Craig Roberts Physics Division

The Physics of Cold, Sparse Hadrons Craig Roberts Physics Division

Standard Model Prospects for the physics of cold, sparse hadrons (87p)

Quantum Chromodynamics 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 Prospects for the physics of cold, sparse hadrons (87p)

Prospects for the physics of cold, sparse hadrons (87p)

Hadron: Any of a class of subatomic particles that are composed of quarks and/or gluons and take part in the strong interaction. Examples: proton, neutron, & pion. International Scientific Vocabulary: hadr- thick, heavy (from Greek hadros thick) + 2on First Known Use: 1962 Baryon: hadron with half-integer-spin Meson: hadron with integer-spin Hadrons Prospects for the physics of cold, sparse hadrons (87p)

Facilities Prospects for the physics of cold, sparse hadrons (87p)

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

FacilitiesQCD Machines A three dimensional view of the calculated particle paths resulting from collisions occurring within RHIC's STAR detector Prospects for the physics of cold, sparse hadrons (87p) USA 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, Long Island, New York Strong phase transition, 10μs after Big Bang

FacilitiesQCD Machines Prospects for the physics of cold, sparse hadrons (87p) USA Thomas Jefferson National Accelerator Facility, Newport News, Virginia Nature of cold hadronic matter Upgrade underway Construction cost $310-million New generation experiments in 2014

Science Challenges for the coming decade: 2013-2022 Prospects for the physics of cold, sparse hadrons (87p) All composite systems have “Form Factors”, which describe the distribution of an observable quantity amongst the constituents.

Science Challenges for the coming decade: 2013-2022 Prospects for the physics of cold, sparse hadrons (87p) 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

Science Challenges for the coming decade: 2013-2022 Prospects for the physics of cold, sparse hadrons (87p) 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.

Science Challenges for the coming decade: 2013-2022 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. Prospects for the physics of cold, sparse hadrons (87p) 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

Grand Challenge Prospects for the physics of cold, sparse hadrons (87p)

Overarching Science Challenges for the coming decade: 2013-2022 Prospects for the physics of cold, sparse hadrons (87p) Discover the meaning of confinement Determine its connection with DCSB (dynamical chiral symmetry breaking) Elucidate their signals in observables … so experiment and theory together can map the nonperturbativebehaviour of the strong interaction In my view, it is unlikely that two phenomena, so critical in the Standard Model and tied to the dynamical generation of a single mass-scale, can have different origins and fates.

What is QCD? Prospects for the physics of cold, sparse hadrons (87p)

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

What is QCD? Prospects for the physics of cold, sparse hadrons (87p) 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

cf.Quantum Electrodynamics Prospects for the physics of cold, sparse hadrons (87p) QED is the archetypal gauge field theory Perturbatively simple but nonperturbatively undefined Chracteristic feature: Light-by-light scattering; i.e., photon-photon interaction – leading-order contribution takes place at order α4. Extremely small probability because α4 ≈10-9 !

What is QCD? Relativistic Quantum Gauge Field Theory: Interactions mediated by vector boson exchange Vector bosons are perturbatively-massless Similar interaction in QED Special feature of QCD – gluon self-interactions 3-gluon vertex 4-gluon vertex Prospects for the physics of cold, sparse hadrons (87p)

Strong-interaction: QCD Nature’sonly (now known) example of a truly nonperturbative, fundamental theory A-priori, no idea as to what such a theory can produce Prospects for the physics of cold, sparse hadrons (87p) Asymptotically free Perturbation theory is valid and accurate tool at large-Q2 Hence chiral limit is defined Essentiallynonperturbative for Q2 < 2 GeV2

What is Confinement? Prospects for the physics of cold, sparse hadrons (87p)

Light quarks & Confinement Folklore … JLab Hall-DConceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes. Prospects for the physics of cold, sparse hadrons (87p) 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.”

Light quarks & Confinement Prospects for the physics of cold, sparse hadrons (87p) Problem: 16 tonnes of force makes a lot of pions.

G. Bali et al., PoS LAT2005 (2006) 308 Light quarks & Confinement Prospects for the physics of cold, sparse hadrons (87p) 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

Confinement Confined particle Normal particle complex-P2 complex-P2 timelike axis: P2<0 s ≈ 1/Im(m) ≈ 1/2ΛQCD≈ ½fm Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities, (or other qualitatively analogous structures chracterised by a dynamically generated mass-scale) State described by rapidly damped wave & hence state cannot exist in observable spectrum Prospects for the physics of cold, sparse hadrons (87p) 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

Light quarks & Confinement Prospects for the physics of cold, sparse hadrons (87p) 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?

