Published collaborations in 20102011 Craig Roberts Physics Division

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

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 2

Standard Model - History (a part) Ø In the early 20 th Century, the only matter particles known to exist were the proton, neutron, and electron. Ø With the advent of cosmic ray science and particle accelerators, numerous additional particles were discovered: o muon (1937), pion (1947), kaon (1947), Roper resonance (1963), … Ø By the mid-1960 s, it was apparent that not all the particles could be fundamental. o A new paradigm was necessary. Ø Gell-Mann's and Zweig's constituent-quark theory (1964) was a critical step forward. o Gell-Mann, Nobel Prize 1969: "for his contributions and discoveries concerning the classification of elementary particles and their interactions". Ø Over the more than forty intervening years, theory now called the Standard Model of Particle Physics has passed almost all tests. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 3

Standard Model - The Heavy Piece Ø Strong interaction – Existence and composition of the vast bulk of visible matter in the Universe: • proton, neutron • the forces that form and bind them to form nuclei • responsible for more than 98% of the visible matter in the Universe – Politzer, Gross and Wilczek – 1973 -1974 Perturbative Quantum Chromodynamics – QCD • Nobel Prize (2004): "for the discovery of asymptotic freedom in theory of the strong interaction". Ø NB. Worth noting that the character of 96% of the matter in the Universe is completely unknown Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 4

Simple picture - Proton Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchange Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 5

Simple picture - Pion Two quantum-mechanical constituent-quarks - particle+antiparticle interacting via a potential, derived from one constituent-gluon exchange Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 6

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 7

Excerpts from the top-10, or top-24, or … Ø What is dark energy? o 1998: A group of scientists had recorded several dozen supernovae, including some so distant that their light had started to travel toward Earth when the universe was only a fraction of its present age. o Contrary to their expectation, the scientists found that the expansion of the universe is not slowing, but accelerating. Saul Perlmutter, Brian P. Schmidt, Adam G. Riess, Nobel Prize 2011: for the discovery of the accelerating expansion of the Universe through observations of distant supernovae. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 8

Excerpts from the top-10, or top-24, or … Ø Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap? o Quantum chromodynamics, or QCD, is theory describing the strong nuclear force. o Carried by gluons, it binds quarks into particles like protons and neutrons. o Apparently, the tiny subparticles are permanently confined: one can't pull a quark or a gluon from a proton because the strong force gets stronger with distance and snaps them right back inside. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 9

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 10

cf. Quantum Electrodynamics Ø QED is the archetypal gauge field theory Ø Perturbatively simple but nonperturbatively undefined Ø 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 ! Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 11

What is QCD? Relativistic Quantum Gauge Field Theory: Ø Interactions mediated by vector boson exchange Ø Vector bosons are perturbatively-massless 3 -gluon vertex Ø Similar interaction in QED Ø Special feature of QCD – gluon self-interactions 4 -gluon vertex Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 12

What is QCD? Ø Novel feature of QCD – Tree-level interactions between gauge-bosons – O(αs) cross-section cf. O(αem 4) in QED Ø One might guess that this is going to have a big impact Ø Elucidating part of that impact is the origin of the 2004 Nobel Prize to Politzer, and Gross & Wilczek 3 -gluon vertex 4 -gluon vertex Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 13

Running couplings Ø Quantum gauge-field theories are all typified by the feature that Nothing is Constant Ø Distribution of charge and mass, the number of particles, etc. , indeed, all the things that quantum mechanics holds fixed, depend upon the wavelength of the tool being used to measure them – particle number is not conserved in quantum field theory Ø Couplings and masses are renormalised via processes involving virtual-particles. Such effects make these quantities depend on the energy scale at which one observes them Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 14

QED cf. QCD? ü 2004 Nobel Prize in Physics : Gross, Politzer and Wilczek 5 x 10 -5 Add 3 -gluon self-interaction gluon antiscreening Craig Roberts: The Physics of Hadrons fermion screening Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 15

