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Craig Roberts Physics Division

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 2

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QCD: The piece of the Standard Model that describes strong interactions. Hadron Physics is a nonperturbative problem in QCD Notwithstanding the 2013 Nobel Prize in Physics, the origin of 98% of the visible mass in the Universe is – somehow – found within QCD Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 3

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 4

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 5

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 6

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Facilities QCD Machines China –Beijing Electron-Positron ColliderBeijing Electron-Positron Collider Germany –COSY (Jülich Cooler Synchrotron)COSY (Jülich Cooler Synchrotron) –ELSA (Bonn Electron Stretcher and Accelerator)ELSA (Bonn Electron Stretcher and Accelerator) –MAMI (Mainz Microtron)MAMI (Mainz Microtron) –Facility for Antiproton and Ion Research,Facility for Antiproton and Ion Research under construction near Darmstadt. New generation experiments in 2018 (perhaps) Japan –J-PARC (Japan Proton Accelerator Research Complex),J-PARC under construction in Tokai-Mura, 150km NE of Tokyo. New generation experiments to begin soon −KEK: Tsukuba, Belle CollaborationBelle Collaboration Switzerland (CERN) –Large Hadron Collider: ALICE Detector and COMPASS DetectorALICE DetectorCOMPASS “Understanding deconfinement and chiral-symmetry restoration” Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 7

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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 2014 –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 Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 8 A three dimensional view of the calculated particle paths resulting from collisions occurring within RHIC's STAR detectorSTAR detector

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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 2014 Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 9

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All composite systems have “Form Factors”, which describe the distribution of an observable quantity amongst the constituents. Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 10

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Exploit opportunities provided by new data on hadron elastic and transition form factors –Chart infrared evolution of QCD’s coupling and dressed-masses –Reveal correlations that are key to nucleon structure –Expose the facts and fallacies in modern descriptions of hadron structure Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 11

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Quarks were discovered in deep inelastic scattering experiments at SLAC, more than 40yrs ago. We are finally acquiring the tools and expertise necessary to compute the distributions that are measured in such experiments. Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 12

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Precision experimental study of (far) valence region (Bjorken-x > 0.5), and theoretical computation of distribution functions and distribution amplitudes –Computation is critical –Without it, no amount of data will reveal anything about the theory underlying the phenomena of strong interaction physics within the Standard Model Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 13 Parton distribution functions (PDFs) and distribution amplitudes (PDAs) are a quantum field theory analogue of wave functions. They have a probability interpretation and hence relate to concepts familiar from quantum mechanics.

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 14

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 15

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 16

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Very likely a self-contained, nonperturbatively renormalisable and hence well defined Quantum Field Theory This is not true of QED – cannot be defined nonperturbatively No confirmed breakdown over an enormous energy domain: 0 GeV < E < 8000 GeV Increasingly likely that any extension of the Standard Model will be based on the paradigm established by QCD –Extended Technicolour: electroweak symmetry breaks via a fermion bilinear operator in a strongly-interacting non-Abelian theory. ( Andersen et al. “Discovering Technicolor” Eur.Phys.J.Plus 126 (2011) 81 )Eur.Phys.J.Plus 126 (2011) 81 Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg- Landau theory of superconductivity Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 17

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What is QCD? Lagrangian of QCD –G = gluon fields –Ψ = quark fields The key to complexity in QCD … gluon field strength tensor Generates gluon self-interactions, whose consequences are quite extraordinary Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 18

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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 Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 19

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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? Prospects for the physics of cold, sparse hadrons (87p) 20 3-gluon vertex 4-gluon vertex Craig Roberts: USTC Hefei, October 2013

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Strong-interaction: QCD Asymptotically free –Perturbation theory is valid and accurate tool at large-Q 2 –Hence chiral limit is defined Essentially nonperturbative for Q 2 < 2 GeV 2 Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 21 Nature’s only (now known) example of a truly nonperturbative, fundamental theory A-priori, no idea as to what such a theory can produce

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 22

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Light quarks & Confinement 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.” Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 23 Folklore … JLab Hall-D Conceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes.

