1. The Physics of Hadrons Craig D. Roberts Physics Division Argonne National Laboratory & School of Physics Peking University

2. Length-Scales of Physics Craig Roberts, Physics Division: The Physics of Hadrons 2 Northwestern University: 7 Jan '11

3. Hadron Physics Craig Roberts, Physics Division: The Physics of Hadrons 3 “Hadron physics is unique at the cutting edge of modern science because Nature has provided us with just one instance of a fundamental strongly-interacting theory; i.e., Quantum Chromodynamics (QCD). The community of science has never before confronted such a challenge as solving this theory.” Northwestern University: 7 Jan '11

4. Nuclear Science Advisory Committee Long Range Plan Craig Roberts, Physics Division: The Physics of Hadrons 4 “ A central goal of (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. ” Northwestern University: 7 Jan '11

5. Relativistic Quantum Gauge Theory:  Interactions mediated by vector boson exchange  Vector bosons are perturbatively-massless  Similar interaction in QED  Special feature of QCD – gluon self-interactions, which completely change the character of the theory What is QCD? Craig Roberts, Physics Division: The Physics of Hadrons 5 3-gluon vertex 4-gluon vertex Northwestern University: 7 Jan '11

6. QED cf. QCD? Craig Roberts, Physics Division: The Physics of Hadrons 6 2004 Nobel Prize in Physics : Gross, Politzer and Wilczek fermion screening gluon antiscreening Northwestern University: 7 Jan '11 Add 3-gluon self-interaction 5 x10 -5

7. Quarks and Nuclear Physics Craig Roberts, Physics Division: The Physics of Hadrons 7 Standard Model of Particle Physics : SSix quark flavours Real World NNormal matter – only two light-quark flavours are active OOr, perhaps, three For numerous good reasons, much research also focuses on accessible heavy-quarks NNevertheless, I will focus on the light-quarks; i.e., u & d. Northwestern University: 7 Jan '11

8. Ford Nucleon, 1958 atomic powered car  Fermions – two static properties: proton electric charge = +1; and magnetic moment, μ p  Magnetic Moment discovered by Stern & collaborators -1933; Awarded Nobel Prize in 1943 Dirac (1928) – pointlike fermion: μ p = e/[2 M]  Stern (1933) – μ p = (1 + 1.79) e/[2 M] 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 Quantum Chromo-dynamics Northwestern University: 7 Jan '11 Craig Roberts, Physics Division: The Physics of Hadrons 8 Two Key Hadrons nucleon = neutron & proton

9.  Electron is an excellent probe because it’s structureless relativistic current:  Nucleon’s relativistic current Hadron structure exposed via studies of form factors Northwestern University: 7 Jan '11 Craig Roberts, Physics Division: The Physics of Hadrons 9 Point particle (Dirac): F 2 =0, hence μ p G E =G M

10. Pre-2000 μ p G E /G M Northwestern University: 7 Jan '11 Craig Roberts, Physics Division: The Physics of Hadrons 10 Distribution of charge and magnetisation is identical Strong support for simple s-wave models of nucleon structure

11. Simple picture - Proton Craig Roberts, Physics Division: The Physics of Hadrons 11 Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchange Northwestern University: 7 Jan '11

12. Simple picture - Pion Craig Roberts, Physics Division: The Physics of Hadrons 12 Two quantum-mechanical constituent-quarks - particle+antiparticle - interacting via a potential, derived from one constituent-gluon exchange Northwestern University: 7 Jan '11

13. Thomas Jefferson National Accelerator Facility (JLAB) Northwestern University: 7 Jan '11 Craig Roberts, Physics Division: The Physics of Hadrons 13 Newport News, Virginia  1 1994 – JLab begins operation  1995 – Reaches design energy of 4GeV e – beams  2000 – Reaches energy of 6GeV e – beams 009 – Construction begins on 12GeV upgrade Annual budget in excess of $200-million Upgrade is $310-million project Underground target halls Racecourse Accelerator

