The Physics of Hadrons Adnan - PowerPoint Presentation

Slide1

The Physics of Hadrons

Adnan BASHIR (U Michoacan);Stan BRODSKY (SLAC);Lei CHANG (ANL & PKU); Huan CHEN (BIHEP);Ian CLOËT (UW);Bruno EL-BENNICH (Sao Paulo);Xiomara GUTIERREZ-GUERRERO (U Michoacan);Roy HOLT (ANL);Mikhail IVANOV (Dubna);Yu-xin LIU (PKU);Trang NGUYEN (KSU);Si-xue QIN (PKU);Hannes ROBERTS (ANL, FZJ, UBerkeley);Robert SHROCK (Stony Brook);Peter TANDY (KSU);David WILSON (ANL)

Craig Roberts

Physics Divisionwww.phy.anl.gov/theory/staff/cdr.html

StudentsEarly-career scientists

Published collaborations in 2010/2011

Slide2

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

2Standard Model of Particle PhysicsSlide3

Standard Model- History (a part)In the early 20th Century, the only matter particles known to exist were the proton, neutron, and electron. Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

Craig Roberts: The Physics of Hadrons3With the advent of cosmic ray science and particle accelerators, numerous additional particles were discovered:muon (1937), pion (1947), kaon (1947), Roper resonance (1963), … By the mid-1960s, it was apparent that not all the particles could be fundamental

.

A new paradigm was necessary.

Gell

-Mann's and Zweig's constituent-quark theory (1964) was a critical step forward.

Gell-Mann, Nobel Prize 1969:

"for his contributions and discoveries concerning the classification of elementary particles and their interactions"

.

Over the more than forty intervening years, the theory now called the

Standard Model of Particle Physics

has passed

almost

all tests. Slide4

Standard Model- The Heavy Piece Strong interactionExistence and composition of the vast bulk of visible matter in the Universe: proton, neutron the forces that form and bind them to form nucleiresponsible for more than 98% of the visible matter in the UniverseOhio U., Physics & Astronomy, 7.10.2011, 88pgs

Craig Roberts: The Physics of Hadrons4Politzer, Gross and Wilczek – 1973-1974 Perturbative Quantum Chromodynamics – QCDNobel Prize (2004):

"for the discovery of asymptotic freedom in the theory of the strong interaction".

NB. Worth noting that the character of 96% of the matter in the Universe is completely unknownSlide5

Simple picture- ProtonCraig Roberts: The Physics of Hadrons5

Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchangeOhio U., Physics & Astronomy, 7.10.2011, 88pgsSlide6

Simple picture- PionCraig Roberts: The Physics of Hadrons6

Two quantum-mechanical constituent-quarks - particle+antiparticle -interacting via a potential, derived from one constituent-gluon exchangeOhio U., Physics & Astronomy, 7.10.2011, 88pgsSlide7

Top Open Questions in Physics

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons7Slide8

Excerpts from the top-10, or top-24, or … What is dark energy?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. Contrary to their expectation, the scientists found that the expansion of the universe is not slowing, but accelerating.

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons8Saul 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. Slide9

Excerpts from the top-10, or top-24, or … Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap?Quantum chromodynamics, or QC

D, is the theory describing the strong nuclear force. Carried by gluons, it binds quarks into particles like protons and neutrons. Apparently, the tiny subparticles are permanently confined: one can't pull a quark or a gluon from a proton because the strong force gets stronger with distance and snaps them right back inside.Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons9Slide10

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

10Quantum ChromodynamicsSlide11

QED is the archetypal gauge field theoryPerturbatively simple but nonperturbatively undefinedChracteristic 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 !cf.Quantum ElectrodynamicsOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons11Slide12

Relativistic Quantum Gauge Field Theory:

Interactions mediated by vector boson exchangeVector bosons are perturbatively-masslessSimilar interaction in QEDSpecial feature of QCD – gluon self-interactions

What is

QCD?