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Light quarks & Confinement Problem: 16 tonnes of force makes a lot of pions. Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 24

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Light quarks & Confinement Problem: 16 tonnes of force makes a lot of pions. Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 25

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Light quarks & Confinement 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 Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 26 G. Bali et al., PoS LAT2005 (2006) 308PoS LAT2005 (2006) 308

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Confinement 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 Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 27 complex-P 2 o Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities, (or other qualitatively analogous structures chracterised by a dynamically generated mass-scale) o State described by rapidly damped wave & hence state cannot exist in observable spectrum Normal particle Confined particle timelike axis: P 2 <0 s ≈ 1/Im(m) ≈ 1/2Λ QCD ≈ ½fm

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Light quarks & Confinement In the study of hadrons, attention should turn from equal-time potential models toward the continuum bound-state problem in quantum field theory Such approaches offer the possibility of posing simultaneously the questions –What is confinement? –What is dynamical chiral symmetry breaking? –How are they related? –What are their empirical signals? Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 28

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 29

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 30

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Dynamical Chiral Symmetry Breaking DCSB is a fact in QCD –Dynamical, not spontaneous Add nothing to QCD, no Higgs field, nothing! Effect achieved purely through the quark+gluon dynamics. –It’s the most important mass generating mechanism for visible matter in the Universe. Responsible for ≈98% of the proton’s mass. Higgs mechanism is ( almost ) irrelevant to light-quarks. Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 31

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DCSB Prospects for the physics of cold, sparse hadrons (87p) 32 Mass from nothing! Craig Roberts: USTC Hefei, October 2013 C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50Prog. Part. Nucl. Phys. 61 (2008) 50 M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227AIP Conf.Proc. 842 (2006) 225-227 In QCD, all “constants” of quantum mechanics are actually strongly momentum dependent: couplings, number density, mass, etc. So, a quark’s mass depends on its momentum. Mass function can be calculated and is depicted here. Continuum- and Lattice-QCD are in agreement: the vast bulk of the light-quark mass comes from a cloud of gluons, dragged along by the quark as it propagates.

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 33

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 34

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“Orthodox Vacuum” 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! Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 35 u u u d u u d d u

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However, just like gluons and quarks, and for the same reasons: Condensates are confined within hadrons. There are no vacuum condensates. Historically, DCSB came to be associated with a presumed existence of spacetime- independent condensates that permeated the universe. Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 36

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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" Prospects for the physics of cold, sparse hadrons (87p) 37 Craig Roberts: USTC Hefei, October 2013

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Nambu – Jona-Lasinio Model Prospects for the physics of cold, sparse hadrons (87p) 38 Treats a chirally-invariant four-fermion Lagrangian & solves the gap equation in Hartree-Fock approximation (analogous to rainbow truncation) Possibility of dynamical generation of nucleon mass is elucidated Essentially inequivalent vacuum states are identified (Wigner and Nambu states) & demonstration that there are infinitely many, degenerate but distinct Nambu vacua, related by a chiral rotation Nontrivial Vacuum is “Born” Craig Roberts: USTC Hefei, October 2013 Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961) 345–358 Dynamical Model Of Elementary Particles Based On An Analogy With Superconductivity. II Y. Nambu, G. Jona-Lasinio, Phys.Rev. 124 (1961) 246-254

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Original Note of Warning Prospects for the physics of cold, sparse hadrons (87p) 39 Craig Roberts: USTC Hefei, October 2013 Chiral Magnetism (or Magnetohadrochironics) A. Casher and L. Susskind, Phys. Rev. D9 (1974) 436 These authors argue that dynamical chiral- symmetry breaking can be realised as a property of hadrons, instead of via a nontrivial vacuum exterior to the measurable degrees of freedom The essential ingredient required for a spontaneous symmetry breakdown in a composite system is the existence of a divergent number of constituents – DIS provided evidence for divergent sea of low-momentum partons – parton model.

