1. Adnan BASHIR (U Michoacan); Stan BRODSKY (SLAC); Lei CHANG (ANL & PKU); Huan CHEN (BIHEP); Ian CLOËT (UW); Bruno EL-BENNICH (Sao Paulo); Xiomara GUTIERREZ-GUERRERO (U Michoacan); Roy HOLT (ANL); Mikhail IVANOV (Dubna); Yu-xin LIU (PKU); Trang NGUYEN (KSU); Si-xue QIN (PKU); Hannes ROBERTS (ANL, FZJ, UBerkeley); Robert SHROCK (Stony Brook); Peter TANDY (KSU); David WILSON (ANL) Craig Roberts Physics Division www.phy.anl.gov/theory/staff/cdr.html Students Early-career scientists Published collaborations in 2010/2011

2. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 2

3. Standard Model - History (a part)  In the early 20th Century, the only matter particles known to exist were the proton, neutron, and electron. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 3  With the advent of cosmic ray science and particle accelerators, numerous additional particles were discovered: o muon (1937), pion (1947), kaon (1947), Roper resonance (1963), …  By the mid-1960s, it was apparent that not all the particles could be fundamental. o A new paradigm was necessary.  Gell-Mann's and Zweig's constituent-quark theory (1964) was a critical step forward. o Gell-Mann, Nobel Prize 1969: "for his contributions and discoveries concerning the classification of elementary particles and their interactions".  Over the more than forty intervening years, the theory now called the Standard Model of Particle Physics has passed almost all tests.

4. Standard Model - The Heavy Piece  Strong interaction –Existence and composition of the vast bulk of visible matter in the Universe: proton, neutron the forces that form and bind them to form nuclei responsible for more than 98% of the visible matter in the Universe Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 4 –Politzer, Gross and Wilczek – 1973-1974 Perturbative Quantum Chromodynamics – QCD Nobel Prize (2004): "for the discovery of asymptotic freedom in the theory of the strong interaction".  NB. Worth noting that the character of 96% of the matter in the Universe is completely unknown

5. Simple picture - Proton Craig Roberts: The Physics of Hadrons 5 Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchange Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

6. Simple picture - Pion Craig Roberts: The Physics of Hadrons 6 Two quantum-mechanical constituent-quarks - particle+antiparticle - interacting via a potential, derived from one constituent-gluon exchange Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

7. Craig Roberts: The Physics of Hadrons 7

8. Excerpts from the top-10, or top-24, or …  What is dark energy? o 1998: A group of scientists had recorded several dozen supernovae, including some so distant that their light had started to travel toward Earth when the universe was only a fraction of its present age. o Contrary to their expectation, the scientists found that the expansion of the universe is not slowing, but accelerating. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 8 Saul Perlmutter, Brian P. Schmidt, Adam G. Riess, Nobel Prize 2011: for the discovery of the accelerating expansion of the Universe through observations of distant supernovae.

9. Excerpts from the top-10, or top-24, or …  Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap? o Quantum chromodynamics, or QCD, is the theory describing the strong nuclear force. o Carried by gluons, it binds quarks into particles like protons and neutrons. o Apparently, the tiny subparticles are permanently confined: one can't pull a quark or a gluon from a proton because the strong force gets stronger with distance and snaps them right back inside. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 9

10. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 10

11.  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 α 4. Extremely small probability because α 4 ≈10 -9 ! cf.Quantum Electrodynamics Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 11

12. 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 What is QCD? Craig Roberts: The Physics of Hadrons 12 3-gluon vertex 4-gluon vertex Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

13. What is QCD?  Novel feature of QCD –Tree-level interactions between gauge-bosons –O(α s ) cross-section cf. O( α em 4 ) in QED  One might guess that this is going to have a big impact  Elucidating part of that impact is the origin of the 2004 Nobel Prize to Politzer, and Gross & Wilczek Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 13 3-gluon vertex 4-gluon vertex

14. Running couplings  Quantum gauge-field theories are all typified by the feature that Nothing is Constant  Distribution of charge and mass, the number of particles, etc., indeed, all the things that quantum mechanics holds fixed, depend upon the wavelength of the tool being used to measure them –particle number is not conserved in quantum field theory  Couplings and masses are renormalised via processes involving virtual-particles. Such effects make these quantities depend on the energy scale at which one observes them Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 14