Craig Roberts: The Physics of Hadrons

12

3-gluon vertex

4-gluon vertex

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide13

What is QCD? Novel feature of QCDTree-level interactions between gauge-bosons

O(αs) cross-section cf. O(αem4) in QEDOne might guess that this is going to have a big impactElucidating part of that impact is the origin of the 2004 Nobel Prize to Politzer, and Gross & WilczekOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons133-gluon vertex4-gluon vertexSlide14

Running couplingsQuantum gauge-field theories are all typified by the feature that Nothing is ConstantDistribution 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 themparticle number is not conserved in quantum field theoryCouplings and masses are renormalised via processes involving virtual-particles. Such effects make these quantities depend on the energy scale at which one observes them

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons14Slide15

QED cf. QCD? Craig Roberts: The Physics of Hadrons

152004 Nobel Prize in Physics : Gross, Politzer and Wilczekfermionscreeninggluon

antiscreening

Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

Add 3-gluon self-interaction

5 x10

-5Slide16

What is QCD?This momentum-dependent coupling translates into a coupling that depends strongly on separation. Namely, the interaction between quarks, between gluons, and between quarks and gluons grows rapidly with separation

Coupling is huge at separations r = 0.2fm ≈ ⅟₄ rprotonOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons16↔0.002fm 0.02fm0.2fmαs(r)0.10.20.3

0.4

0.5Slide17

Confinement in QCD A peculiar circumstance; viz., an interaction that becomes stronger as the participants try to separateIf coupling grows so strongly with separation, thenperhaps it is unbounded?perhaps it would require an infinite amount of energy in order to extract a quark or gluon from the interior of a hadron?

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons170.002fm 0.02fm0.2fmαs(r)0.10.20.30.40.5

The

Confinement Hypothesis:

Colour-charged particles cannot be isolated and therefore cannot be directly observed. They clump together in colour-neutral bound-states

Thi

s is hitherto an

empirical fact.Slide18

Confinement?

Millennium prize of $1,000,000 for proving that SUc(3) gauge theory is mathematically well-defined, which will necessarily prove or disprove the confinement conjecture, but in the absence of dynamical quarksOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons18Slide19

Strong-interaction: QCDAsymptotically freePerturbation theory is valid and accurate tool at large-Q

2 Hence chiral limit (massless theory) is definedEssentially nonperturbative for Q2 < 2 GeV2Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons19 Nature’s only example of truly nonperturbative, fundamental theory A-priori, no idea as to what such a theory can produceSlide20

What is the interaction throughout more than 98% of the proton’s volume?

The Problem with QCD Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons20

Perhaps?!

What we know unambiguously …

Is that we know too little!Slide21

Hadron

PhysicsThe study of nonperturbative QCD is the puriew of …Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons21Slide22

Hadrons

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) +

2

on

First Known Use: 1962

Baryon:

hadron

with half-integer-spin

Meson:

hadron

with integer-spin

Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

Craig Roberts: The Physics of Hadrons

22Slide23

Nuclear Science Advisory Council 2007 – Long Range PlanCraig Roberts: The Physics of Hadrons23 “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.”Ohio U., Physics & Astronomy, 7.10.2011, 88pgsInternationally, this is an approximately $1-billion/year effort in experiment and theory, with approximately $375-million/year in the USA. Roughly 90% of these funds are spent on experiment$1-billion/year is the order of the operating budget of CERNSlide24

FacilitiesOhio U., Physics & Astronomy, 7.10.2011, 88pgs

Craig Roberts: The Physics of Hadrons24Slide25

FacilitiesQCD MachinesUSAThomas Jefferson National Accelerator Facility, Newport News, Virginia Nature of cold

hadronic matter Upgrade underway Construction cost $310-million New generation experiments in 2016Relativistic Heavy Ion Collider, Brookhaven National Laboratory, Long Island, New York Strong phase transition, 10μs after Big BangOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons25A three dimensional view of the calculated particle paths resulting from collisions occurring within RHIC's STAR detectorSlide26