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QCD Sum Rules Introduction of the gluon vacuum condensate and development of “sum rules” relating properties of low-lying hadronic states to vacuum condensates Prospects for the physics of cold, sparse hadrons (87p) 40 Craig Roberts: USTC Hefei, October 2013 QCD and Resonance Physics. Sum Rules. M.A. Shifman, A.I. Vainshtein, and V.I. Zakharov Nucl.Phys. B147 (1979) 385-447; citations: 3713

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QCD Sum Rules Introduction of the gluon vacuum condensate and development of “sum rules” relating properties of low-lying hadronic states to vacuum condensates At this point (1979), the cat was out of the bag: a physical reality was seriously attributed to a plethora of vacuum condensates Prospects for the physics of cold, sparse hadrons (87p) 41 Craig Roberts: USTC Hefei, October 2013 QCD and Resonance Physics. Sum Rules. M.A. Shifman, A.I. Vainshtein, and V.I. Zakharov Nucl.Phys. B147 (1979) 385-447; citations: 3781

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“quark condensate” 1960-1980 Instantons in non-perturbative QCD vacuum, Instantons in non-perturbative QCD vacuum MA Shifman, AI Vainshtein… - Nuclear Physics B, 1980 Instanton density in a theory with massless quarks, Instanton density in a theory with massless quarks MA Shifman, AI Vainshtein… - Nuclear Physics B, 1980 Exotic new quarks and dynamical symmetry breaking, Exotic new quarks and dynamical symmetry breaking WJ Marciano - Physical Review D, 1980 The pion in QCD The pion in QCD J Finger, JE Mandula… - Physics Letters B, 1980 No references to this phrase before 1980 Prospects for the physics of cold, sparse hadrons (87p) 42 Craig Roberts: USTC Hefei, October 2013

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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: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 43

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Overview Worth noting that nonzero vacuum expectation values of local operators in QCD—the so-called vacuum condensates—are phenomenological parameters, which were introduced at a time of limited computational resources in order to assist with the theoretical estimation of essentially nonperturbative strong- interaction matrix elements. A universality of these condensates was assumed, namely, that the properties of all hadrons could be expanded in terms of the same condensates. While this helps to retard proliferation, there are nevertheless infinitely many of them. As qualities associated with an unmeasurable state (the vacuum), such condensates do not admit direct measurement. Practitioners have attempted to assign values to them via an internally consistent treatment of many separate empirical observables. However, only one, the so-called quark condensate, is attributed a value with any confidence. Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 44

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QCDQCD How should one approach this problem, understand it, within Quantum ChromoDynamics? 1)Are the quark and gluon “condensates” theoretically well- defined? 2)Is there a physical meaning to this quantity or is it merely just a mass-dimensioned parameter in a theoretical computation procedure? Prospects for the physics of cold, sparse hadrons (87p) 45 Craig Roberts: USTC Hefei, October 2013 1973-1974

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QCDQCD Why does it matter? Prospects for the physics of cold, sparse hadrons (87p) 46 Craig Roberts: USTC Hefei, October 2013 1973-1974

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“Dark Energy” Two pieces of evidence for an accelerating universe 1)Observations of type Ia supernovae → the rate of expansion of the Universe is growing 2)Measurements of the composition of the Universe point to a missing energy component with negative pressure: CMB anisotropy measurements indicate that the Universe is at Ω 0 = 1 ⁺⁄₋ 0.04. In a flat Universe, the matter density and energy density must sum to the critical density. However, matter only contributes about ⅓ of the critical density, Ω M = 0.33 ⁺⁄₋ 0.04. Thus, ⅔ of the critical density is missing. Prospects for the physics of cold, sparse hadrons (87p) 47 Craig Roberts: USTC Hefei, October 2013

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“Dark Energy” In order not to interfere with the formation of structure (by inhibiting the growth of density perturbations) the energy density in this component must change more slowly than matter (so that it was subdominant in the past). Accelerated expansion can be accommodated in General Relativity through the Cosmological Constant, Λ. Einstein introduced the repulsive effect of the cosmological constant in order to balance the attractive gravity of matter so that a static universe was possible. He promptly discarded it after the discovery of the expansion of the Universe. Prospects for the physics of cold, sparse hadrons (87p) 48 Craig Roberts: USTC Hefei, October 2013 In order to have escaped detection, the missing energy must be smoothly distributed. Contemporary cosmological observations mean:

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“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.” Prospects for the physics of cold, sparse hadrons (87p) 49 Craig Roberts: USTC Hefei, October 2013 “The advent of quantum field theory made consideration of the cosmological constant obligatory not optional.” Michael Turner, “Dark Energy and the New Cosmology”

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“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: Prospects for the physics of cold, sparse hadrons (87p) 50 Craig Roberts: USTC Hefei, October 2013 “The biggest embarrassment in theoretical physics.” Mass-scale generated by spacetime-independent condensate Enormous and even greater contribution from Higgs VEV!