What is QCD? Ø This momentum-dependent coupling translates into a coupling that depends strongly on separation. Ø Namely, the interaction between quarks, between gluons, and between quarks and gluons grows rapidly with separation Ø Coupling is huge at separations r = 0. 2 fm ≈ ⅟₄ rproton 0. 5 0. 4 0. 3 αs(r) ↔ 0. 2 0. 1 0. 002 fm 0. 02 fm 0. 2 fm Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 16

0. 5 Confinement in QCD 0. 4 0. 2 0. 1 0. 002 fm 0. 02 fm 0. 2 fm αs(r) 0. 3 Ø A peculiar circumstance; viz. , an interaction that becomes stronger as the participants try to separate Ø If coupling grows so strongly with separation, then – perhaps it is unbounded? – perhaps it would require an infinite amount of energy in order to extract a quark or gluon from the interior of a hadron? Ø The Confinement Hypothesis: Colour-charged particles cannot be isolated and therefore cannot be directly observed. They clump together in colour-neutral boundstates Ø This is hitherto an empirical fact. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 17

Millennium prize of $1, 000 for proving that SUc(3) gauge theory is mathematically welldefined, which will necessarily prove or disprove the confinement conjecture, but in the absence of dynamical quarks Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 18

Strong-interaction: QCD Ø Asymptotically free – Perturbation theory is valid and accurate tool at large-Q 2 – Hence chiral limit (massless theory) is defined Ø Essentially nonperturbative for Q 2 < 2 Ge. V 2 Ø Nature’s only example of truly nonperturbative, fundamental theory Ø A-priori, no idea as to what such a theory can produce Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 19

Ø Perhaps? ! The Problem with Ø What we know unambiguously … Is that we know too little! QCD What is the interaction throughout more than 98% of the proton’s volume? Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 20

The study of nonperturbative QCD is the puriew of … Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 21

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 22

Nuclear Science Advisory Council 2007 – Long Range Plan “A central goal of (the DOE Office of ) Nuclear Physics is to understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD. ” Ø Internationally, this is an approximately $1 -billion/year effort in experiment and theory, with approximately $375 -million/year in the USA. Ø Roughly 90% of these funds are spent on experiment Ø $1 -billion/year is the order of the operating budget of CERN Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 23

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 24

Facilities QCD Machines Ø USA – Thomas Jefferson National Accelerator Facility, Newport News, Virginia Nature of cold hadronic matter Upgrade underway Construction cost $310 -million New generation experiments in 2016 – Relativistic Heavy Ion Collider, Brookhaven National Laboratory, Long Island, New York Strong phase transition, 10μs after Big Bang A three dimensional view of the calculated particle paths resulting from collisions occurring within RHIC's STAR detector Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 25

pion proton The structure of matter Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 26

Nature’s strong messenger q 1947 – Pion discovered by Cecil Frank Powell – Pion The beginning of Particle Physics q Then came § Disentanglement of confusion between (1937) muon and pion – similar masses § Discovery of particles with “strangeness” (e. g. , kaon 1947 -1953) q Subsequently, a complete spectrum of mesons and baryons with mass below ≈1 Ge. V § 28 states π 140 Me. V ρ 780 Me. V q Became clear that P 940 Me. V pion is “too light” - hadrons supposed to be heavy, yet … Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 27

q Gell-Mann and Ne’eman: § Eightfold way(1961) – a picture based on group theory: SU(3) § Subsequently, quark model – where the u-, d-, s-quarks became the basis vectors in the fundamental representation of SU(3) q Pion = Two quantum-mechanical constituent -quarks - particle+antiparticle - interacting via a potential Simple picture - Pion Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 28

Some of the Light Mesons IG(JPC) 140 Me. V 780 Me. V Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 29