Hadron

TheoryThe structure of matterOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons26pionprotonSlide27

Nature’s strong messenger – PionCraig Roberts: The Physics of Hadrons27Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

1947 – Pion discovered by Cecil Frank Powell The beginning of Particle PhysicsThen came Disentanglement of confusion between (1937) muon and pion – similar massesDiscovery of particles with “strangeness” (e.g., kaon1947-1953)Subsequently, a complete spectrum of mesons and baryons with mass below ≈1 GeV28 statesBecame clear that pion is “too light” - hadrons supposed to be heavy, yet …π

140

MeV

ρ

780

MeV

P

940

MeVSlide28

Simple picture- PionCraig Roberts: The Physics of Hadrons28

Gell-Mann and Ne’eman: Eightfold way(1961) – a picture based on group theory: SU(3) Subsequently, quark model – where the u-, d-, s-quarks became the basis vectors in the fundamental representation of SU(3) Pion = Two quantum-mechanical constituent-quarks - particle+antiparticle - interacting via a potentialOhio U., Physics & Astronomy, 7.10.2011, 88pgsSlide29

Some of the Light MesonsOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons29

140 MeV780 MeVIG(JPC)Slide30

Modern Miraclesin Hadron PhysicsCraig Roberts: The Physics of Hadrons30

proton = three constituent quarksMproton ≈ 1GeVTherefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeVpion = constituent quark + constituent antiquarkGuess Mpion ≈ ⅔ × Mproton ≈ 700MeVWRONG . . . . . . . . . . . . . . . . . . . . . . Mpion = 140MeVRho-mesonAlso constituent quark + constituent antiquark – just pion with spin of one constituent flippedMrho ≈ 770MeV ≈ 2 × Mconstituent−quark What is “wrong” with the pion?

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide31

Dichotomy of the pionCraig Roberts: The Physics of Hadrons31

How does one make an almost massless particle from two massive constituent-quarks?Naturally, one could always tune a potential in quantum mechanics so that the ground-state is massless – but some are still making this mistakeHowever: current-algebra (1968) This is impossible in quantum mechanics, for which one always finds: Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide32

Dichotomy of the pionGoldstone mode and bound-stateThe correct understanding of pion observables; e.g. mass, decay constant and form factors, requires an approach to contain awell-defined and valid chiral

limit;and an accurate realisation of dynamical chiral symmetry breaking.Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons32HIGHLY NONTRIVIALImpossible in quantum mechanicsOnly possible in asymptotically-free gauge theoriesSlide33

Chiral SymmetryCraig Roberts: The Physics of Hadrons33

Interacting gauge theories, in which it makes sense to speak of massless fermions, have a nonperturbative chiral symmetryIt is realised in the theory’s spectrum via the appearance of degenerate parity partnersPerturbative QCD: u- & d- quarks are very light mu /md ≈ 0.5 & md ≈ 4 MeV H. Leutwyler, 0911.1416 [hep-ph]However, splitting between parity partners is greater-than 100-times this mass-scale; e.g.,Ohio U., Physics & Astronomy, 7.10.2011, 88pgsJP⅟₂+ (p)⅟₂-Mass940

MeV1535

MeVSlide34

Dynamical Chiral Symmetry BreakingSomething is happening in QCD

some inherent dynamical effect is dramatically changing the pattern by which the Lagrangian’s chiral symmetry is expressedQualitatively different from spontaneous symmetry breaking aka the Higgs mechanismNothing is added to the theoryHave only fermions & gauge-bosonsYet, the mass-operatorgenerated by the theory produces a spectrumwith no sign of chiral symmetryOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons34Craig D RobertsJohn D RobertsSlide35

QCD’s ChallengesDynamical

Chiral Symmetry Breaking Very unnatural pattern of bound state masses; e.g., Lagrangian (pQCD) quark mass is small but . . . no degeneracy between JP=+ and JP=− (parity partners)Neither of these phenomena is apparent in QCD’s Lagrangian Yet they are the dominant determining characteristics of real-world QCD.QCD – Complex behaviour arises from apparently simple rules.