Dynamical ChiralSymmetry Breaking Prospects for the physics of cold, sparse hadrons (87p)

Mass from Nothing Prospects for the physics of cold, sparse hadrons (87p)

Dynamical Chiral Symmetry Breaking Prospects for the physics of cold, sparse hadrons (87p) 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.

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

Dynamical Chiral Symmetry BreakingVacuum Condensates? Prospects for the physics of cold, sparse hadrons (87p)

Condensates are properties of hadrons Prospects for the physics of cold, sparse hadrons (87p)

“Orthodox Vacuum” u d u u d u u u d Prospects for the physics of cold, sparse hadrons (87p) 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!

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

Spontaneous(Dynamical)Chiral Symmetry Breaking Prospects for the physics of cold, sparse hadrons (87p) The 2008Nobel Prize in Physics was divided, one half awarded to YoichiroNambu "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics"

Nambu – Jona-LasinioModel 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 Prospects for the physics of cold, sparse hadrons (87p) Treats a chirally-invariant four-fermionLagrangian & 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 Nambuvacua, related by a chiral rotation Nontrivial Vacuum is “Born”

Original Note of Warning Chiral Magnetism (or Magnetohadrochironics) A. Casher and L. Susskind, Phys. Rev. D9 (1974) 436 These authors argue thatdynamical chiralsymmetry 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. Prospects for the physics of cold, sparse hadrons (87p)

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

QCD Sum Rules QCD and Resonance Physics. Sum Rules. M.A. Shifman, A.I. Vainshtein, and V.I. Zakharov Nucl.Phys. B147 (1979) 385-447; citations: 3781 Prospects for the physics of cold, sparse hadrons (87p) 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

“quark condensate”1960-1980 8300+ references to this phrase since 1980 Prospects for the physics of cold, sparse hadrons (87p) Instantons in non-perturbative QCD vacuum, MA Shifman, AI Vainshtein… - Nuclear Physics B, 1980 Instanton density in a theory with massless quarks, MA Shifman, AI Vainshtein… - Nuclear Physics B, 1980 Exotic new quarks and dynamical symmetry breaking, WJ Marciano - Physical Review D, 1980 The pion in QCD J Finger, JE Mandula… - Physics Letters B, 1980 No references to this phrase before 1980

Universal Conventions Prospects for the physics of cold, sparse hadrons (87p) Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum) “The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.”

Overview Prospects for the physics of cold, sparse hadrons (87p) 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.

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

QCD 1973-1974 Prospects for the physics of cold, sparse hadrons (87p) Why does it matter?

“Dark Energy” Prospects for the physics of cold, sparse hadrons (87p) Two pieces of evidence for an accelerating universe Observations of type Ia supernovae →the rate of expansion of the Universe is growing 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 Ω0 = 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, ΩM = 0.33 ⁺⁄₋ 0.04. Thus, ⅔of the critical density is missing.

“Dark Energy” In order to have escaped detection, the missing energy must be smoothly distributed. Contemporary cosmological observations mean: Prospects for the physics of cold, sparse hadrons (87p) 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.

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

“Dark Energy” Enormous and even greater contribution from Higgs VEV! Mass-scale generated by spacetime-independent condensate “The biggest embarrassment in theoretical physics.” Prospects for the physics of cold, sparse hadrons (87p) 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 MQCD≈0.3GeV One obtains therefrom:

GMOR Relation Prospects for the physics of cold, sparse hadrons (87p)

Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R) GMOR Relation Prospects for the physics of cold, sparse hadrons (87p) Valuable to highlight the precise form of the Gell-Mann–Oakes–Renner (GMOR) relation: Eq. (3.4) in Phys.Rev. 175 (1968) 2195 mπ is the pion’s mass Hχsb 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.

GMOR is synonymous with “Vacuum Quark Condensate” Prospects for the physics of cold, sparse hadrons (87p)

Concept of in-hadron condensates Prospects for the physics of cold, sparse hadrons (87p)

Gell-Mann Oakes Renner Relation Prospects for the physics of cold, sparse hadrons (87p) 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 Q2 = 0.