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 51

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GMOR Relation Valuable to highlight the precise form of the Gell-Mann– Oakes–Renner (GMOR) relation: Eq. (3.4) in Phys.Rev. 175 (1968) 2195Phys.Rev. 175 (1968) 2195 o m π is the pion’s mass o H χsb is that part of the hadronic Hamiltonian density which explicitly breaks chiral symmetry. The operator expectation value in this equation is evaluated between pion states. Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 52 Expanding the concept of in-hadron condensates Lei Chang, Craig D. Roberts and Peter C. Tandy arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R) arXiv:1109.2903 [nucl-th]Phys. Rev. C85 (2012) 012201(R)

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 53

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 54

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Gell-Mann Oakes Renner Relation Demonstrated algebraically that the so-called Gell-Mann – Oakes – Renner relation is the following statement Namely, the mass of the pion is completely determined by the pion’s scalar form factor at zero momentum transfer Q 2 = 0. Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 55

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Hadron Charges Hadron Form factor matrix elements Scalar charge of a hadron is an intrinsic property of that hadron … no more a property of the vacuum than the hadron’s electric charge, axial charge, tensor charge, etc. … Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 56

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 57

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“Orthodox Vacuum” 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! Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 58 u u u d u u d d u

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New Paradigm Vacuum = hadronic fluctuations but no condensates Hadrons = complex, interacting systems within which perturbative behaviour is restricted to just 2% of the interior Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 59 u u u d u u d d u

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“ 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: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 60 “Void that is truly empty solves dark energy puzzle” Rachel Courtland, New Scientist 4 th Sept. 2010 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 Paradigm shift: In-Hadron Condensates

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 61 Valence quarks

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Deep inelastic scattering Quark discovery experiment at SLAC (1966-1978, Nobel Prize in 1990) Completely different to elastic scattering –Blow the target to pieces instead of keeping only those events where it remains intact. Cross-section is interpreted as a measurement of the momentum-fraction probability distribution for quarks and gluons within the target hadron: q(x), g(x) Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 62 Probability that a quark/gluon within the target will carry a fraction x of the bound-state’s light-front momentum Distribution Functions of the Nucleon and Pion in the Valence Region, Roy J. Holt and Craig D. Roberts, arXiv:1002.4666 [nucl-th], Rev. Mod. Phys. 82 (2010) pp. 2991-3044 arXiv:1002.4666 [nucl-th]Rev. Mod. Phys. 82 (2010) pp. 2991-3044

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Parton Structure of Hadrons Valence-quark structure of hadrons –Definitive of a hadron. After all, it’s how we distinguish a proton from a neutron –Expresses charge; flavour; baryon number; and other Poincaré-invariant macroscopic quantum numbers –Via evolution, determines background at LHC Sea-quark distributions –Flavour content, asymmetry, intrinsic: yes or no? Answers are essentially nonperturbative features of QCD Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 63

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Parton Structure of Hadrons Light front provides a link with quantum mechanics –If a probability interpretation is ever valid, then it’s in the infinite-momentum frame Enormous amount of intuitively expressive information about hadrons & processes involving them is encoded in –Parton distribution functions –Generalised parton distribution functions –Transverse-momentum-dependent parton distribution functions Information will be revealed by the measurement of these functions – so long as they can be calculated Success of programme demands very close collaboration between experiment and theory Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 64

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Exact expression in QCD for the pion’s valence-quark parton distribution amplitude Expression is Poincaré invariant but a probability interpretation is only valid on the light-front because only thereupon does one have particle-number conservation. Probability that a valence-quark or antiquark carries a fraction x=k + / P + of the pion’s light-front momentum { n 2 =0, n.P = -m π } Pion’s valence-quark Distribution Amplitude Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 65 Pion’s Bethe-Salpeter wave function Whenever a nonrelativistic limit is realistic, this would correspond to the Schroedinger wave function.

