Observing Dynamical Chiral - PowerPoint Presentation

Slide1

Observing Dynamical Chiral Symmetry Breaking

Craig Roberts

Physics DivisionSlide2

Q

CD’s Challenges

Dynamical

Chiral

Symmetry Breaking

Very unnatural pattern of bound state masses;

e.g., Lagrangian (pQCD) quark mass is small but . . . no degeneracy between 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. Both will be important herein QCD – Complex behaviour arises from apparently simple rules.

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

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Quark and Gluon ConfinementNo matter how hard one strikes the proton, one cannot liberate an individual quark or gluon

Understand emergent phenomenaSlide3

Universal Truths

Spectrum of hadrons (ground, excited and exotic states), and

hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron's

characterising

properties amongst its QCD constituents.

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 calculations at even modest Q2 require a Poincaré-covariant approach. Covariance requires 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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs3Slide4

Dyson-Schwinger

Equations

Well suited to Relativistic Quantum Field Theory

Simplest level: Generating Tool for Perturbation Theory . . . Materially Reduces Model-Dependence … Statement about long-range

behaviour

of quark-quark interaction

NonPerturbative, Continuum approach to 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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs4

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 couplingExperiment ↔ Theory comparison leads to an understanding of long- range behaviour of strong running-couplingSlide5

ConfinementQuark and Gluon Confinement

No matter how hard one strikes the proton, or any other hadron, one

cannot liberate an individual quark or gluonEmpirical fact. HoweverThere is no agreed, theoretical definition of light-quark confinementStatic-quark confinement is irrelevant to real-world QCDThere are no long-lived, very-massive quarksConfinement entails quark-

hadron

duality

; i.e., that all observable consequences of

QCD can, in principle, be computed using an hadronic basis. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs5XSlide6

ConfinementConfinement is expressed through a

violent change in the analytic structure of propagators for coloured

particles & can almost be read from a plot of a states’ dressed-propagatorGribov (1978); Munczek (1983); Stingl (1984); Cahill (1989); Krein

, Roberts & Williams (1992); …

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

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complex-P2complex-P2

Real-axis mass-pole splits, moving into pair(s) of complex conjugate poles or branch points

Spectral density no longer positive

semidefinite

& hence state cannot exist in observable spectrum

Normal particle

Confined particleSlide7

Dressed-gluon propagator

Gluon propagator satisfies

a Dyson-Schwinger Equation

Plausible possibilities

for the solution

DSE and lattice-QCD

agree on the resultConfined gluonIR-massive but UV-masslessmG ≈ 2-4 ΛQCD Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs7perturbative, massless gluonmassive , unconfined gluonIR-massive but UV-massless, confined gluonA.C. Aguilar et al., Phys.Rev. D80 (2009) 085018Slide8

S(p) … Dressed-quark propagator

- nominally, a 1-body problem

Gap equationDμν(k) – dressed-gluon propagator

Γ

ν

(

q,p) – dressed-quark-gluon vertexCraig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs8Slide9

With QCD’s

dressed-gluon propagator

What is the dressed-quark mass function?Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

9Slide10

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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs10Slide11

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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs11DSE prediction of DCSB confirmedMass from nothing!Slide12

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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs12Hint of lattice-QCD support for DSE prediction of violation of reflection positivity Slide13

12GeV

The Future of

JLab

Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs13Jlab 12GeV: Scanned by 2<Q2<9 GeV2 elastic & transition form factors. Slide14

Dynamical Chiral Symmetry Breaking

Strong-interaction: Q

CDConfinementEmpirical factModern theory and lattice-QCD support conjecture that light-quark confinement is real

associated with violation of reflection positivity; i.e., novel analytic structure for propagators and vertices

Still circumstantial, no proof yet of confinement

On the other hand,

DCSB is a fact in QCDIt is the most important mass generating mechanism for visible matter in the Universe. Responsible for approximately 98% of the proton’s mass. Higgs mechanism is (almost) irrelevant to light-quarks.Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs14Slide15

Strong-interaction: QC

D

Gluons and quarks acquire momentum-dependent massescharacterised by an infrared mass-scale m ≈ 2-4 ΛQCDSignificant body of work, stretching back to 1980, which shows that, in the presence of DCSB, the dressed-

fermion

-photon vertex is materially altered from the bare form:

γ

μ.Obvious, because with A(p2) ≠ 1 and B(p2) ≠ constant, the bare vertex cannot satisfy the Ward-Takahashi identity; viz., Number of contributors is too numerous to list completely (300 citations to 1st J.S. Ball paper), but prominent contributions by: J.S. Ball, C.J. Burden, C.D. Roberts, R. Delbourgo, A.G. Williams, H.J. Munczek, M.R. Pennington, A. Bashir, A. Kizilersu, L. Chang, Y.-X. Liu …Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs15Dressed-quark-gluon vertexSlide16