14. After-2000 μ p G E /G M Northwestern University: 7 Jan '11 Craig Roberts, Physics Division: The Physics of Hadrons 14 Data from JLab, using new method allowed by high-luminosity, changes picture completely Charge distribution is markedly differtent from magnetisation distribution. Strong indication that nucleon has complicated internal structure. Two puzzles: 1.Reconcile the data 2.If JLab correct, explain

15. Modern Miracles in Hadron Physics Craig Roberts, Physics Division: The Physics of Hadrons 15 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? Northwestern University: 7 Jan '11

16. Dichotomy of the pion Craig Roberts, Physics Division: The Physics of Hadrons 16  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: Northwestern University: 7 Jan '11

17. NSAC Long Range Plan? Craig Roberts, Physics Division: The Physics of Hadrons 17 IIf not, with what should they be replaced? WWhat is the meaning of the NSAC Challenge?  What is a constituent quark, a constituent-gluon?  Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom? Northwestern University: 7 Jan '11

18. Under these circumstances: CCan 12 C be stable? I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, Physics Division: The Physics of Hadrons 18 If m π =m ρ, then Repulsive & attractive forces in the Nucleon-Nucleon potential have the SAME range … and … There is NO intermediate range attraction. Northwestern University: 7 Jan '11

19. 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, Physics Division: The Physics of Hadrons 19  Quark and Gluon Confinement No matter how hard one strikes the proton, one cannot liberate an individual quark or gluon Northwestern University: 7 Jan '11 Understand emergent phenomena

20. Why don’t we just stop talking & solve the problem?  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 Craig Roberts, Physics Division: The Physics of Hadrons 20 Northwestern University: 7 Jan '11

21. Universal Truths SSpectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron's characterising properties amongst its QCD constituents. DDynamical Chiral Symmetry Breaking (DCSB) is most important mass generating mechanism for visible matter in the Universe. Higgs mechanism is ( almost ) irrelevant to light-quarks. RRunning of quark mass entails that calculations at even modest Q 2 require a Poincaré-covariant approach. Covariance requires existence of quark orbital angular momentum in hadron's rest-frame wave function. CConfinement is expressed through a violent change of the propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator. It is intimately connected with DCSB. Craig Roberts, Physics Division: The Physics of Hadrons 21 Northwestern University: 7 Jan '11

22. Chiral symmetry Craig Roberts, Physics Division: Much Ado About Nothing 22  Feature of massless fermions in relativistic quantum field theory  Realised in the spectrum of the theory 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., Physics Division: 17 Dec 2010 JPJP ⅟₂ + (p)⅟₂ - Mass940 MeV1535 MeV

23. Universal Conventions  Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum)(http://en.wikipedia.org/wiki/QCD_vacuum) “The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non- perturbative vacuum state, characterized by many non- vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.” Craig Roberts, Physics Division: The Physics of Hadrons 23 Northwestern University: 7 Jan '11

24. Universal Misapprehensions  Since 1979, DCSB has commonly been associated literally with a spacetime- independent mass-dimension-three “vacuum condensate.”  Under this assumption, “condensates” couple directly to gravity in general relativity and make an enormous contribution to the cosmological constant  Experimentally, the answer is Ω cosm. const. = 0.76  This mismatch is a bit of a problem. Craig Roberts, Physics Division: The Physics of Hadrons 24 Northwestern University: 7 Jan '11 “The biggest embarrassment in theoretical physics.”

25. The Traditional Approach – Modelling – has its problems. How can we tackle the SM’s Strongly-interacting piece? Craig Roberts, Physics Division: The Physics of Hadrons 25 Northwestern University: 7 Jan '11

26. How can we tackle the SM’s Strongly-interacting piece? Lattice-QCD Craig Roberts, Physics Division: The Physics of Hadrons 26 – Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom Northwestern University: 7 Jan '11

27. How can we tackle the SM’s Strongly-interacting piece? Lattice-QCD – Craig Roberts, Physics Division: The Physics of Hadrons 27 – Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom – Approximately 500 people worldwide & 20-30 people per collaboration. Northwestern University: 7 Jan '11

28. 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, Physics Division: The Physics of Hadrons 28 Northwestern University: 7 Jan '11