Modern Miracles in Hadron Physics o proton = three constituent quarks • Mproton ≈ 1 Ge. V • Therefore guess Mconstituent−quark ≈ ⅓ × Ge. V ≈ 350 Me. V o pion = constituent quark + constituent antiquark • Guess Mpion ≈ ⅔ × Mproton ≈ 700 Me. V o WRONG. . . . . Mpion = 140 Me. V o Rho-meson • Also constituent quark + constituent antiquark – just pion with spin of one constituent flipped • Mrho ≈ 770 Me. V ≈ 2 × Mconstituent−quark What is “wrong” with the pion? Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 30

Dichotomy of the pion Ø How does one make an almost massless particle from two massive constituent-quarks? Ø Naturally, one could always tune a potential in quantum mechanics so that the ground-state is massless – but some are still making this mistake Ø However: current-algebra (1968) Ø This is impossible in quantum mechanics, for which one always finds: Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 31

Dichotomy of the pion Goldstone mode and bound-state Ø The correct understanding of pion observables; e. g. mass, decay constant and form factors, requires an approach to contain a – well-defined and valid chiral limit; – and an accurate realisation of dynamical chiral symmetry breaking. HIGHLY NONTRIVIAL Impossible in quantum mechanics Only possible in asymptotically-free gauge theories Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 32

Chiral Symmetry Ø Interacting gauge theories, in which it makes sense to speak of massless fermions, have a nonperturbative chiral symmetry Ø It is realised in theory’s spectrum via the appearance of degenerate parity partners Ø Perturbative QCD: u- & d- quarks are very light mu /md ≈ 0. 5 & md ≈ 4 Me. V H. Leutwyler, 0911. 1416 [hep-ph] Ø However, splitting between parity partners is greater-than 100 -times this mass-scale; e. g. , JP Mass ⅟₂+ (p) 940 Me. V ⅟₂1535 Me. V Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 33

Dynamical Chiral Symmetry Breaking Ø Something is happening in QCD – some inherent dynamical effect is dramatically changing the pattern by which the Lagrangian’s chiral symmetry is expressed Ø Qualitatively different from spontaneous symmetry breaking aka the Higgs mechanism – Nothing is added to theory – Have only fermions & gauge-bosons Yet, the mass-operator generated by theory produces a spectrum with no sign of chiral symmetry Craig D Roberts John D Roberts Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 34

QCD’s Challenges Understand emergent phenomena Ø Quark and Gluon Confinement No matter how hard one strikes the proton, one cannot liberate an individual quark or gluon Ø Dynamical Chiral Symmetry Breaking Very unnatural pattern of bound state masses; e. g. , Lagrangian (p. QCD) quark mass is small but . . . no degeneracy between JP=+ and JP=− (parity partners) Ø Neither of these phenomena is apparent in QCD’s Lagrangian Yet they are the dominant determining characteristics of real-world QCD. Ø QCD – Complex behaviour arises from apparently simple rules. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 35

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 36

Nucleon … Two Key Hadrons Proton and Neutron Ø Fermions – two static properties: proton electric charge = +1; and magnetic moment, μp Ø Magnetic Moment discovered by Otto Stern and collaborators in 1933; Stern awarded Nobel Prize (1943): "for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton". Friedman, Kendall, Taylor, Nobel Ø Dirac (1928) – pointlike fermion: Prize (1990): "for their pioneering Ø Stern (1933) – Ø Big Hint that Proton is not a point particle – Proton has constituents – These are Quarks and Gluons investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics" Ø Quark discovery via e-p-scattering at SLAC in 1968 – the elementary quanta of QCD Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 37

Nucleon Structure Probed in scattering experiments Ø Electron is a good probe because it is structureless Electron’s relativistic current is Ø Proton’s electromagnetic current F 1 = Dirac form factor GE = Sachs Electric form factor If a nonrelativistic limit exists, this relates to the charge density F 2 = Pauli form factor GM = Sachs Magntic form factor If a nonrelativistic limit exists, this relates to the magnetisation density Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 38

Ø Data before 1999 – Looks like the structure of the proton is simple Ø The properties of JLab (high luminosity) enabled a new technique to be employed. Ø First data released in 1999 and paint a VERY DIFFERENT PICTURE Which is correct? How is the difference to be explained? Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 39