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Pion’s valence-quark Distribution Amplitude Methods have recently been developed to compute φ π (x); viz., the projection of the pion’s Poincaré-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. x α (1-x) α, with α=0.3 Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 66 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].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]

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Pion’s valence-quark Distribution Amplitude Both kernels agree: marked broadening of φ π (x), which owes to DCSB Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 67 Asymptotic RL DB This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB. Difference between RL and DB results is readily understood: B(p 2 ) is more slowly varying with DB kernel and hence a more balanced result 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].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]

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Pion’s valence-quark Distribution Amplitude Both kernels agree: marked broadening of φ π (x), which owes to DCSB Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 68 Asymptotic RL DB This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB. Difference between RL and DB results is readily understood: B(p 2 ) is more slowly varying with DB kernel and hence a more balanced result 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].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]

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Pion’s valence-quark Distribution Amplitude Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 69 Established a one-to-one connection between DCSB and the pointwise form of the pion’s wave function. Dilation measures the rate at which dressed-quark approaches the asymptotic bare-parton limit Experiments at JLab12 can empirically verify the behaviour of M(p), and hence chart the IR limit of QCD C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50Prog. Part. Nucl. Phys. 61 (2008) 50 Dilation of pion’s wave function is measurable in pion’s electromagnetic form factor at JLab12 A-rated: E12-06-10E12-06-10 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].arXiv:1301.0324 [nucl-th] Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 70

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Form Factors Elastic Scattering Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 71 Elastic Form factors have long been recognised as a basic tool for elucidating bound-state properties. They are of particular value in hadron physics because they provide information on structure as a function of Q 2, the squared momentum-transfer: –Small-Q 2 is the nonperturbative domain –Large-Q 2 is the perturbative domain –Nonperturbative methods in hadron physics must explain the behaviour from Q 2 =0 through the transition domain, whereupon the behaviour is currently being measured Experimental and theoretical studies of hadron electromagnetic form factors have made rapid and significant progress during the last several years, including new data in the time like region, and material gains have been made in studying the pion form factor.

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 72

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 73 P. Maris & P.C. Tandy, Phys.Rev. C62 (2000) 055204: numerical procedure is practically useless for Q 2 >4GeV 2, so prediction ends!Phys.Rev. C62 (2000) 055204 Pion electromagnetic form factor at spacelike momenta L. 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) arXiv:1307.0026 [nucl-th]Phys. Rev. Lett. 111, 141802 (2013)

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 74

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 75

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 76 P. Maris & P.C. Tandy, Phys.Rev. C62 (2000) 055204: numerical procedure is practically useless for Q 2 >4GeV 2, so prediction ends!Phys.Rev. C62 (2000) 055204 Algorithm developed for pion PDA overcomes this obstacle Solves the practical problem of continuing from Euclidean metric formulation to Minkowski space Pion electromagnetic form factor at spacelike momenta L. 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) arXiv:1307.0026 [nucl-th]Phys. Rev. Lett. 111, 141802 (2013)

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 77 Improved DSE interaction kernel, based on DSE and lattice-QCD studies of gluon sector S.-x. Qin, L. Chang et al. Phys.Rev. C84 (2011) 042202(R) Phys.Rev. C84 (2011) 042202(R) New prediction in better agreement with available data than old DSE result Prediction extends from Q 2 =0 to arbitrarily large Q 2, without interruption, unifying both domains DSE 2000 … Breakdown here Pion electromagnetic form factor at spacelike momenta L. 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) arXiv:1307.0026 [nucl-th]Phys. Rev. Lett. 111, 141802 (2013)

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 78 Unlimited domain of validity emphasised in this figure Depict prediction on domain 0
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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 79 Predict a maximum at 6-GeV 2, which lies within domain that is accessible to JLab12 Difficult, however, to distinguish DSE prediction from Amendolia-1986 monopole What about comparison with perturbative QCD? Amendolia et al. DSE 2013 ρ-meson pole VMD maximum A-rated: E12-06-10E12-06-10 Pion electromagnetic form factor at spacelike momenta L. 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) arXiv:1307.0026 [nucl-th]Phys. Rev. Lett. 111, 141802 (2013)