29. 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, Physics Division: The Physics of Hadrons 29 Northwestern University: 7 Jan '11

30. 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, Physics Division: The Physics of Hadrons 30 Northwestern University: 7 Jan '11

31. 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, Physics Division: The Physics of Hadrons 31 Northwestern University: 7 Jan '11

32. A Compromise? DSEs Craig Roberts, Physics Division: The Physics of Hadrons 32  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 to the Lagrange equations of motion.  Essential in simplifying the general proof of renormalisability of gauge field theories. Northwestern University: 7 Jan '11

33. 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, Physics Division: The Physics of Hadrons 33  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 Northwestern University: 7 Jan '11

34.  QCD is asymptotically-free (2004 Nobel Prize)  Chiral-limit is well-defined; i.e., one can truly speak of a massless quark.  NB. This is nonperturbatively impossible in QED.  Dressed-quark propagator:  Weak coupling expansion of gap equation yields every diagram in perturbation theory  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, Physics Division: The Physics of Hadrons 34 Northwestern University: 7 Jan '11

35. 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, Physics Division: The Physics of Hadrons 35 Northwestern University: 7 Jan '11

36. Gell-Mann – Oakes – Renner Relation (1968)  Pion’s leptonic decay constant, mass-dimensioned observable which describes rate of process π + →μ + ν  Vacuum quark condensate How is this expression modified and interpreted in a theory with confinement? Craig Roberts, Physics Division: The Physics of Hadrons 36 Northwestern University: 7 Jan '11

37. 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, Physics Division: The Physics of Hadrons 37 Northwestern University: 7 Jan '11

38. 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, Physics Division: The Physics of Hadrons 38 DSE prediction of DCSB confirmed Mass from nothing! Northwestern University: 7 Jan '11

39. 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, Physics Division: The Physics of Hadrons 39 Hint of lattice-QCD support for DSE prediction of violation of reflection positivity Northwestern University: 7 Jan '11

40. 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, Physics Division: The Physics of Hadrons 40 Jlab 12GeV: Scanned by 2<Q 2 <9 GeV 2 elastic & transition form factors. Northwestern University: 7 Jan '11

41. Universal Conventions  Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum)(http://en.wikipedia.org/wiki/QCD_vacuum) “The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non- perturbative vacuum state, characterized by many non- vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.” Craig Roberts, Physics Division: The Physics of Hadrons 41 Northwestern University: 7 Jan '11 What does this approach tell us? ?

42.  Building on the concepts and theory that produces the features that have been described, one can derive numerous exact results in QCD.  One of them explains the peculiar nature of the pion’s mass; i.e., it’s relationship to the Lagrangian current-quark mass m(ς): Dichotomy of the pion Craig Roberts, Physics Division: The Physics of Hadrons 42 This is an almost-familiar relation, a peculiar, non-quantum-mechanical Identity – looks like the GMOR What are the constants of proportionality, physically? P. Maris, C.D. Roberts & P.C. Tandy nucl-th/9707003 nucl-th/9707003 Northwestern University: 7 Jan '11

43. In-meson condensate Craig Roberts, Physics Division: The Physics of Hadrons 43 Maris & Roberts nucl-th/9708029  Pseudoscalar projection of pion’s Bethe-Salpeter wave- function onto the origin in configuration space: |Ψ π PS (0)| – or the pseudoscalar pion-to-vacuum matrix element  Rigorously defined in QCD – gauge-independent, cutoff- independent, etc.  For arbitrary current-quark masses  For any pseudoscalar meson Northwestern University: 7 Jan '11

44. In-meson condensate Craig Roberts, Physics Division: The Physics of Hadrons 44  Pseudovector projection of pion’s Bethe-Salpeter wave- function onto the origin in configuration space: |Ψ π AV (0)| – or the pseudoscalar pion-to-vacuum matrix element – or the pion’s leptonic decay constant  Rigorously defined in QCD – gauge-independent, cutoff- independent, etc.  For arbitrary current-quark masses  For any pseudoscalar meson Northwestern University: 7 Jan '11 Maris & Roberts nucl-th/9708029