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 40

Nuclear Science Advisory Council 2007 – Long Range Plan Ø So, what’re the holdups? They are legion … “A central goal of (the DOE Office of ) Nuclear Physics is to understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD. ” – Confinement – Dynamical chiral symmetry breaking – A fundamental theory of unprecedented complexity Ø QCD defines the difference between nuclear and particle physicists: – Nuclear physicists try to solve this theory – Particle physicists run away to a place where tree-level computations are all that’re necessary – perturbation theory, the last refuge of a scoundrel Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 41

Understanding NSAC’s Long Range Plan Ø What are the quarks and gluons of QCD? Ø Is there such a thing as a constituent quark, a constituent-gluon? After all, these are the concepts for which Gell -Mann won the Nobel Prize. Ø Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom? Ø If not, with what should they be replaced? What is the meaning of the NSAC Challenge? Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 42

What is the meaning of all this? Suppose QCD behaved reasonably →mπ=mρ , then repulsive and attractive forces in the Nucleon potential have the SAME range and there is NO intermediate range attraction. Under these circumstances: Ø Can 12 C be produced, can it be stable? Ø 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. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 43

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 44

Just get on with it! Ø But … QCD’s emergent phenomena can’t be studied using perturbation theory Ø So what? Same is true of bound-state problems in quantum mechanics! Ø Differences: Ø Here relativistic effects are crucial – virtual particles Quintessence of Relativistic Quantum Field Theory Ø Interaction between quarks – the Interquark Potential – Unknown throughout > 98% of the pion’s/proton’s volume! Ø Understanding requires ab initio nonperturbative solution of fullyfledged interacting relativistic quantum field theory, something which Mathematics and Theoretical Physics are a long way from achieving. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 45

How can we tackle the SM’s Strongly-interacting piece? The Traditional Approach – Modelling – has its problems. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 46

How can we tackle the SM’s Strongly-interacting piece? Lattice-QCD – Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 47

How can we tackle the SM’s Strongly-interacting piece? Lattice-QCD – – Spacetime becomes an hypercubic lattice – Computational challenge, many millions of degrees of freedom – Approximately 500 people worldwide & 20 -30 people per collaboration. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 48

A Compromise? Dyson-Schwinger Equations Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 49

A Compromise? Dyson-Schwinger Equations Ø 1994. . . “As computer technology continues to improve, lattice gauge theory [LGT] will become an increasingly useful means of studying hadronic physics through investigations of discretised quantum chromodynamics [QCD]. . . ” Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 50

A Compromise? Dyson-Schwinger Equations Ø 1994. . . “However, it is equally important to develop other complementary nonperturbative methods based on continuum descriptions. In particular, with the advent of new accelerators such as CEBAF (VA) and RHIC (NY), there is a need for the development of approximation techniques and models which bridge the gap between short-distance, perturbative QCD and the extensive amount of low- and intermediate-energy phenomenology in a single covariant framework. . ” Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 51

A Compromise? Dyson-Schwinger Equations Ø 1994. . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD. ” Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 52

A Compromise? Dyson-Schwinger Equations Ø 1994. . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD. ” Ø C. D. Roberts and A. G. Williams, “Dyson-Schwinger equations and their application to hadronic physics, ” Prog. Part. Nucl. Phys. 33, 477 (1994) [ar. Xiv: hep-ph/9403224]. (473 citations) Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 53

A Compromise? DSEs Ø 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 Ø These are nonperturbative equivalents in quantum field theory of the Lagrange equations of motion. Ø Essential in simplifying the general proof of renormalisability of gauge field theories. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 54