Craig Roberts: The Physics of Hadrons

35 Quark and Gluon Confinement

No matter how hard one strikes the proton, one cannot liberate an individual quark or gluon

Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

Understand emergent phenomenaSlide36

Hadron

PhysicsOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons36Slide37

Nucleon … Two Key HadronsProton and NeutronFermions – two static properties: proton electric charge = +1; and magnetic moment, μpMagnetic Moment discovered by Otto Stern and collaborators in 1933; Stern awarded Nobel Prize (1943): "for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton"

.Dirac (1928) – pointlike fermion: Stern (1933) – Big Hint that Proton is not a point particleProton has constituentsThese are Quarks and GluonsQuark discovery via e-p-scattering at SLAC in 1968the elementary quanta of QCDOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons37Friedman, Kendall, Taylor, Nobel Prize (1990): "for their pioneering investigations concerning deep inelastic scattering of electrons on protons and bound neutrons, which have been of essential importance for the development of the quark model in particle physics"Slide38

Nucleon StructureProbed in scattering experimentsElectron is a good probe because it is structureless Electron’s relativistic current isProton’s electromagnetic current

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons38F1 = Dirac form factorF2 = Pauli form factorGE = Sachs Electric form factorIf a nonrelativistic limit exists, this relates to the charge densityGM = Sachs Magntic form factorIf a nonrelativistic

limit exists, this relates to the magnetisation

density

Structureless

fermion

, or simply structured

fermion

, F

1

=1 & F

2

=0, so that G

E

=G

M

and hence distribution of charge and

magnetisation

within this

fermion

are identicalSlide39

Data before 1999 Looks like the structure of the proton is simpleThe properties of JLab (high luminosity) enabled a new technique to be employed. First data released in 1999 and paint a VERY DIFFERENT PICTURE

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons39Which is correct?How is the difference to be explained?Slide40

We were all agogOhio U., Physics & Astronomy, 7.10.2011, 88pgs

Craig Roberts: The Physics of Hadrons40Slide41

Nuclear Science Advisory Council 2007 – Long Range PlanSo, what’re the holdups? They are legion … ConfinementDynamical chiral symmetry breakingA fundamental theory of unprecedented complexity

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 scoundrelOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons41 “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.”Slide42

Understanding NSAC’sLong Range PlanCraig Roberts: The Physics of Hadrons42

Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom?If not, with what should they be replaced? What is the meaning of the NSAC Challenge?What are the quarks and gluons of QCD? Is there such a thing as a constituent quark, a constituent-gluon? After all, these are the concepts for which Gell-Mann won the Nobel Prize.Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide43

Under these circumstances:Can 12C be produced, can it be stable?Is the deuteron stable; can Big-Bang

Nucleosynthesis occur? (Many more existential questions …) Probably not … but it wouldn’t matter because we wouldn’t be around to worry about it.What is themeaning of all this?Craig Roberts: The Physics of Hadrons43Suppose QCD behaved reasonably →mπ

=m

ρ , then repulsive and attractive forces in the Nucleon-Nucleon potential have the SAME range and there is

NO intermediate range attraction.Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide44

Why don’t we just stop talking and solve the problem?

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons44Slide45

Just get on with it!But … QCD’s emergent phenomena can’t be studied using perturbation theorySo what? Same is true of bound-state problems in quantum mechanics!

Differences:Here relativistic effects are crucial – virtual particles Quintessence of Relativistic Quantum Field TheoryInteraction between quarks – the Interquark Potential – Unknown throughout > 98% of the pion’s/proton’s volume!Understanding requires ab initio nonperturbative solution of fully-fledged interacting relativistic quantum field theory, something which Mathematics and Theoretical Physics are a long way from achieving.Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons45Slide46

The Traditional Approach – Modelling – has its problems.