15. QED cf. QCD? Craig Roberts: The Physics of Hadrons 15 2004 Nobel Prize in Physics : Gross, Politzer and Wilczek fermion screening gluon antiscreening Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Add 3-gluon self-interaction 5 x10 -5

16. What is QCD?  This momentum-dependent coupling translates into a coupling that depends strongly on separation.  Namely, the interaction between quarks, between gluons, and between quarks and gluons grows rapidly with separation  Coupling is huge at separations r = 0.2fm ≈ ⅟₄ r proton Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 16 ↔ 0.002fm 0.02fm0.2fm α s (r) 0.1 0.2 0.3 0.4 0.5

17. Confinement in QCD  A peculiar circumstance; viz., an interaction that becomes stronger as the participants try to separate  If coupling grows so strongly with separation, then –perhaps it is unbounded? –perhaps it would require an infinite amount of energy in order to extract a quark or gluon from the interior of a hadron? Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 17 0.002fm 0.02fm0.2fm α s (r) 0.1 0.2 0.3 0.4 0.5  The Confinement Hypothesis: Colour-charged particles cannot be isolated and therefore cannot be directly observed. They clump together in colour-neutral bound- states  This is hitherto an empirical fact.

18. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 18

19. Strong-interaction: QCD  Asymptotically free –Perturbation theory is valid and accurate tool at large-Q 2 –Hence chiral limit (massless theory) is defined  Essentially nonperturbative for Q 2 < 2 GeV 2 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 19  Nature’s only example of truly nonperturbative, fundamental theory  A-priori, no idea as to what such a theory can produce

20. The Problem with QCD Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 20  Perhaps?!  What we know unambiguously … Is that we know too little!

21. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 21

22. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 22

23. Nuclear Science Advisory Council 2007 – Long Range Plan Craig Roberts: The Physics of Hadrons 23 “ A central goal of (the DOE Office of ) Nuclear Physics is to understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD. ”Nuclear Physics Ohio U., Physics & Astronomy, 7.10.2011, 88pgs  Internationally, this is an approximately $1-billion/year effort in experiment and theory, with approximately $375-million/year in the USA.  Roughly 90% of these funds are spent on experiment  $1-billion/year is the order of the operating budget of CERN

24. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 24

25. Facilities QCD Machines  USA –Thomas Jefferson National Accelerator Facility,Thomas Jefferson National Accelerator Facility Newport News, Virginia Nature of cold hadronic matter Upgrade underway Construction cost $310-million New generation experiments in 2016 –Relativistic Heavy Ion Collider, Brookhaven National Laboratory,Relativistic Heavy Ion Collider, Brookhaven National Laboratory Long Island, New York Strong phase transition, 10μs after Big Bang Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 25 A three dimensional view of the calculated particle paths resulting from collisions occurring within RHIC's STAR detectorSTAR detector

26. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 26

27. Nature’s strong messenger – Pion Craig Roberts: The Physics of Hadrons 27 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs  1947 – Pion discovered by Cecil Frank Powell The beginning of Particle Physics  Then came  Disentanglement of confusion between (1937) muon and pion – similar masses  Discovery of particles with “strangeness” (e.g., kaon 1947-1953 )  Subsequently, a complete spectrum of mesons and baryons with mass below ≈1 GeV  28 states  Became clear that pion is “too light” - hadrons supposed to be heavy, yet … π140 MeV ρ780 MeV P940 MeV

28. Simple picture - Pion Craig Roberts: The Physics of Hadrons 28  Gell-Mann and Ne’eman:  Eightfold way (1961) – a picture based on group theory: SU(3)  Subsequently, quark model – where the u-, d-, s-quarks became the basis vectors in the fundamental representation of SU(3)  Pion = Two quantum-mechanical constituent-quarks - particle+antiparticle - interacting via a potential Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