Dyson-Schwinger Equations Ø Well suited to Relativistic Quantum Field Theory Ø Simplest level: Generating Tool for Perturbation Theory . . . Materially Reduces Model. Dependence … Statement about long-range behaviour of quark-quark interaction Ø Non. Perturbative, Continuum approach to QCD Ø Hadrons as Composites of Quarks and Gluons Ø Qualitative and Quantitative Importance of: v Dynamical Chiral Symmetry Breaking – Generation of fermion mass from nothing v Quark & Gluon Confinement – Coloured objects not detected, Not detectable? ØApproach yields Schwinger functions; i. e. , propagators and vertices ØCross-Sections built from Schwinger Functions ØHence, method connects observables with long range behaviour of the running coupling ØExperiment ↔ Theory comparison leads to an understanding of long range behaviour of strong running-coupling Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 55

Mass from Nothing? ! Perturbation Theory Ø QCD is asymptotically-free (2004 Nobel Prize) v Chiral-limit is well-defined; i. e. , one can truly speak of a massless quark. v NB. This is nonperturbatively impossible in QED. Ø Dressed-quark propagator: Ø Weak coupling expansion of gap equation yields every diagram in perturbation theory Ø In perturbation theory: If m=0, then M(p 2)=0 Start with no mass, Always have no mass. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 56

Craig D Roberts John D Roberts Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 57

Spontaneous(Dynamical) Chiral Symmetry Breaking The 2008 Nobel Prize in Physics was divided, one half awarded to Yoichiro Nambu "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics" Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 58

Frontiers of Nuclear Science: Theoretical Advances In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 59

Frontiers of Nuclear Science: Theoretical Advances In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies. DSE prediction Craig Roberts: The Physics of Hadrons Mass from nothing! of DCSB confirmed Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 60

12 Ge. V 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 Jlab 12 Ge. V: Scanned by 2<Q 2<9 Ge. V 2 low energies. Craig Roberts: The Physics of Hadrons elastic & transition form factors. Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 61

Universal Truths Ø Hadron spectrum, and elastic and transition form factors provide unique information about long-range interaction between lightquarks and distribution of hadron's characterising properties amongst its QCD constituents. Ø 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. Ø Running of quark mass entails that hadron physics calculations at even modest Q 2 require a Poincaré-covariant approach. Covariance + M(p 2) require existence of quark orbital angular momentum in hadron's rest-frame wave function. Ø Confinement is expressed through a violent change of the propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator. It is intimately connected with DCSB. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 62

Universal Conventions ? Ø 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 nonperturbative vacuum state, characterized by many nonvanishing 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: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 63

“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” Ø The only possible covariant form for the energy of the (quantum) vacuum; viz. , is mathematically equivalent to the cosmological constant. “It is a perfect fluid and precisely spatially uniform” “Vacuum energy is almost the perfect candidate for dark energy. ” Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 64

“Dark Energy” Enormous and even greater contribution from Higgs VEV! Ø QCD vacuum contribution Ø 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 Mass-scale generated by MQCD≈0. 3 Ge. V Ø One obtains therefrom: Craig Roberts: The Physics of Hadrons spacetime-independent condensate “The biggest embarrassment in theoretical physics. ” Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 65

Resolution? Ø Quantum Healing Central: Ø “KSU physics professor [Peter Tandy] publishes groundbreaking research on inconsistency in Einstein theory. ” Ø Paranormal Psychic Forums: Ø “Now Stanley Brodsky of the SLAC National Accelerator Laboratory in Menlo Park, California, and colleagues have found a way to get rid of the discrepancy. “People have just been taking it on faith that this quark condensate is present throughout the vacuum, ” says Brodsky. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 66

Paradigm shift: In-Hadron Condensates Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C 82 (Rapid Comm. ) (2010) 022201 Brodsky and Shrock, PNAS 108, 45 (2011) Chang, Roberts, Tandy, ar. Xiv: 1109. 2903 [nucl-th] Ø 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. QCD Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 67

Paradigm shift: In-Hadron Condensates Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C 82 (Rapid Comm. ) (2010) 022201 Brodsky and Shrock, PNAS 108, 45 (2011) Chang, Roberts, Tandy, ar. Xiv: 1109. 2903 [nucl-th] Ø 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, And |π> →|0> in their Bethe-Salpeter or matrix elements light-front wavefunctions. – No qualitative difference between fπ and ρπ – Both are equivalent order parameters for DCSB Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 68