HadronCharges Prospects for the physics of cold, sparse hadrons (87p) 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. …

Confinement contains condensates Prospects for the physics of cold, sparse hadrons (87p)

“Orthodox Vacuum” u d u u d u u u d Prospects for the physics of cold, sparse hadrons (87p) 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!

New Paradigm u d u u d u u u d Prospects for the physics of cold, sparse hadrons (87p) Vacuum = hadronic fluctuations but no condensates Hadrons = complex, interacting systems within which perturbativebehaviour is restricted to just 2% of the interior

Paradigm shift:In-Hadron Condensates “Void that is truly empty solves dark energy puzzle” Rachel Courtland, New Scientist 4th Sept. 2010 Cosmological Constant: Putting QCD condensates back into hadrons reduces the mismatch between experiment and theory by a factor of 1046 Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard Model Prospects for the physics of cold, sparse hadrons (87p) “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.”

Valence quarks Parton structure of hadrons Prospects for the physics of cold, sparse hadrons (87p)

Deep inelastic scattering Probability that a quark/gluon within the target will carry a fraction x of the bound-state’s light-front momentum Distribution Functions of the Nucleon and Pion in the Valence Region, Roy J. Holt and Craig D. Roberts, arXiv:1002.4666 [nucl-th], Rev. Mod. Phys. 82 (2010) pp. 2991-3044 Prospects for the physics of cold, sparse hadrons (87p) 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)

Parton Structure of Hadrons Prospects for the physics of cold, sparse hadrons (87p) 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

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

Pion’s valence-quark Distribution Amplitude Pion’s Bethe-Salpeter wave function Whenever a nonrelativistic limit is realistic, this would correspond to the Schroedinger wave function. Prospects for the physics of cold, sparse hadrons (87p) 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 { n2=0, n.P = -mπ}

Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude Prospects for the physics of cold, sparse hadrons (87p) Methods have recently been developed to compute φπ(x);viz., theprojection of the pion’sPoincaré-covariant wave-function onto the light-front Results have been obtained with rainbow-ladder DSE kernel, simplest symmetry preserving form; and the best DCSB-improved kernel that is currently available. xα (1-x)α, with α=0.3

Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB. Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result Asymptotic DB RL Prospects for the physics of cold, sparse hadrons (87p) Both kernels agree: marked broadening of φπ(x), which owes to DCSB

Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude These computations are the first to directly expose DCSB – pointwise – on the light-front; i.e., in the infinite momentum frame. This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB. Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result Asymptotic DB RL Prospects for the physics of cold, sparse hadrons (87p) Both kernels agree: marked broadening of φπ(x), which owes to DCSB

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

ElasticScattering Prospects for the physics of cold, sparse hadrons (87p)

Form FactorsElastic Scattering 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 Q2, the squared momentum-transfer: Small-Q2 is the nonperturbative domain Large-Q2 is the perturbative domain Nonperturbative methods in hadron physics must explain the behaviour from Q2=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. Prospects for the physics of cold, sparse hadrons (87p)

JLab 12 GeV Prospects for the physics of cold, sparse hadrons (87p)

Pion electromagnetic form factor at spacelikemomentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013) Charged pionelastic form factor P. Maris & P.C. Tandy,Phys.Rev. C62 (2000) 055204: numerical procedure is practically useless for Q2>4GeV2, so prediction ends! Prospects for the physics of cold, sparse hadrons (87p)

New Algorithm Prospects for the physics of cold, sparse hadrons (87p)

Pivotal emergent phenomenon Prospects for the physics of cold, sparse hadrons (87p)

Pion electromagnetic form factor at spacelikemomentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013) Charged pionelastic form factor P. Maris & P.C. Tandy,Phys.Rev. C62 (2000) 055204: numerical procedure is practically useless for Q2>4GeV2, so prediction ends! Algorithm developed for pion PDA overcomes this obstacle Solves the practical problem of continuing from Euclidean metric formulation to Minkowski space Prospects for the physics of cold, sparse hadrons (87p)

Pion electromagnetic form factor at spacelikemomentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013) Charged pionelastic form factor 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) New prediction in better agreement with available data than old DSE result Prediction extends from Q2=0 to arbitrarily large Q2, without interruption, unifying both domains DSE 2000 … Breakdown here Prospects for the physics of cold, sparse hadrons (87p)