29. Some of the Light Mesons Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 29 140 MeV 780 MeV I G (J PC )

30. Modern Miracles in Hadron Physics Craig Roberts: The Physics of Hadrons 30 o proton = three constituent quarks M proton ≈ 1GeV Therefore guess M constituent−quark ≈ ⅓ × GeV ≈ 350MeV o pion = constituent quark + constituent antiquark Guess M pion ≈ ⅔ × M proton ≈ 700MeV o WRONG...................... M pion = 140MeV o Rho-meson Also constituent quark + constituent antiquark – just pion with spin of one constituent flipped M rho ≈ 770MeV ≈ 2 × M constituent−quark What is “wrong” with the pion? Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

31. Dichotomy of the pion Craig Roberts: The Physics of Hadrons 31  How does one make an almost massless particle from two massive constituent-quarks?  Naturally, one could always tune a potential in quantum mechanics so that the ground-state is massless – but some are still making this mistake  However: current-algebra (1968)  This is impossible in quantum mechanics, for which one always finds: Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

32. Dichotomy of the pion Goldstone mode and bound-state  The correct understanding of pion observables; e.g. mass, decay constant and form factors, requires an approach to contain a –well-defined and valid chiral limit; –and an accurate realisation of dynamical chiral symmetry breaking. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 32

33. Chiral Symmetry Craig Roberts: The Physics of Hadrons 33  Interacting gauge theories, in which it makes sense to speak of massless fermions, have a nonperturbative chiral symmetry  It is realised in the theory’s spectrum via the appearance of degenerate parity partners  Perturbative QCD: u- & d- quarks are very light m u /m d ≈ 0.5 & m d ≈ 4 MeV H. Leutwyler, 0911.1416 [hep-ph]0911.1416 [hep-ph]  However, splitting between parity partners is greater-than 100-times this mass-scale; e.g., Ohio U., Physics & Astronomy, 7.10.2011, 88pgs JPJP ⅟₂ + (p)⅟₂ - Mass940 MeV1535 MeV

34. Dynamical Chiral Symmetry Breaking  Something is happening in QCD –some inherent dynamical effect is dramatically changing the pattern by which the Lagrangian’s chiral symmetry is expressed  Qualitatively different from spontaneous symmetry breaking aka the Higgs mechanism –Nothing is added to the theory –Have only fermions & gauge-bosons Yet, the mass-operator generated by the theory produces a spectrum with no sign of chiral symmetry Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 34 Craig D RobertsJohn D Roberts

35. QCD’s Challenges  Dynamical Chiral Symmetry Breaking Very unnatural pattern of bound state masses; e.g., Lagrangian (pQCD) quark mass is small but... no degeneracy between J P =+ and J P =− (parity partners)  Neither of these phenomena is apparent in QCD’s Lagrangian Yet they are the dominant determining characteristics of real-world QCD. QCDQCD – Complex behaviour arises from apparently simple rules. Craig Roberts: The Physics of Hadrons 35  Quark and Gluon Confinement No matter how hard one strikes the proton, one cannot liberate an individual quark or gluon Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Understand emergent phenomena

36. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 36

37. Nucleon … Two Key Hadrons Proton and Neutron  Fermions – two static properties: proton electric charge = +1; and magnetic moment, μ p  Magnetic Moment discovered by Otto Stern and collaborators in 1933; Stern awarded Nobel Prize (1943): "for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton".  Dirac (1928) – pointlike fermion:  Stern (1933) –  Big Hint that Proton is not a point particle –Proton has constituents –These are Quarks and Gluons  Quark discovery via e-p-scattering at SLAC in 1968 –the elementary quanta of QCD Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 37 Friedman, Kendall, Taylor, Nobel Prize (1990): "for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics"

38. Nucleon Structure Probed in scattering experiments  Electron is a good probe because it is structureless Electron’s relativistic current is  Proton’s electromagnetic current Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 38 F 1 = Dirac form factorF 2 = Pauli form factor G E = Sachs Electric form factor If a nonrelativistic limit exists, this relates to the charge density G M = Sachs Magntic form factor If a nonrelativistic limit exists, this relates to the magnetisation density

39. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 39 Which is correct? How is the difference to be explained?

40. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 40

41. Nuclear Science Advisory Council 2007 – Long Range Plan Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 41 “ A central goal of (the DOE Office of ) Nuclear Physics is to understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD. ” Nuclear Physics

42. Understanding NSAC’s Long Range Plan Craig Roberts: The Physics of Hadrons 42  Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom?  If not, with what should they be replaced? What is the meaning of the NSAC Challenge?  What are the quarks and gluons of QCD?  Is there such a thing as a constituent quark, a constituent-gluon? After all, these are the concepts for which Gell-Mann won the Nobel Prize. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

43. Under these circumstances:  Can 12 C be produced, can it be stable?  Is the deuteron stable; can Big-Bang Nucleosynthesis occur? (Many more existential questions …) Probably not … but it wouldn’t matter because we wouldn’t be around to worry about it. What is the meaning of all this? Craig Roberts: The Physics of Hadrons 43 Suppose QCD behaved reasonably →m π =m ρ, then repulsive and attractive forces in the Nucleon- Nucleon potential have the SAME range and there is NO intermediate range attraction. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

44. Craig Roberts: The Physics of Hadrons 44

45. Just get on with it!  But … QCD’s emergent phenomena can’t be studied using perturbation theory  So what? Same is true of bound-state problems in quantum mechanics!  Differences:  Here relativistic effects are crucial – virtual particles Quintessence of Relativistic Quantum Field Theory  Interaction between quarks – the Interquark Potential – Unknown throughout > 98% of the pion’s/proton’s volume!  Understanding requires ab initio nonperturbative solution of fully- fledged interacting relativistic quantum field theory, something which Mathematics and Theoretical Physics are a long way from achieving. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 45

46. The Traditional Approach – Modelling – has its problems. How can we tackle the SM’s Strongly-interacting piece? Craig Roberts: The Physics of Hadrons 46 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

47. How can we tackle the SM’s Strongly-interacting piece? Lattice-QCD Craig Roberts: The Physics of Hadrons 47 – Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

48. How can we tackle the SM’s Strongly-interacting piece? Lattice-QCD – Craig Roberts: The Physics of Hadrons 48 – Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom – Approximately 500 people worldwide & 20-30 people per collaboration. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

49. A Compromise? Dyson-Schwinger Equations Craig Roberts: The Physics of Hadrons 49 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

50. A Compromise? Dyson-Schwinger Equations  1994... “As computer technology continues to improve, lattice gauge theory [LGT] will become an increasingly useful means of studying hadronic physics through investigations of discretised quantum chromodynamics [QCD].....” Craig Roberts: The Physics of Hadrons 50 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

51. A Compromise? Dyson-Schwinger Equations  1994... “However, it is equally important to develop other complementary nonperturbative methods based on continuum descriptions. In particular, with the advent of new accelerators such as CEBAF (VA) and RHIC (NY), there is a need for the development of approximation techniques and models which bridge the gap between short-distance, perturbative QCD and the extensive amount of low- and intermediate-energy phenomenology in a single covariant framework.... ” Craig Roberts: The Physics of Hadrons 51 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

52. A Compromise? Dyson-Schwinger Equations  1994... “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.” Craig Roberts: The Physics of Hadrons 52 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

53. A Compromise? Dyson-Schwinger Equations  1994... “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.”  C. D. Roberts and A. G. Williams, “Dyson-Schwinger equations and their application to hadronic physics,” Prog. Part. Nucl. Phys. 33, 477 (1994) [arXiv:hep-ph/9403224].[arXiv:hep-ph/9403224]. (473 citations) Craig Roberts: The Physics of Hadrons 53 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

54. A Compromise? DSEs Craig Roberts: The Physics of Hadrons 54  Dyson (1949) & Schwinger (1951)... One can derive a system of coupled integral equations relating all the Green functions for a theory, one to another. Gap equation: o fermion self energy o gauge-boson propagator o fermion-gauge-boson vertex  These are nonperturbative equivalents in quantum field theory of the Lagrange equations of motion.  Essential in simplifying the general proof of renormalisability of gauge field theories. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