Paradigm shift: In-Hadron Condensates Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C 82 (Rapid Comm. ) (2010) 022201 Brodsky and Shrock, PNAS 108, 45 (2011) Chang, Roberts, Tandy, ar. Xiv: 1109. 2903 [nucl-th] Ø 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 Chiral limit light-front wavefunctions. – No qualitative difference between fπ and ρπ – And One of ONLY TWO expressions related to the condensate that are Craig Roberts: The Physics of Hadrons rigorously defined in QCD for nonzero current-quark mass Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 69

Paradigm shift: In-Hadron Condensates “Void that is truly empty solves dark energy puzzle” Rachel Courtland, New Scientist 4 th Sept. 2010 “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. ” Cosmological Constant: üPutting QCD condensates back into hadrons reduces the mismatch between experiment and theory by a factor of 1046 üPossibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard Model Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 70

Gap Equation General Form Ø Dμν(k) – dressed-gluon propagator Ø Γν(q, p) – dressed-quark-gluon vertex Ø Suppose one has in hand – from anywhere – the exact form of the dressed-quark-gluon vertex What is the associated symmetrypreserving Bethe-Salpeter kernel? ! Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 71

Bethe-Salpeter Equation Bound-State DSE Ø K(q, k; P) – fully amputated, two-particle irreducible, quark-antiquark scattering kernel Ø Textbook material. Ø Compact. Visually appealing. Correct Blocked progress for more than 60 years. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 72

Bethe-Salpeter Equation Lei Chang and C. D. Roberts General Form 0903. 5461 [nucl-th] Phys. Rev. Lett. 103 (2009) 081601 Ø 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 Ø Enables derivation of a Ward-Takahashi identity for Λ(q, k; P) Ø Now, for first time, by using this identity, it’s possible to formulate Ansatz for Bethe-Salpeter kernel given any form for dressed-quark-gluon vertex Ø This enables the identification and elucidation of a wide range of novel consequences of DCSB Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 73

Dressed-quark anomalous magnetic moments Ø Schwinger’s result for QED: Ø p. QCD: two diagrams o (a) is QED-like o (b) is only possible in QCD – involves 3 -gluon vertex Ø 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 αs/2π ” ~ (– ⅙) QED-result Ø But, in QED and QCD, the anomalous chromo- and electromagnetic moments vanish identically in the chiral limit! Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 74

Dressed-quark anomalous magnetic moments Ø 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 Ø Follows that in fermion’s e. m. current γμF 1 does cannot mix with σμνqνF 2 No Gordon Identity o Hence massless fermions cannot possess a measurable chromo- or electro-magnetic moment Ø But what if the chiral symmetry is dynamically broken, strongly, as it is in QCD? Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 75

L. Chang, Y. –X. Liu and C. D. Roberts ar. Xiv: 1009. 3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001 Dressed-quark anomalous magnetic moments Ø DCSB Three strongly-dressed and essentiallynonperturbative contributions to dressed-quark-gluon vertex: 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 p. QCD • Constructive interference with Γ 5 Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 76

L. Chang, Y. –X. Liu and C. D. Roberts ar. Xiv: 1009. 3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001 Dressed-quark anomalous magnetic moments ØFormulated and solved general Bethe-Salpeter equation ØObtained dressed Factor of 10 electromagnetic vertex magnification ØConfined quarks don’t have a mass-shell o Can’t unambiguously define magnetic moments o But can define magnetic moment distribution Ø AEM is opposite in sign but of roughly equal magnitude as ACM Full vertex ME κACM κAEM 0. 44 -0. 22 0. 45 0 0. 048 Rainbow-ladder 0. 35 Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 77