Dressed-

quark-gluon vertex

Single most important featurePerturbative vertex is helicity-conserving:Cannot cause spin-flip transitionsHowever,

DCSB introduces

nonperturbatively

generated structures that very strongly break

helicity conservationThese contributionsAre large when the dressed-quark mass-function is largeTherefore vanish in the ultraviolet; i.e., on the perturbative domainExact form of the contributions is still the subject of debate but their existence is model-independent - a fact. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs16Slide17

Gap Equation

General Form

Dμν(k) – dressed-gluon propagator

good deal of information available

Γ

ν

(q,p) – dressed-quark-gluon vertexInformation accumulating Straightforward to insert Ansatz for Γν(q,p) into gap equation & from the solution obtain values forin-pion condensateestimate of pion’s leptonic decay constantHowever, there’s a little more than that to hadron physicsCraig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs17Many are still doing only thisSlide18

Gap Equation

General Form

Dμν(k) – dressed-gluon propagator

Γ

ν

(

q,p) – dressed-quark-gluon vertexUntil 2009, all studies of other hadron phenomena used the leading-order term in a symmetry-preserving truncation scheme; viz., Dμν(k) = dressed, as described previouslyΓν(q,p) = γμ … plainly, key nonperturbative effects are missed and cannot be recovered through any step-by-step improvement procedureCraig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs18Bender, Roberts & von SmekalPhys.Lett. B380 (1996) 7-12Slide19

Gap Equation

General Form

Dμν(k) – dressed-gluon propagator

good deal of information available

Γ

ν

(q,p) – dressed-quark-gluon vertexInformation accumulating Suppose one has in hand – from anywhere – the exact form of the dressed-quark-gluon vertex What is the associated symmetry- preserving Bethe-Salpeter kernel?! Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs19If kernels of Bethe-Salpeter

and gap equations don’t match,one won’t even get right charge for the

pion.Slide20

Bethe-

Salpeter

EquationBound-State DSE

K(

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: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs20Slide21

Bethe-

Salpeter Equation

General 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)Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs21Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601Slide22

Ward-Takahashi Identity

Bethe-

Salpeter Kernel

Now, for first time, it’s possible to formulate an

Ansatz

for

Bethe-Salpeter kernel given any form for the dressed-quark-gluon vertex by using this identityThis enables the identification and elucidation of a wide range of novel consequences of DCSBCraig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs22Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601iγ5iγ5Slide23

Dressed-quark anomalousmagnetic moments

Three strongly-dressed and essentially-

nonperturbative

contributions to dressed-quark-gluon vertex:

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs23DCSBBall-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/0303176

L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [nucl-th]Phys. Rev. Lett. 106

 (2011) 072001Slide24

Dressed-quark anomalous

chromomagnetic moment

Lattice-QCDm = 115 MeVNonperturbative result is two orders-of-magnitude

larger than the

perturbative

computation

This level of magnification is typical of DCSBcf. Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs24Skullerud, Kizilersu et al.JHEP 0304 (2003) 047Prediction from perturbative QCD Quenched lattice-QCDQuark mass function:M(p2=0)= 400MeVM(p2=10GeV2)=4 MeVSlide25

Dressed-quark anomalousmagnetic moments

Three strongly-dressed and essentially-

nonperturbative

contributions to dressed-quark-gluon vertex:

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs25DCSBBall-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/0303176

Role and importance isnovel discoveryEssential to recover pQCDConstructive interference with

Γ5L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [nucl-th]Phys. Rev. Lett. 106 (2011) 072001Slide26

Dressed-quark anomalousmagnetic moments

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

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Formulated 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 ACM

L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [nucl-th]Phys. Rev. Lett. 106

 (2011) 072001Factor of 10 magnificationSlide27

Dressed-quark anomalousmagnetic moments

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

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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 distributionContemporary theoretical estimates:

1 – 10 x 10-10 Largest value reduces discrepancy expt.↔theory from 3.3σ to below 2σ.Slide28

DSEs and Baryons

Dynamical

chiral symmetry breaking (DCSB) – has enormous impact on meson properties.Must be included in description and prediction of baryon properties.