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 80 Prediction of pQCD obtained when the pion valence-quark PDA has the form appropriate to the scale accessible in modern experiments is markedly different from the result obtained using the asymptotic PDA Near agreement between the pertinent perturbative QCD prediction and DSE- 2013 prediction is striking. DSE 2013 pQCD obtained with φ π asy (x) pQCD obtained with φ π (x;2GeV), i.e., the PDA appropriate to the scale of the experiment 15% Single DSE interaction kernel, determined fully by just one parameter and preserving the one-loop renormalisation group behaviour of QCD, has unified the F π (Q 2 ) and φ π (x) (and numerous other quantities) Pion electromagnetic form factor at spacelike momenta L. 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) arXiv:1307.0026 [nucl-th]Phys. Rev. Lett. 111, 141802 (2013)

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 81 Leading-order, leading-twist QCD prediction, obtained with φ π (x) evaluated at a scale appropriate to the experiment underestimates DSE-2013 prediction by merely an approximately uniform 15%. Small mismatch is explained by a combination of higher- order, higher-twist corrections & and shortcomings in the rainbow-ladder truncation. DSE 2013 pQCD obtained with φ π asy (x) pQCD obtained φ π (x;2GeV), i.e., the PDA appropriate to the scale of the experiment 15% Hence, one should expect dominance of hard contributions to the pion form factor for Q 2 >8GeV 2. Nevertheless, the normalisation of the form factor is fixed by a pion wave- function whose dilation with respect to φ π asy (x) is a definitive signature of DCSB Pion electromagnetic form factor at spacelike momenta L. 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) arXiv:1307.0026 [nucl-th]Phys. Rev. Lett. 111, 141802 (2013)

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We now have a comprehensive understanding of the nature and structure of QCD’s dichotomous Goldstone Mode! Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 82

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Theory Lattice-QCD –Significant progress in the last five years –This must continue Bound-state problem in continuum quantum field theory –Significant progress, too Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 83

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 84 arXiv:1310.2651 [nucl-th]

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Theory Lattice-QCD –Significant progress in the last five years –This must continue Bound-state problem in continuum quantum field theory –Significant progress, too –This must continue First Sino-Americas School & Workshop on the Continuum Bound-State Problem, Hefei, China. First Sino-Americas School & Workshop on the Continuum Bound-State Problem 22-26/Oct./2013 Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 85

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 86

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 87

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Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 88

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1.Rocio BERMUDEZ (U Michoácan); 2.Xiomara GUTIERREZ-GUERRERO (U Michoácan); 3.S. HERNÁNDEZ (U Michoácan); 4.Trang NGUYEN (KSU); 5.Khépani RAYA (U Michoácan); 6.Hannes ROBERTS (ANL, FZJ, UBerkeley); 7.Chien-Yeah SENG (UW-Mad) 8.Kun-lun WANG (PKU); 9.Chen CHEN (USTC); 10.J. Javier COBOS-MARTINEZ (U.Sonora); 11.Mario PITSCHMANN (ANL & UW-Mad); 12.Si-xue QIN (U. Frankfurt am Main); 13.Jorge SEGOVIA (ANL); 14.David WILSON (ODU); 15.Lei CHANG (U.Adelaide); 16.Ian CLOËT (ANL); 17.Bruno EL-BENNICH (São Paulo); Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 89 18.Adnan BASHIR (U Michoácan); 19.Stan BRODSKY (SLAC); 20.Gastão KREIN (São Paulo) 21.Roy HOLT (ANL); 22.Mikhail IVANOV (Dubna); 23.Yu-xin LIU (PKU); 24.Michael RAMSEY-MUSOLF (UW-Mad) 25.Alfredo RAYA (U Michoácan); 26.Sebastian SCHMIDT (IAS-FZJ & JARA); 27.Robert SHROCK (Stony Brook); 28.Peter TANDY (KSU); 29.Tony THOMAS (U.Adelaide) 30.Shaolong WAN (USTC) Students Postdocs Asst. Profs.

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I.IntroductionIntroduction II.What is QCD?What is QCD? III.Confinement?Confinement? IV.DCSBDCSB V.Condensates?Condensates? VI.Pion valence-quark parton distribution amplitudePion valence-quark parton distribution amplitude VII.Charged pion elastic form factorCharged pion elastic form factor Craig Roberts: USTC Hefei, October 2013 Prospects for the physics of cold, sparse hadrons (87p) 90

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