L. Chang, Y. –X. Liu and C. D. Roberts ar. Xiv: 1009. 3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001 Dressed-quark anomalous magnetic moments ØFormulated and solved general Bethe-Salpeter equation ØObtained dressed Factor of 10 electromagnetic vertex magnification ØConfined quarks don’t have a mass-shell o Can’t unambiguously define magnetic moments o But can define magnetic moment distribution Contemporary theoretical estimates: 1 – 10 x 10 -10 Largest value reduces discrepancy expt. ↔theory from 3. 3σ to below 2σ. Ø Potentially important for elastic and transition form factors, etc. Ø Significantly, also quite possibly for muon g-2 – via Box diagram, which is not constrained by extant data. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 78

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 79

R. T. Cahill et al. , Austral. J. Phys. 42 (1989) 129 -145 DSEs and Baryons Ø M(p 2) – effects have enormous impact on meson properties. q Must be included in description and prediction of baryon properties. Ø M(p 2) is essentially a quantum field theoretical effect. In quantum field theory q Meson appears as pole in four-point quark-antiquark Green function → Bethe-Salpeter Equation q Nucleon appears as a pole in a six-point quark Green function → Faddeev Equation. Ø Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarks Ø 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 Craig Roberts: The Physics of Hadrons rqq ≈ rπ Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 80

Faddeev Equation R. T. Cahill et al. , Austral. J. Phys. 42 (1989) 129 -145 quark exchange ensures Pauli statistics quark diquark Ø Linear, Homogeneous Matrix equation v Yields wave function (Poincaré Covariant Faddeev Amplitude) that describes quark-diquark relative motion within the nucleon Ø Scalar and Axial-Vector Diquarks. . . v Both have “correct” parity and “right” masses v In Nucleon’s Rest Frame Amplitude has s−, p− & d−wave correlations Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 81

I. C. Cloët et al. ar. Xiv: 0812. 0416 [nucl-th] Nucleon Elastic Form Factors Ø Photon-baryon vertex Oettel, Pichowsky and von Smekal, nucl-th/9909082 Ø “Survey of nucleon electromagnetic form factors” – unification of meson and baryon observables; and prediction of nucleon elastic form factors to 15 Ge. V 2 Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 82

I. C. Cloët, C. D. Roberts, et al. ar. Xiv: 0812. 0416 [nucl-th] I. C. Cloët, C. D. Roberts, et al. In progress ØDSE result Dec 08 ØDSE result – including the anomalous magnetic moment distribution ØHighlights again the critical importance of DCSB in explanation of real-world observables. Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 83

Ø DSE studies indicate that the proton has a very rich internal structure Ø The JLab data, obtained using the polarisaton transfer method, are an accurate indication of the behaviour of this ratio Ø The pre-1999 data (Rosenbluth) receive large corrections from so-called 2 -photon exchange contributions Proton plus proton-like resonances Does this ratio pass through zero? Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 84

I. C. Cloët, C. D. Roberts, et al. ar. Xiv: 0812. 0416 [nucl-th] I. C. Cloët, C. D. Roberts, et al. In progress Ø Does this ratio pass through zero? Ø DSE studies say YES, with a zero crossing at 8 Ge. V 2, as a consequence of strong correlations within the nucleon Linear fit to data ⇒ zero at 8 Ge. V 2 Ø Experiments at the [1, 1] Padé fit ⇒ zero at 10 Ge. V 2 upgraded JLab facility will provide the answer Ø In the meantime, the DSE studies will be refined Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 85

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 86

Epilogue Standard Model’s truly Nonperturbative Ø Physics is an experimental science; and there’s Challenge an international experimental programme … – Just what is the Ø Goal to understand … interaction that – how the interactions between dressed–quarks produces the pion, and –gluons create ground & excited hadrons; proton, indeed, all – how these interactions emerge from QCD hadrons? Ø No single approach is yet able to provide a unified description of all hadron phenomena – E. g. , intelligent reaction theory will long be necessary as bridge between experiment and QCD-based theory Ø Nevertheless, DSEs today provide an insightful connection between QCD and experiment: – DCSB explained & developing a perspective on confinement Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 87

Craig Roberts: The Physics of Hadrons Ohio U. , Physics & Astronomy, 7. 10. 2011, 88 pgs 88