55. Dyson-Schwinger Equations  Well suited to Relativistic Quantum Field Theory  Simplest level: Generating Tool for Perturbation Theory... Materially Reduces Model- Dependence … Statement about long-range behaviour of quark-quark interaction  NonPerturbative, Continuum approach to QCD  Hadrons as Composites of Quarks and Gluons  Qualitative and Quantitative Importance of:  Dynamical Chiral Symmetry Breaking – Generation of fermion mass from nothing  Quark & Gluon Confinement – Coloured objects not detected, Not detectable? Craig Roberts: The Physics of Hadrons 55  Approach yields Schwinger functions; i.e., propagators and vertices  Cross-Sections built from Schwinger Functions  Hence, method connects observables with long- range behaviour of the running coupling  Experiment ↔ Theory comparison leads to an understanding of long- range behaviour of strong running-coupling Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

56. QQCD is asymptotically-free (2004 Nobel Prize) CChiral-limit is well-defined; i.e., one can truly speak of a massless quark. NNB. This is nonperturbatively impossible in QED. DDressed-quark propagator: WWeak coupling expansion of gap equation yields every diagram in perturbation theory IIn perturbation theory: If m=0, then M(p 2 )=0 Start with no mass, Always have no mass. Mass from Nothing?! Perturbation Theory Craig Roberts: The Physics of Hadrons 56 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

57. Craig Roberts: The Physics of Hadrons 57 Craig D RobertsJohn D Roberts

58. Spontaneous(Dynamical) Chiral Symmetry Breaking The 2008 Nobel Prize in Physics was divided, one half awarded to Yoichiro Nambu "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics" Craig Roberts: The Physics of Hadrons 58 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

59. 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: The Physics of Hadrons 59 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

60. 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: The Physics of Hadrons 60 DSE prediction of DCSB confirmed Mass from nothing! Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

61. 12GeV The Future of JLab 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: The Physics of Hadrons 61 Jlab 12GeV: Scanned by 2<Q 2 <9 GeV 2 elastic & transition form factors. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

62. Universal Truths HHadron spectrum, and 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. 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 hadron physics calculations at even modest Q 2 require a Poincaré-covariant approach. Covariance + M(p 2 ) require 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. Craig Roberts: The Physics of Hadrons 62 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

63. 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.” Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 63 ?

64. “Dark Energy”  The only possible covariant form for the energy of the (quantum) vacuum; viz., is mathematically equivalent to the cosmological constant. “It is a perfect fluid and precisely spatially uniform” “Vacuum energy is almost the perfect candidate for dark energy.” Craig Roberts: The Physics of Hadrons 64 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs “The advent of quantum field theory made consideration of the cosmological constant obligatory not optional.” Michael Turner, “Dark Energy and the New Cosmology”

65. “Dark Energy”  QCD vacuum contribution  If chiral symmetry breaking is expressed in a nonzero expectation value of the quark bilinear, then the energy difference between the symmetric and broken phases is of order M QCD ≈0.3 GeV  One obtains therefrom: Craig Roberts: The Physics of Hadrons 65 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs “The biggest embarrassment in theoretical physics.” Mass-scale generated by spacetime-independent condensate Enormous and even greater contribution from Higgs VEV!

66. Resolution?  Quantum Healing Central:  “KSU physics professor [Peter Tandy] publishes groundbreaking research on inconsistency in Einstein theory.”  Paranormal Psychic Forums:  “Now Stanley Brodsky of the SLAC National Accelerator Laboratory in Menlo Park, California, and colleagues have found a way to get rid of the discrepancy. “People have just been taking it on faith that this quark condensate is present throughout the vacuum,” says Brodsky. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 66

67.  Resolution –Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime. –So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions. –GMOR cf. QCDQCD Paradigm shift: In-Hadron Condensates Craig Roberts: The Physics of Hadrons 67 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, PNAS 108, 45 (2011)PNAS 108, 45 (2011) Chang, Roberts, Tandy, arXiv:1109.2903 [nucl-th]arXiv:1109.2903 [nucl-th]