How can we tackle the SM’sStrongly-interacting piece?Craig Roberts: The Physics of Hadrons46Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide47

How can we tackle the SM’sStrongly-interacting piece? Lattice-QCD

Craig Roberts: The Physics of Hadrons47– Spacetime becomes an hypercubic lattice– Computational challenge, many millions of degrees of freedomOhio U., Physics & Astronomy, 7.10.2011, 88pgsSlide48

How can we tackle the SM’sStrongly-interacting piece? Lattice-QCD –

Craig Roberts: The Physics of Hadrons48– Spacetime becomes an hypercubic lattice– Computational challenge, many millions of degrees of freedom– Approximately 500 people worldwide & 20-30 people per collaboration.Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide49

A Compromise?Dyson-Schwinger EquationsCraig Roberts: The Physics of Hadrons

49Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide50

A Compromise?Dyson-Schwinger Equations1994 . . . “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 Hadrons50Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide51

A Compromise?Dyson-Schwinger Equations1994 . . . “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 Hadrons51Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide52

A Compromise?Dyson-Schwinger Equations1994 . . . “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 Hadrons52Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide53

A Compromise?Dyson-Schwinger Equations1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of

nonperturbative QCD.”C. D. Roberts and A. G. Williams, “Dyson-Schwinger equations and their application to hadronic physics,” Prog. Part. Nucl. Phys. 33, 477 (1994) [arXiv:hep-ph/9403224]. (473 citations)Craig Roberts: The Physics of Hadrons53Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide54

A Compromise?DSEsCraig Roberts: The Physics of Hadrons

54Dyson (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: fermion self energy gauge-boson propagatorfermion-gauge-boson vertexThese are nonperturbative equivalents in quantum field theory of the Lagrange equations of motion.Essential in simplifying the general proof of renormalisability

of gauge field theories.

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide55

Dyson-SchwingerEquationsWell suited to Relativistic Quantum Field TheorySimplest level: Generating Tool for Perturbation Theory . . . Materially Reduces Model-Dependence … Statement about long-range

behaviour of quark-quark interactionNonPerturbative, Continuum approach to QCDHadrons as Composites of Quarks and GluonsQualitative and Quantitative Importance of:Dynamical Chiral Symmetry Breaking – Generation of fermion mass from nothingQuark & Gluon Confinement – Coloured objects not detected, Not detectable?Craig Roberts: The Physics of Hadrons55

Approach yields

Schwinger functions; i.e.,

propagators and vertices

Cross-Sections built from Schwinger FunctionsHence, method connects

observables with long- range

behaviour of the running coupling

Experiment

↔

Theory

comparison leads to an

understanding of long-

range

behaviour

of

strong running-coupling

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide56

QCD is asymptotically-free (2004 Nobel Prize)Chiral-limit is well-defined; i.e., one can truly speak of a massless quark. NB. This is

nonperturbatively impossible in QED.Dressed-quark propagator: Weak coupling expansion of gap equation yields every diagram in perturbation theoryIn perturbation theory: If m=0, then M(p2)=0 Start with no mass, Always have no mass.

Mass from Nothing?!Perturbation Theory

Craig Roberts: The Physics of Hadrons56

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide57

Dynamical

Chiral Symmetry BreakingOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons57Craig D RobertsJohn D RobertsSlide58

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 Hadrons58Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide59

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 Hadrons59Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide60

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 Hadrons60DSE prediction of DCSB confirmedMass from nothing!Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide61

12GeVThe Future of JLab

Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.Craig Roberts: The Physics of Hadrons61Jlab 12GeV: Scanned by 2<Q2<9 GeV2 elastic & transition form factors. Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide62

Universal TruthsHadron spectrum, and elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron's characterising properties amongst its QCD constituents.

