Images of the Origin of Mass - PowerPoint Presentation

Slide1

Images of theOrigin of Mass

Craig Roberts

Physics DivisionSlide2

Collaborators: 2011-PresentRocio BERMUDEZ (U Michoácan

);

Xiomara GUTIERREZ-GUERRERO (

U Michoácan);S. HERNÁNDEZ

(

U

Michoácan);Trang NGUYEN (KSU);Khépani RAYA (U Michoácan);Hannes ROBERTS (ANL, FZJ, UBerkeley);Chien-Yeah SENG (UW-Mad)Kun-lun WANG (PKU);Chen CHEN (USTC, ANL);J. Javier COBOS-MARTINEZ (U.Sonora);Mario PITSCHMANN (Vienna);Si-xue QIN (PKU, U. Frankfurt am Main);Jorge SEGOVIA (ANL);David WILSON (ODU);Lei CHANG (PKU, U.Adelaide); Ian CLOËT (ANL);Bruno EL-BENNICH (São Paulo);

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

2

Adnan BASHIR (U Michoácan);Stan BRODSKY (SLAC);Gastão KREIN (São Paulo)Roy HOLT (ANL);Mikhail IVANOV (Dubna);Yu-xin LIU (PKU);Michael RAMSEY-MUSOLF (UW-Mad)Alfredo RAYA (U Michoácan);Sebastian SCHMIDT (IAS-FZJ & JARA);Robert SHROCK (Stony Brook);Peter TANDY (KSU);Tony THOMAS (U.Adelaide)Shaolong WAN (USTC)

StudentsPostdocsAsst. Profs.Slide3

Ian Cloët

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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Pretend from

now on that I am a vegetarian with a pon

y-tail, who was born in Australia and enjoys Belgian beer.Slide4

Overarching Science Challenges for the coming decade: 2013-2022Discover the meaning of confinementDetermine its connection with DCSB (dynamical chiral symmetry breaking)Elucidate their signals in observables

… so experiment and theory together can map the nonperturbative

behaviour of the strong interaction

In my view, it is unlikely that two phenomena, so critical in the Standard Model and tied to the dynamical generation of a single mass-scale, can have different origins and fates.1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

4Slide5

Immediate Science Challenges for the coming decade: 2013-2022Exploit opportunities provided by new data on hadron elastic and transition form factorsChart infrared evolution of

QC

D’s coupling and dressed-masses Reveal correlations that are key to baryon structure

Expose facts & fallacies in modern descriptions of hadron structurePrecision experimental study of (far) valence region, and theoretical computation of distribution functions and distribution amplitudesComputation is criticalWithout it, no amount of data will reveal anything about the theory underlying the phenomena of strong interaction physics

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

5Slide6

What is

Q

C

D

?

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)6Slide7

Very likely a self-contained, nonperturbatively renormalisable and hence well defined Quantum Field Theory This is not true of QED – cannot be defined nonperturbativelyNo confirmed breakdown over an enormous energy domain: 0 GeV < E < 8 TeVIncreasingly likely that any extension of the Standard Model will be based on the paradigm established by Q

CD

Extended T

echnico

l

o

ur: electroweak symmetry breaks via a fermion bilinear operator in a strongly-interacting non-Abelian theory. (Andersen et al. “Discovering Technicolor” Eur.Phys.J.Plus 126 (2011) 81) Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg-Landau theory of superconductivity1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)7(not an effective theory)QCD is a Theory Slide8

Contrast: so-called Effective Field TheoriesEFTs applicable over a very restricted energy domain; e.g., ChPT known to breakdown for E > 2mπCan be used to help explore how features of QCD influence observables

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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Q

C

D appears valid at all energy scales that have been tested so far: no breakdown below E ≈ 60000 mπCannot be used to test QCD Any mismatch between EF-Theory and experiment owes to an error in the formulation of one or conduct of the otherCanCannotSlide9

What is Confinement?1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

9Slide10

Light quarks & Confinement A unit area placed midway between the quarks and perpendicular to the line connecting them intercepts a constant number of field lines, independent of the distance between the quarks. This leads to a constant force between the quarks – and a large force at that, equal to about 16 metric tons.”1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

10

Folklore

…

Hall-D

Conceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes. Slide11

Light quarks & ConfinementProblem: 16 tonnes of force makes a lot of pions.1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

11Slide12

Light quarks & ConfinementProblem: 16 tonnes of force makes a lot of pions.1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

12Slide13

Light quarks & ConfinementIn the presence of light quarks, pair creation seems to occur non-localized and instantaneouslyNo flux tube in a theory with light-quarks. Flux-tube is not the correct paradigm for confinement in hadron physics1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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G. Bali et al., PoS

LAT2005 (2006) 308Slide14

ConfinementQFT Paradigm: Confinement is expressed through a dramatic change in the analytic structure of propagators for coloured statesIt can almost be read from a plot of the dressed-propagator for a coloured state1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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complex-P

2

complex-P

2

Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities,

(or other qualitatively analogous structures

chracterised

by a dynamically generated mass-scale) State described by rapidly damped wave & hence state cannot exist in observable spectrumNormal particleConfined particletimelike axis: P2<0s ≈ 1/Im(m) ≈ 1/2ΛQCD ≈ ½fmSlide15

Dynamical

Chiral

Symmetry Breaking

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

15Slide16

Mass from Nothing

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

16Slide17

Dynamical Chiral Symmetry BreakingDCSB is a fact in QCDDynamical, not spontaneousAdd nothing to QCD , no Higgs field, nothing!

Effect achieved purely through the quark+gluon dynamics.