Pion electromagnetic form factor at spacelikemomentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013) Charged pionelastic form factor Unlimited domain of validity emphasised in this figure Depict prediction on domain 0<Q2<20GeV2 but have computed the result to Q2=100GeV2. If it were necessary, reliable results could readily be obtained at even higher values. DSE 2013 Prospects for the physics of cold, sparse hadrons (87p)

Pion electromagnetic form factor at spacelikemomentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013) Charged pionelastic form factor ρ-meson pole VMD Predict a maximum at 6-GeV2, 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? Amendoliaet al. DSE 2013 maximum A-rated:E12-06-10 Prospects for the physics of cold, sparse hadrons (87p)

Pion electromagnetic form factor at spacelikemomentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013) Charged pionelastic form factor 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 15% pQCD obtained with φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment pQCD obtained withφπasy(x) Single DSE interaction kernel, determined fully by just one parameter and preserving the one-loop renormalisation group behaviour of QCD, has unified the Fπ(Q2) and φπ(x) (and numerous other quantities) Prospects for the physics of cold, sparse hadrons (87p)

Pion electromagnetic form factor at spacelikemomentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013) Charged pionelastic form factor Leading-order, leading-twist QCD prediction, obtained with φπ(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 15% pQCD obtained φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment pQCD obtained withφπasy(x) Hence, one should expect dominance of hard contributions to the pion form factor for Q2>8GeV2. Nevertheless, the normalisation of the form factor is fixed by a pion wave-function whose dilation with respect to φπasy(x) is a definitive signature of DCSB Prospects for the physics of cold, sparse hadrons (87p)

Achieved a longstanding goal We now have a comprehensive understanding of the nature and structure of QCD’s dichotomous Goldstone Mode! Prospects for the physics of cold, sparse hadrons (87p)

Theory Prospects for the physics of cold, sparse hadrons (87p) Lattice-QCD Significant progress in the last five years This must continue Bound-state problem in continuum quantum field theory Significant progress, too

Enormous progress since 2010 arXiv:1310.2651 [nucl-th] Prospects for the physics of cold, sparse hadrons (87p)

Theory Prospects for the physics of cold, sparse hadrons (87p) 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. 22-26/Oct./2013

Epilogue Prospects for the physics of cold, sparse hadrons (87p)

Epilogue Prospects for the physics of cold, sparse hadrons (87p) The Physics of Hadrons is Unique: Confronting a fundamental theory in which the elementary degrees-of-freedom are intangible and only composites reach detectors Confinement in real-world is NOT understood DCSB is crucial to any understanding of hadron phenomena They must have a common origin Experimental and theoretical study of the Bound-state problem in continuum QCD promises to provide many more insights and answers.

This is not the end Prospects for the physics of cold, sparse hadrons (87p)

Students Postdocs Asst. Profs. Collaborators: 2011-Present Adnan BASHIR (U Michoácan); Stan BRODSKY (SLAC); Gastão KREIN (São Paulo) Roy HOLT (ANL); Mikhail IVANOV (Dubna); Yu-xin LIU (PKU); Michael RAMSEY-MUSOLF (UW-Mad) Alfredo RAYA (U Michoácan); Sebastian SCHMIDT (IAS-FZJ & JARA); Robert SHROCK (Stony Brook); Peter TANDY (KSU); Tony THOMAS (U.Adelaide) Shaolong WAN (USTC) Prospects for the physics of cold, sparse hadrons (87p) Rocio BERMUDEZ (U Michoácan); Xiomara GUTIERREZ-GUERRERO (U Michoácan); S. HERNÁNDEZ(U Michoácan); Trang NGUYEN (KSU); Khépani RAYA (U Michoácan); Hannes ROBERTS (ANL, FZJ, UBerkeley); Chien-Yeah SENG (UW-Mad) Kun-lun WANG (PKU); Chen CHEN (USTC); J. JavierCOBOS-MARTINEZ (U.Sonora); Mario PITSCHMANN (ANL & UW-Mad); Si-xue QIN(U. Frankfurt am Main); Jorge SEGOVIA (ANL); David WILSON (ODU); Lei CHANG (U.Adelaide); Ian CLOËT (ANL); Bruno EL-BENNICH (São Paulo);

Table of Contents Prospects for the physics of cold, sparse hadrons (87p) Introduction What is QCD? Confinement? DCSB Condensates? Pionvalence-quark parton distribution amplitude Charged pion elastic form factor

Craig Roberts Physics Division