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.Running of quark mass entails that hadron physics calculations at even modest Q2 require a Poincaré-covariant approach. Covariance + M(p2) require existence of quark orbital angular momentum in hadron's rest-frame wave function.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 Hadrons62Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide63

Universal ConventionsWikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum) “The QCD vacuum is the vacuum state of quantum

chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.”Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons63?Slide64

“Dark Energy”The only possible covariant form for the energy of the (quantum) vacuum; viz., is mathematically equivalent to the cosmological constant.

“It is a perfect fluid and precisely spatially uniform” “Vacuum energy is almost the perfect candidate for dark energy.” Craig Roberts: The Physics of Hadrons64Ohio U., Physics & Astronomy, 7.10.2011, 88pgs“The advent of quantum field theory made consideration of the cosmological constant obligatory not optional.”Michael Turner, “Dark Energy and the New Cosmology”Slide65

“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 MQCD≈0.3 GeVOne obtains therefrom: Craig Roberts: The Physics of Hadrons65Ohio U., Physics & Astronomy, 7.10.2011, 88pgs“The biggest embarrassment in theoretical physics.”Mass-scale generated by spacetime-independent condensate

Enormous and even greater contribution from Higgs VEV!Slide66

Resolution?Quantum Healing Central: “KSU physics professor [Peter Tandy] publishes groundbreaking research on inconsistency in Einstein theory.”Paranormal Psychic Forums:

“Now Stanley Brodsky of the SLAC National Accelerator Laboratory in Menlo Park, California, and colleagues have found a way to get rid of the discrepancy. “People have just been taking it on faith that this quark condensate is present throughout the vacuum,” says Brodsky. Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons66Slide67

ResolutionWhereas 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.QCDParadigm shift:In-Hadron CondensatesCraig Roberts: The Physics of Hadrons67

Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

Brodsky, Roberts,

Shrock

, Tandy,

Phys. Rev. C

82

(Rapid Comm.) (2010) 022201

Brodsky and

Shrock

,

PNAS

108

, 45 (2011)

Chang, Roberts, Tandy,

arXiv:1109.2903 [

nucl-th

]Slide68

Paradigm shift:In-Hadron CondensatesResolution

Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime. So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions. No qualitative difference between fπ and ρπBoth are equivalent order parameters for DCSBCraig Roberts: The Physics of Hadrons68Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

And |

π

>

→|0> matrix elements

Brodsky, Roberts,

Shrock, Tandy, Phys. Rev. C

82

(Rapid Comm.) (2010) 022201

Brodsky and

Shrock

,

PNAS

108

, 45 (2011)

Chang, Roberts, Tandy,

arXiv:1109.2903 [

nucl-th

]Slide69

ResolutionWhereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime. So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter

or light-front wavefunctions. No qualitative difference between fπ and ρπAnd Paradigm shift:In-Hadron CondensatesCraig Roberts: The Physics of Hadrons69

Chiral limit

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsOne of ONLY TWO expressions related to the condensate that are

rigorously defined in QCD for nonzero current-quark massBrodsky, Roberts, Shrock

, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201Brodsky and Shrock

, PNAS 108

, 45 (2011)Chang, Roberts, Tandy, arXiv:1109.2903 [nucl-th

]Slide70

“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.”Paradigm shift:In-Hadron Condensates Craig Roberts: The Physics of Hadrons70“Void that is truly empty solves dark energy puzzle”Rachel Courtland, New Scientist 4th Sept. 2010Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCosmological Constant: Putting QCD condensates back into hadrons reduces the mismatch between experiment and theory by a factor of 1046Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard ModelSlide71

Gap EquationGeneral FormDμν(k) – dressed-gluon propagatorΓ

ν(q,p) – dressed-quark-gluon vertexSuppose one has in hand – from anywhere – the exact form of the dressed-quark-gluon vertex What is the associated symmetry- preserving Bethe-Salpeter kernel?! Craig Roberts: The Physics of Hadrons71Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide72

