable of computing hadron wave functions • Capable of predicting and unifying meson & nucleon elastic and transition form factors on 0<Q2<15 GeV2 • Possessing direct connection to QCD, so that connection with established predictions of (perturbative) QCD can be established

  15. Contemporary Theory Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states • Dyson-Schwinger equations • Insightful computational framework • Established connection with predictions of (perturbative) QCD • Capable of predicting and unifying meson & nucleon elastic and transition form factors on 0<Q2<20 GeV2 … and beyond • Capable of predicting pointwisebehaviour of hadronic parton distribution functions/amplitudes … valence-quark domain is understood

  16. Significant Progress on All Fronts • Novel understanding of gluonand quark • confinement and its consequences • is emerging from quantum field theory • Arriving at a clear picture of how hadron masses emerge dynamically in a universe with light quarks • Dynamical Chiral Symmetry Breaking (DCSB) • Realistic computations of ground-state hadron wave functions with a direct connection to QCD are now available • Quark-quark correlations are crucial in hadron structure and accumulating empirical evidence in support of this prediction Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  17. What is Confinement? Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  18. Light quarks & Confinement • Folklore … JLab Hall-DConceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes. Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states 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.”

  19. Light quarks & Confinement Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states • Problem: Pions … They’re unnaturally light 16 tonnes of force makes a lot of them.

  20. Light quarks & Confinement Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states Problem: 16 tonnes of force makes a lot of pions.

  21. G. Bali et al., PoS LAT2005 (2006) 308 Light quarks & Confinement Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states In the presence of light quarks, pair creation seems to occur non-localized and instantaneously

  22. G. Bali et al., PoS LAT2005 (2006) 308 Light quarks & Confinement Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states 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

  23. What is Dressing? Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  24. Quark Gap Equation Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  25. Dynamical ChiralSymmetry Breaking Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states • 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.

  26. In QCD: Gluons alsobecome massive! Gluon mass-squared function Present level of uncertainty using phenomenology and theory ∼ 30% Power-law suppressed in ultraviolet, so invisible in perturbation theory Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states Not just quarks … Gluons also have a gap equation … Gluons are cannibals – a particle species whose members become massive by eating each other!

  27. Massive Gauge Bosons! Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states • Gauge boson cannibalism … a new physics frontier … within the Standard Model • Asymptotic freedom means … ultraviolet behaviour of QCD is controllable • Dynamically generated masses for gluons and quarks means that QCD dynamically generates its own infrared cutoffs • Gluons and quarks with wavelength λ > 2/mass ≈ 1 fm decouple from the dynamics … Confinement?! • How does that affect observables? • It will have an impact in any continuum study • Must play a role in gluon saturation ... In fact, perhaps it’s a harbinger of gluon saturation?

  28. Confinement is dynamical! Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  29. Confinement Confined particle Normal particle Propagation described by rapidly damped wave & hence state cannot exist in observable spectrum σ ≈ 1/Im(m) ≈ 1/2ΛQCD≈ ½fm Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities, (or qualitatively analogous structures chracterised by a dynamically generated mass-scale) Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states • 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

  30. Quark Fragmentation An EIC will enable “3D” measurements relating to fragmentation and insight into real-world confinement meson meson meson Baryon meson Real-world confinement is a dynamical phenomenon, surrounded by mystery! σ Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states A quark begins to propagate in spacetime But after each “step” of length σ, on average, an interaction occurs, so that the quark losesits identity, sharing it with other partons Finally, a cloud of partons is produced, which coalesces into colour-singlet final states

  31. Symmetry preserving analyses in continuum QCD Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  32. Maris, Roberts and Tandy nucl-th/9707003, Phys.Lett. B420 (1998) 267-273  Pion’s Goldberger-Treiman relation 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: Strong-coupling QCD and the ins and outs of bound-states • Pion’s Bethe-Salpeter amplitude Solution of the Bethe-Salpeter equation • Dressed-quark propagator • Axial-vector Ward-Takahashi identity entails

  33. fπ Eπ(p2) = B(p2) This is the most fundamental expression of Goldstone’s Theorem and DCSB Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  34. fπ Eπ(p2) = B(p2) Enigma of mass Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states • 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.