68. Paradigm shift: In-Hadron Condensates  Resolution –Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime. –So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions. –No qualitative difference between f π and ρ π –Both are equivalent order parameters for DCSB Craig Roberts: The Physics of Hadrons 68 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs And |π> →|0> matrix elements Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, PNAS 108, 45 (2011)PNAS 108, 45 (2011) Chang, Roberts, Tandy, arXiv:1109.2903 [nucl-th]arXiv:1109.2903 [nucl-th]

69.  Resolution –Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime. –So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions. –No qualitative difference between f π and ρ π –And Paradigm shift: In-Hadron Condensates Craig Roberts: The Physics of Hadrons 69 Chiral limit Ohio U., Physics & Astronomy, 7.10.2011, 88pgs One of ONLY TWO expressions related to the condensate that are rigorously defined in QCD for nonzero current-quark mass Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, PNAS 108, 45 (2011)PNAS 108, 45 (2011) Chang, Roberts, Tandy, arXiv:1109.2903 [nucl-th]arXiv:1109.2903 [nucl-th]

70. “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.”dark energy Paradigm shift: In-Hadron Condensates Craig Roberts: The Physics of Hadrons 70 “Void that is truly empty solves dark energy puzzle” Rachel Courtland, New Scientist 4 th Sept. 2010 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Cosmological Constant: Putting QCD condensates back into hadrons reduces the mismatch between experiment and theory by a factor of 10 46 Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard Model

71. Gap Equation General Form  D μν (k) – dressed-gluon propagator  Γ ν (q,p) – dressed-quark-gluon vertex  Suppose one has in hand – from anywhere – the exact form of the dressed-quark-gluon vertex What is the associated symmetry- preserving Bethe-Salpeter kernel?! Craig Roberts: The Physics of Hadrons 71 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

72. Bethe-Salpeter Equation Bound-State DSE  K(q,k;P) – fully amputated, two-particle irreducible, quark-antiquark scattering kernel  Textbook material.  Compact. Visually appealing. Correct Blocked progress for more than 60 years. Craig Roberts: The Physics of Hadrons 72 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

73. Bethe-Salpeter Equation General Form  Equivalent exact bound-state equation but in this form K(q,k;P) → Λ(q,k;P), which is completely determined by dressed-quark self-energy  Enables derivation of a Ward-Takahashi identity for Λ(q,k;P)  Now, for first time, by using this identity, it’s possible to formulate Ansatz for Bethe-Salpeter kernel given any form for dressed-quark-gluon vertex  This enables the identification and elucidation of a wide range of novel consequences of DCSB Craig Roberts: The Physics of Hadrons 73 Lei Chang and C.D. Roberts 0903.5461 [nucl-th] Phys. Rev. Lett. 103 (2009) 081601 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

74. Dressed-quark anomalous magnetic moments  Schwinger’s result for QED:  pQCD: two diagrams o (a) is QED-like o (b) is only possible in QCD – involves 3-gluon vertex  Analyse (a) and (b) o (b) vanishes identically: the 3-gluon vertex does not contribute to a quark’s anomalous chromomag. moment at leading-order o (a) Produces a finite result: “ – ⅙ α s /2π ” ~ (– ⅙) QED-result  But, in QED and QCD, the anomalous chromo- and electro- magnetic moments vanish identically in the chiral limit! Craig Roberts: The Physics of Hadrons 74 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

75. Dressed-quark anomalous magnetic moments  Interaction term that describes magnetic-moment coupling to gauge field o Straightforward to show that it mixes left ↔ right o Thus, explicitly violates chiral symmetry  Follows that in fermion’s e.m. current γ μ F 1 does cannot mix with σ μν q ν F 2 No Gordon Identity o Hence massless fermions cannot not possess a measurable chromo- or electro-magnetic moment  But what if the chiral symmetry is dynamically broken, strongly, as it is in QCD? Craig Roberts: The Physics of Hadrons 75 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

76. Dressed-quark anomalous magnetic moments  Three strongly-dressed and essentially- nonperturbative contributions to dressed-quark-gluon vertex: Craig Roberts: The Physics of Hadrons 76 DCSB Ball-Chiu term Vanishes if no DCSB Appearance driven by STI Anom. chrom. mag. mom. contribution to vertex Similar properties to BC term Strength commensurate with lattice-QCD Skullerud, Bowman, Kizilersu et al. hep-ph/0303176 Role and importance is Novel discovery Essential to recover pQCD Constructive interference with Γ 5 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs L. Chang, Y. –X. Liu and C.D. Roberts arXiv:1009.3458 [nucl-th] arXiv:1009.3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001