Bethe-Salpeter EquationBound-State DSEK(

q,k;P) – fully amputated, two-particle irreducible, quark-antiquark scattering kernelTextbook material.Compact. Visually appealing. CorrectBlocked progress for more than 60 years.Craig Roberts: The Physics of Hadrons72Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide73

Bethe-Salpeter EquationGeneral FormE

quivalent exact bound-state equation but in this form K(q,k;P) → Λ(q,k;P), which is completely determined by dressed-quark self-energyEnables derivation of a Ward-Takahashi identity for Λ(q,k;P)Now, for first time, by using this identity, it’s possible to formulate Ansatz for Bethe-Salpeter kernel given any form for dressed-quark-gluon vertexThis enables the identification and elucidation of a wide range of novel consequences of DCSBCraig Roberts: The Physics of Hadrons73Lei Chang and C.D. Roberts0903.5461 [nucl-th

]Phys. Rev.

Lett. 103 (2009) 081601Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide74

Dressed-quark anomalousmagnetic momentsSchwinger’s result for QED: pQCD: two diagrams

(a) is QED-like(b) is only possible in QCD – involves 3-gluon vertexAnalyse (a) and (b)(b) vanishes identically: the 3-gluon vertex does not contribute to a quark’s anomalous chromomag. moment at leading-order(a) Produces a finite result: “ – ⅙ αs/2π ” ~ (– ⅙) QED-result But, in QED and QCD, the anomalous chromo- and electro-magnetic moments vanish identically in the chiral limit!Craig Roberts: The Physics of Hadrons74

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide75

Dressed-quark anomalousmagnetic momentsInteraction term that describes magnetic-moment coupling to gauge fieldStraightforward to show that it mixes left ↔ rightThus, explicitly violates

chiral symmetryFollows that in fermion’s e.m. current γμF1 does cannot mix with σμνqνF2No Gordon IdentityHence massless fermions cannot not possess a measurable chromo- or electro-magnetic momentBut what if the chiral symmetry is dynamically broken, strongly, as it is in QCD?Craig Roberts: The Physics of Hadrons75

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide76

Dressed-quark anomalousmagnetic moments Three strongly-dressed and essentially- nonperturbative

contributions to dressed-quark-gluon vertex:Craig Roberts: The Physics of Hadrons76DCSBBall-Chiu termVanishes if no DCSBAppearance driven by STIAnom. chrom. mag. mom.contribution to vertexSimilar properties to BC termStrength commensurate with lattice-QCDSkullerud, Bowman, Kizilersu

et al.

hep-ph/0303176Role and importance isNovel discoveryEssential to recover

pQCDConstructive interference with Γ5

Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

L. Chang, Y. –X. Liu and C.D. Roberts

arXiv:1009.3458 [

nucl-th

]

Phys. Rev.

Lett

. 

106

 (2011) 072001Slide77

Dressed-quark anomalousmagnetic momentsCraig Roberts: The Physics of Hadrons

77Formulated and solved general Bethe-Salpeter equation Obtained dressed electromagnetic vertex Confined quarks don’t have a mass-shell Can’t unambiguously define magnetic moments But can define magnetic moment distributionMEκACMκAEMFull vertex0.44-0.220.45Rainbow-ladder0.3500.048

AEM is opposite in sign but of

roughly equal magnitude as ACML. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [

nucl-th]Phys. Rev. Lett. 106 (2011) 072001

Factor of 10

magnification

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide78

Dressed-quark anomalousmagnetic momentsCraig Roberts: The Physics of Hadrons

78 Potentially important for elastic and transition form factors, etc. Significantly, also quite possibly for muon g-2 – via Box diagram, which is not constrained by extant data.L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [nucl-th]Phys. Rev. Lett. 106 (2011) 072001Factor of 10 magnificationFormulated and solved general Bethe-Salpeter equation Obtained dressed electromagnetic vertex