DCSB

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 based on observation that an interaction which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channelCraig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs28R.T. Cahill et al.,

Austral. J. Phys. 42 (1989) 129-145

rqq ≈ r

πSlide29

Faddeev

Equation

Linear, Homogeneous Matrix equation

Yields

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 correlationsCraig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs29R.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145diquark

quark

quark exchange

ensures Pauli statistics

composed of strongly-dressed quarks bound by dressed-gluonsSlide30

Photon-nucleon current

Composite nucleon must interact with photon via nontrivial current constrained by Ward-Takahashi identities

DSE, BSE, Faddeev equation, current → nucleon form factorsCraig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

30

Vertex contains dressed-quark anomalous magnetic moment

Oettel

, Pichowsky, SmekalEur.Phys.J. A8 (2000) 251-281Slide31

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

31

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 distributionI.C. Cloët, C.D. Roberts, et al.In progressSlide32

Unification of Meson & Baryon Spectra

Correlate the masses of meson and baryon ground- and excited-states within a

single, symmetry-preserving frameworkSymmetry-preserving means: Poincaré-covariant & satisfy relevant Ward-Takahashi identities

Constituent-quark model has hitherto been the most widely applied spectroscopic tool; and whilst its weaknesses are emphasized by critics and acknowledged by proponents, it is of continuing value because there is nothing better that is yet providing a bigger picture.

Nevertheless,

no connection with quantum field theory & certainly not with

QCDnot symmetry-preserving & therefore cannot veraciously connect meson and baryon propertiesCraig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs32Slide33

Faddeev

Equation

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

33

quark-quark scattering matrix

- pole-approximation used to arrive at

Faddeev-equationSlide34

Baryons &

diquarks

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

34

Provided numerous insights into baryon structure; e.g.,

There is a causal connection between m

Δ - mN & m1+- m0+mΔ - mNmN mΔPhysical splitting grows rapidly with increasing diquark mass differenceH.L.L. Roberts et al.,

Masses of ground and excited-state hadrons1101.4244 [nucl-th], Few Body Syst. 

51 (2011) pp. 1-25; DOI:10.1007/s00601-011-0225-xSlide35

Baryons &

diquarks

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

35

Provided numerous insights into baryon structure; e.g.,

m

N ≈ 3 M & mΔ ≈ M+m1+Slide36

Baryon Spectrum

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

36

Our predictions for baryon dressed-quark-core masses match the bare-masses determined by

Jülich

with a

rms-relative-error of 10%. Notably, however, we find a quark-core to the Roper resonance, whereas within the Jülich coupled-channels model this structure in the P11 partial wave is unconnected with a bare three-quark state. H.L.L. Roberts et al., to appear Few Body Syst., 1101.4244 [nucl-th] Masses of ground and excited-state hadronsSlide37

Baryon Spectrum

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

37

In connection with EBAC's analysis, our predictions for the bare-masses agree within a

rms

-relative-error of 14%.

Notably, EBAC does find a dressed-quark-core for the Roper resonance, at a mass which agrees with our prediction.H.L.L. Roberts et al., to appear Few Body Syst., 1101.4244 [nucl-th] Masses of ground and excited-state hadronsSlide38

EBAC

& the Roper resonance

EBAC examined the dynamical origins of the two poles associated with the Roper resonance are examined. Both of them, together with the next higher resonance in the P11 partial wave were found to have the same originating bare stateCoupling to the meson-baryon continuum induces multiple observed resonances from the same bare state. All PDG identified resonances consist of a core state and meson-baryon components.

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

38

N. Suzuki

et al., Phys.Rev.Lett. 104 (2010) 042302 Slide39

Hadron

Spectrum

Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs

39

Legend:

Particle Data Group

H.L.L. Roberts et al. EBAC Jülich

Symmetry-preserving unification of the computation of meson & baryon masses

rms-rel.err./deg-of-freedom = 13% PDG values (almost) uniformly overestimated in both cases - room for the pseudoscalar meson cloud?!Slide40

Next steps …In Hand …

A documented comparison between the electromagnetic form factors of mesons and those diquarks which play a material role in nucleon structure.

In position to complete reference M=constant computation of nucleon elastic form factors & nucleon →

Roper transition form factor

Compare with existing calculations of elastic form factors using

M=M(p

2) Compute M=M(p2) nucleon → Roper transition form factorsIdentify those signals in these observables that are unambiguously related to QCD-behaviour of M=M(p2)Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs40Slide41

Epilogue

Dynamical

chiral symmetry breaking (DCSB) – mass from nothing for 98% of visible matter – is a reality

Expressed in

M(p

2

), with observable signals in experimentPoincaré covariance Crucial in description of contemporary dataFully-self-consistent treatment of an interaction Essential if experimental data is truly to be understood.Dyson-Schwinger equations: single framework, with IR model-input turned to advantage, “almost unique in providing unambiguous path from a defined interaction → Confinement & DCSB → Masses → radii → form factors → distribution functions → etc.”Craig Roberts: Observing Dynamical Chiral Symmetry Breaking. JLab 16 May 2011 - Nucleon Resonance Structure with the CLAS12 Detector - 41pgs41McLerran & PisarskiarXiv:0706.2191 [hep-ph]Confinement is almost Certainly the origin of DCSB

e.g.,

BaBar anomaly