45. In-meson condensate Craig Roberts, Physics Division: The Physics of Hadrons 45  Define  Then, using the pion Goldberger-Treiman relations, one derives, in the chiral limit  Namely, the so-called vacuum quark condensate is the chiral-limit value of the in-pion condensate  The in-pion condensate is the only well-defined function of current-quark mass in QCD that is smoothly connected to the vacuum quark condensate. Northwestern University: 7 Jan '11 Chiral limit Maris & Roberts nucl-th/9708029 |Ψ π PS (0)|*|Ψ π AV (0)|

46. Nature of the Pion: QCD’s Goldstone Mode Craig Roberts, Physics Division: The Physics of Hadrons 46 Northwestern University: 7 Jan '11

47. Nature of the Pion: QCD’s Goldstone Mode Craig Roberts, Physics Division: The Physics of Hadrons 47 2 → many or infinitely many Nature and number of constituents depends on the wavelength of the probe Constituent- quarks are replaced by the dressed-quarks and –gluons of QCD Northwestern University: 7 Jan '11

48.  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, Physics Division: The Physics of Hadrons 48 Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, arXiv:0905.1151 [hep-th], to appear in PNAS Northwestern University: 7 Jan '11

49. 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, Physics Division: The Physics of Hadrons 49 Northwestern University: 7 Jan '11 Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, arXiv:0905.1151 [hep-th], to appear in PNAS And |π> →|0> matrix elements

50.  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, Physics Division: The Physics of Hadrons 50 Chiral limit Northwestern University: 7 Jan '11 Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201 Brodsky and Shrock, arXiv:0905.1151 [hep-th], to appear in PNAS ONLY expression related to the condensate that is rigorously defined in QCD for nonzero current-quark mass

51. Paradigm shift: In-Hadron Condensates “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 Craig Roberts, Physics Division: The Physics of Hadrons 51 “Void that is truly empty solves dark energy puzzle” Rachel Courtland, New Scientist 4 th Sept. 2010 Northwestern University: 7 Jan '11 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

52. 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, Physics Division: The Physics of Hadrons 52 Northwestern University: 7 Jan '11

53. 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, Physics Division: The Physics of Hadrons 53 Northwestern University: 7 Jan '11

54. 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) Craig Roberts, Physics Division: The Physics of Hadrons 54 Lei Chang and C.D. Roberts 0903.5461 [nucl-th] Phys. Rev. Lett. 103 (2009) 081601 Northwestern University: 7 Jan '11

55. Ward-Takahashi Identity Bethe-Salpeter Kernel  Now, for first time, it’s possible to formulate an Ansatz for Bethe-Salpeter kernel given any form for the dressed-quark- gluon vertex by using this identity  This enables the identification and elucidation of a wide range of novel consequences of DCSB Craig Roberts, Physics Division: The Physics of Hadrons 55 Lei Chang and C.D. Roberts 0903.5461 [nucl-th] Phys. Rev. Lett. 103 (2009) 081601 iγ5iγ5 iγ5iγ5 Northwestern University: 7 Jan '11

56. 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, Physics Division: The Physics of Hadrons 56 Northwestern University: 7 Jan '11

57. 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, Physics Division: The Physics of Hadrons 57 Northwestern University: 7 Jan '11

58. Dressed-quark anomalous magnetic moments  Three strongly-dressed and essentially- nonperturbative contributions to dressed-quark-gluon vertex: Craig Roberts, Physics Division: The Physics of Hadrons 58 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 Lei Chang, Yu-Xin Liu and Craig D. Roberts arXiv:1009.3458 [nucl-th], arXiv:1009.3458 [nucl-th] to appear in Phys. Rev. Lett. Northwestern University: 7 Jan '11

59. Dressed-quark anomalous magnetic moments Craig Roberts, Physics Division: The Physics of Hadrons 59  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 Lei Chang, Yu-Xin Liu and Craig D. Roberts arXiv:1009.3458 [nucl-th], arXiv:1009.3458 [nucl-th] to appear in Phys. Rev. Lett. 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 o Potentially important for elastic & transition form factors, etc. o Muon g-2 ? Northwestern University: 7 Jan '11