Confined quarks don’t have a mass-shell

Can’t unambiguously define magnetic moments But can define magnetic moment distribution

Contemporary theoretical estimates: 1 – 10 x 10

-10 Largest value reduces discrepancy expt.↔theory from 3.3

σ to below 2σ

.Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide79

DCSB entails

Dressed-quarks are not Dirac particles!Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

Craig Roberts: The Physics of Hadrons

79Slide80

DSEs and BaryonsCraig Roberts: The Physics of Hadrons80M(p2)

– effects have enormous impact on meson properties.Must be included in description and prediction of baryon properties.M(p2) is essentially a quantum field theoretical effect. In quantum field theory Meson appears as pole in four-point quark-antiquark Green function → Bethe-Salpeter EquationNucleon appears as a pole in a six-point quark Green function → Faddeev Equation.Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarksTractable equation is founded on observation that an interaction which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channelR.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145

Ohio U., Physics & Astronomy, 7.10.2011, 88pgs

rqq ≈ rπSlide81

Faddeev EquationCraig Roberts: The Physics of Hadrons81

Linear, Homogeneous Matrix equationYields wave function (Poincaré Covariant Faddeev Amplitude) that describes quark-diquark relative motion within the nucleonScalar and Axial-Vector Diquarks . . . Both have “correct” parity and “right” massesIn Nucleon’s Rest Frame Amplitude has s−, p− & d−wave correlationsR.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145diquark

quark

quark exchangeensures Pauli statistics

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide82

Nucleon ElasticForm FactorsCraig Roberts: The Physics of Hadrons82

Photon-baryon vertex Oettel, Pichowsky and von Smekal, nucl-th/9909082I.C. Cloët et al.arXiv:0812.0416 [nucl-th]“Survey of nucleon electromagnetic form factors”

– unification of meson and baryon observables; and prediction of nucleon elastic form factors to

15 GeV

2

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide83

Craig Roberts: The Physics of Hadrons83

I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]Highlights again the critical importance of DCSB in explanation of real-world observables.DSE result Dec 08

DSE result

– including the

anomalous magnetic moment distribution

I.C. Cloët, C.D. Roberts, et al.

In progress

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsSlide84

DSE studies indicate that the proton has a very rich internal structure The JLab data, obtained using the polarisaton transfer method, are an accurate indication of the behaviour of this ratio

The pre-1999 data (Rosenbluth) receive large corrections from so-called 2-photon exchange contributionsOhio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons84Proton plus proton-like resonancesDoes this ratio pass through zero?Slide85

Craig Roberts: The Physics of Hadrons85

I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]I.C. Cloët, C.D. Roberts, et al.In progressOhio U., Physics & Astronomy, 7.10.2011, 88pgs

Does this ratio pass through zero?

DSE studies say YES, with a zero crossing at

8

GeV

2

, as a consequence of strong correlations within the nucleon

Experiments at the upgraded

JLab

facility will provide the answer

In the meantime, the DSE studies will be refined

Linear fit to data ⇒ zero at

8

GeV

2

[1,1]

Padé

fit ⇒ zero at

10

GeV

2Slide86

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons86

EpilogueSlide87

EpilogueNo 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 theoryNevertheless, DSEs today provide an insightful connection between QCD and experiment:DCSB explained & developing a perspective on confinementOhio U., Physics & Astronomy, 7.10.2011, 88pgs

Craig Roberts: The Physics of Hadrons87Physics is an experimental science; and there’s an international experimental programme … Goal to understand …how the interactions between dressed–quarks and –gluons create ground & excited hadrons;

how these interactions emerge from QCD

Standard Model’s truly

Nonperturbative

Challenge

– Just what is the interaction that produces the

pion

, proton,

indeed, all hadrons?Slide88

This is not the end.

Ohio U., Physics & Astronomy, 7.10.2011, 88pgsCraig Roberts: The Physics of Hadrons88