  35. Dynamical Chiral Symmetry BreakingVacuum Condensates? Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  36. Universal Conventions Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states • Wikipedia: (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.”

  37. “Orthodox Vacuum” u d u u d u u u d Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states 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!

  38. Historically, DCSB has come to be associated with the presumed existence of spacetime-independent condensates that permeate the Universe. However, just like gluons and quarks, and for the same reasons:Condensates are confined within hadrons. There are noin-vacuum condensates. Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  39. Confinement contains condensates Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  40. “Orthodox Vacuum” u d u u d u u u d Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states 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!

  41. New Paradigm u d u u d u u u d Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states Vacuum = perturbativehadronic fluctuations but no nonperturbative condensates Hadrons = complex, interacting systems within which perturbativebehaviour is restricted to just 2% of the interior

  42. Paradigm shift:In-Hadron Condensates “Void that is truly empty solves dark energy puzzle” Rachel Courtland, New Scientist 4th Sept. 2010 “The biggest embarrassment in theoretical physics.” • Cosmological Constant: • Putting QCD condensates back into hadrons reduces the • mismatch between experiment and theory by a factor of 1046 • Possibly by far more, if technicolour-like theories are the correct • paradigm for extending the Standard Model Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states “EMPTY space may really be empty. Though quantum theory suggests that a vacuum should be fizzing with particle activity, it turns out that this paradoxical picture of nothingness may not be needed. A calmer view of the vacuum would also help resolve a nagging inconsistency with dark energy, the elusive force thought to be speeding up the expansion of the universe.”

  43. Pion’s Wave Function Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

  44. 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: Strong-coupling QCD and the ins and outs of bound-states • Last two years, methods have been developed that enable direct computation of meson light-front wave functions • φπ(x) = twist-two parton distribution amplitude = 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≈0.5

  45. 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 Asymptotic DB RL Real-world PDAs are squat and fat Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states Continuum-QCD prediction: marked broadening of φπ(x), which owes to DCSB

  46. arXiv:1301.0324 [nucl-th], arXiv:1306.2645 [nucl-th], arXiv:1311.1390 [nucl-th], arXiv:1405.0289 [nucl-th], arXiv:1406:3353 [nucl-th] Features of Ground-state PDAs Concave function: no line segment lies above any point on the graph Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states A diverse array of studies since Caraguatatuba (2012) have shown that ground-state meson PDAs are broad, concave functions Camel-humped distributions – popular with some for many years – are physically unreasonable because they correspond to bound-state amplitudes that disfavour equal momentum partitioning between valence-quark degrees of freedom

  47. Pion electromagnetic form factor E12-06-101 and E12-07-105 Projected JLab reach Result imagined by many to be QCD prediction Evaluated withφπ = 6x(1-x) Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states 2013: existing data and theory – no hint of a trend toward the so-called asymptotic pQCD prediction? Jlab 12 will allow an extension of the Fπ measurement up to a value of Q2 of about 6 (GeV/c)2 & 10% measurement at 9 GeV2

  48. Pion electromagnetic form factor Agreement within 15% maximum Real QCD prediction – obtained with realistic, computed PDA • Predictions: • JLab will see maximum • Experiments to 8GeV2 will see parton model scaling and QCD scaling violations for the first time in a hadron form factor • Pion electromagnetic form factor at spacelikemomentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013) Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states • Understanding – Part 1 • Compare data with the real QCD prediction; i.e. the result calculated using the broad pion PDA predicted by modern analyses of continuum QCD • Understanding – Part 2 • Algorithm used to compute the PDA can also be employed to compute Fπ(Q2) directly, to arbitrarily large Q2

  49. Explanation and Prediction of Observables using Continuum Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv:1310.2651 [nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line] When is asymptotic PDA valid? Basic features of the pion valence-quark distribution function, L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29 Q2=27 GeV2 This is not δ(x)! Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states 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

  50. Explanation and Prediction of Observables using Continuum Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv:1310.2651 [nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line] 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 = 21% • <x>glue = 54%, <x>sea-quarks = 25% Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states 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?

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