77. Dressed-quark anomalous magnetic moments Craig Roberts: The Physics of Hadrons 77  Formulated and solved general Bethe-Salpeter equation  Obtained dressed electromagnetic vertex  Confined quarks don’t have a mass-shell o Can’t unambiguously define magnetic moments o But can define magnetic moment distribution MEME κ ACM κ AEM Full vertex0.44-0.220.45 Rainbow-ladder0.3500.048  AEM is opposite in sign but of roughly equal magnitude as ACM L. Chang, Y. –X. Liu and C.D. Roberts arXiv:1009.3458 [nucl-th] arXiv:1009.3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001 Factor of 10 magnification Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

78. Dressed-quark anomalous magnetic moments Craig Roberts: The Physics of Hadrons 78  Potentially important for elastic and transition form factors, etc.  Significantly, also quite possibly for muon g-2 – via Box diagram, which is not constrained by extant data. L. Chang, Y. –X. Liu and C.D. Roberts arXiv:1009.3458 [nucl-th] arXiv:1009.3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001 Factor of 10 magnification  Formulated and solved general Bethe-Salpeter equation  Obtained dressed electromagnetic vertex  Confined quarks don’t have a mass-shell o Can’t unambiguously define magnetic moments o But can define magnetic moment distribution Contemporary theoretical estimates: 1 – 10 x 10 -10 Largest value reduces discrepancy expt.↔theory from 3.3σ to below 2σ. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

79. Craig Roberts: The Physics of Hadrons 79

80. DSEs and Baryons Craig Roberts: The Physics of Hadrons 80  M(p 2 ) – effects have enormous impact on meson properties.  Must be included in description and prediction of baryon properties.  M(p 2 ) 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 founded on observation that an interaction which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channel R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs r qq ≈ r π

81. Faddeev Equation Craig Roberts: The Physics of Hadrons 81  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 R.T. Cahill et al., Austral. J. Phys. 42 (1989) 129-145 diquark quark quark exchange ensures Pauli statistics Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

82. Nucleon Elastic Form Factors Craig Roberts: The Physics of Hadrons 82  Photon-baryon vertex Oettel, Pichowsky and von Smekal, nucl-th/9909082 I.C. Cloët et al. arXiv:0812.0416 [nucl-th]  “Survey of nucleon electromagnetic form factors” – unification of meson and baryon observables; and prediction of nucleon elastic form factors to 15 GeV 2 Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

83. Craig Roberts: The Physics of Hadrons 83 I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th]  Highlights again the critical importance of DCSB in explanation of real-world observables.  DSE result Dec 08 DDSE result – including the anomalous magnetic moment distribution I.C. Cloët, C.D. Roberts, et al. In progress Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

84.  DSE studies indicate that the proton has a very rich internal structure  The JLab data, obtained using the polarisaton transfer method, are an accurate indication of the behaviour of this ratio  The pre-1999 data (Rosenbluth) receive large corrections from so-called 2-photon exchange contributions Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 84 Proton plus proton-like resonances

85. Craig Roberts: The Physics of Hadrons 85 I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th] I.C. Cloët, C.D. Roberts, et al. In progress Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Linear fit to data ⇒ zero at 8GeV 2 [1,1] Padé fit ⇒ zero at 10GeV 2

86. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 86

87. Epilogue  No single approach is yet able to provide a unified description of all hadron phenomena –E.g., intelligent reaction theory will long be necessary as bridge between experiment and QCD-based theory  Nevertheless, DSEs today provide an insightful connection between QCD and experiment: –DCSB explained & developing a perspective on confinement Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 87  Physics is an experimental science; and there’s an international experimental programme …  Goal to understand … –how the interactions between dressed–quarks and –gluons create ground & excited hadrons; –how these interactions emerge from QCD

88. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs Craig Roberts: The Physics of Hadrons 88