60. DSEs and Baryons Craig Roberts, Physics Division: The Physics of Hadrons 60  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 Northwestern University: 7 Jan '11 r qq ≈ r π

61. Faddeev Equation Craig Roberts, Physics Division: The Physics of Hadrons 61  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 Northwestern University: 7 Jan '11

62. Spectrum of some known u- & d-quark baryons Craig Roberts, Physics Division: The Physics of Hadrons 62 H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts In progress; H.L.L. Roberts, L. Chang and C.D. Roberts arXiv:1007.4318 [nucl-th]arXiv:1007.4318 [nucl-th]; H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts arXiv:1007.3566 [nucl-th]arXiv:1007.3566 [nucl-th];  Baryons: ground-states and 1 st radial exciations mNmN m N* m N (⅟₂)m N* (⅟₂ - )mΔmΔ mΔ*mΔ* m Δ ( 3 ⁄₂ - ) m Δ* ( 3 ⁄₂ - ) DSE1.141.731.862.091.391.851.982.16 EBAC1.761.801.391.98  mean-|relative-error| = 2%-Agreement DSE dressed-quark-core masses cf. Excited Baryon Analysis Center bare masses is significant because no attempt was made to ensure this. 1 st radial Excitation of N(1535)? Northwestern University: 7 Jan '11

63. Nucleon Elastic Form Factors Craig Roberts, Physics Division: The Physics of Hadrons 63  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 Northwestern University: 7 Jan '11

64. Craig Roberts, Physics Division: The Physics of Hadrons 64 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. Northwestern University: 7 Jan '11  DSE result Dec 08 DDSE result – including the anomalous magnetic moment distribution I.C. Cloët, C.D. Roberts, et al. In progress

65. Craig Roberts, Physics Division: The Physics of Hadrons 65  New JLab data: S. Riordan et al., arXiv:1008.1738 [nucl-ex] arXiv:1008.1738 [nucl-ex]  DSE-prediction I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th]  This evolution is very sensitive to momentum-dependence of dressed-quark propagator Northwestern University: 7 Jan '11 Measurement of G E n at nonzero Q 2 is extremely difficult

66. Craig Roberts, Physics Division: The Physics of Hadrons 66  New JLab data: S. Riordan et al., arXiv:1008.1738 [nucl-ex] arXiv:1008.1738 [nucl-ex]  DSE-prediction I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th]  Location of zero measures relative strength of scalar and axial-vector qq-correlations Brooks, Bodek, Budd, Arrington fit to data: hep-ex/0602017 Northwestern University: 7 Jan '11

67. Craig Roberts, Physics Division: The Physics of Hadrons 67 Neutron Structure Function at high x Deep inelastic scattering – the Nobel-prize winning quark-discovery experiments Reviews:  S. Brodsky et al. NP B441 (1995)  W. Melnitchouk & A.W.Thomas PL B377 (1996) 11  R.J. Holt & C.D. Roberts RMP (2010) 2991 SU(6) symmetry pQCD 0 + qq only DSE: 0 + & 1 + qq I.C. Cloët, C.D. Roberts, et al. arXiv:0812.0416 [nucl-th] Distribution of neutron’s momentum amongst quarks on the valence-quark domain Northwestern University: 7 Jan '11 Related measure of 1 + /0 + strength

68. Craig Roberts, Physics Division: The Physics of Hadrons 68 Epilogue  Dynamical chiral symmetry breaking (DCSB) – mass from nothing for 98% of visible matter – is a reality o Expressed in M(p 2 ), with observable signals in experiment  Poincaré covariance o Crucial in description of contemporary data o Quantum mechanics is inadequate as a tool in hadron physics  Fully-self-consistent treatment of an interaction Essential if experimental data is truly to be understood.  Hadron internal structure is far from simple o Distribution of charge, magnetisation, momentum, spin amongst constituents is wavelength (and frame) dependent o Correlations between constituents are key – Confinement is almost certainly the origin of DCSB – DCSB is a property of hadrons, not the “vacuum” Northwestern University: 7 Jan '11