It’s the most important mass generating mechanism for visible matter in the Universe. Responsible for ≈98% of the proton’s mass.

Higgs mechanism is (almost) irrelevant to light-quarks.Just like gluons and quarks, and for the same reasons, condensates are confined within hadrons.

There are

no

vacuum condensates.1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)17Confinement contains condensates, S.J. Brodsky, C.D. Roberts, R. Shrock and P.C. Tandy, arXiv:1202.2376 [nucl-th], Phys. Rev. C85 (2012) 065202Slide18

DCSB1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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Mass from nothing!

C.D. Roberts,

Prog

. Part.

Nucl. Phys. 61 (2008) 50M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227In QCD, all “constants” of quantum mechanics are actually strongly momentum dependent: couplings, number density, mass, etc.So, a quark’s mass depends on its momentum.Mass function can be calculated and is depicted here.Continuum- and Lattice-QCD are in agreement: the vast bulk of the light-quark mass comes from a cloud of gluons, dragged along by the quark as it propagates.Slide19

Just one of the terms that are summed

in a solution of the rainbow-ladder gap equation

Where does the

mass come from?

Deceptively simply picture

Corresponds to the sum of a countable infinity of diagrams.

NB. QED has 12,672 α5 diagramsImpossible to compute this in perturbation theory. The standard algebraic manipulation tools are just inadequate1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)19αS23Slide20

Enigma of Mass

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

20Slide21

Bound-states in Quantum Field TheoryMass and “Wave Function” are obtained from a Bethe-Salpeter equationGeneralisation of the Lippmann-Schwinger equationThe pion … Nature’s strong-interaction messenger … is a critical example

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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Sketching the Bethe-

Salpeter

kernel, Lei Chang and Craig D. Roberts, arXiv:0903.5461 [nucl-th], Phys. Rev. Lett. 103 (2009) 081601 (4 pages)Slide22

Pion’s Goldberger-Treiman relationCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)22

Pion’s

Bethe-Salpeter

amplitude Solution of the Bethe-Salpeter equationDressed-quark propagator

Axial-vector

Ward-Takahashi identity entails

Pseudovector componentsnecessarily nonzero. Cannot be ignored!Exact inChiral QCD

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Miracle

:

two body problem solved, almost completely, once solution of one body problem is knownMaris, Roberts and Tandynucl-th/9707003, Phys.Lett. B420 (1998) 267-273 Slide23

Dichotomy of the pionGoldstone mode and bound-stateGoldstone’s theorem has a pointwise expression in QCD; Namely, in the

chiral limit the wave-function for the two-body bound-state Goldstone mode is intimately connected with, and almost completely specified by, the fully-dressed one-body propagator of its characteristic constituent

The one-body momentum is equated with the relative momentum of the two-body system

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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f

π Eπ(p2) = B(p2)Slide24

Enigma of massThe quark level Goldberger-Treiman relation shows that DCSB has a very deep and far reaching impact on physics within the strong interaction sector of the Standard Model; viz.,

Goldstone's theorem is fundamentally an expression of equivalence between the one-body problem and the two-body problem in

the pseudoscalar channel. 

This emphasises that Goldstone's theorem has a pointwise expression in QCDHence, pion properties are an almost direct measure of the dressed-quark mass function.  Thus, enigmatically, the properties of the massless

pion

are the cleanest expression of the mechanism that is responsible for almost all the visible mass in the universe.1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)24fπ Eπ(p2) = B(p2)Slide25

In QCD, Gluons, too, become massiveNot just quarks … Gluons also have a gap equation … 1/k2 behaviour signals essential singularity in the running coupling:

Impossible to reach in perturbation theory

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)25

Interaction model for the gap equation

Si-

xue Qin, Lei Chang, Y.-x.Liu, C.D. Roberts and D.J. WilsonarXiv:1108.0603 [nucl-th],  Phys. Rev. C 84 (2011) 042202(R) [5 pages]Slide26

Parton structure of hadrons

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Valence quarksSlide27

Parton Structure of HadronsValence-quark structure of hadronsDefinitive of a hadron. After all, it’s how we distinguish a proton from a neutronExpresses charge; flavour; baryon number; and other Poincaré-invariant macroscopic quantum numbersVia evolution, determines background at LHCSea-quark distributionsFlavour

content, asymmetry, intrinsic: yes or no?Answers are essentially nonperturbative

features of QC

D1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

27Slide28

Parton Structure of HadronsNeed for calculation is emphasised by Saga of pion’s valence-quark distribution:

1989: u

vπ ~ (1-x)

1 – inferred from LO-Drell-Yan & disagrees with QCD;

2001: DSE-

Q

CD predicts uvπ ~ (1-x)2 argues that distribution inferred from data can’t be correct; 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)28Valence quark distributions in the pion, M.B. Hecht, Craig D. Roberts, S.M. Schmidt, nucl-th/0008049, Phys.Rev. C63 (2001) 025213 .Slide29

Parton Structure of HadronsNeed for calculation is emphasised by Saga of pion’s valence-quark distribution:

1989: u

vπ ~ (1-x)

1 – inferred from LO-Drell-Yan & disagrees with QCD;

2001: DSE-

Q

CD predicts uvπ ~ (1-x)2 argues that distribution inferred from data can’t be correct; 2010: NLO reanalysis including soft-gluon resummation, inferred distribution agrees with DSE and QCD1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)29Soft-gluon resummation and the valence parton distribution function of the pion, M. Aicher, A. Schafer, W. Vogelsang, Phys.Rev.Lett. 105 (2010) 252003, arXiv:1009.2481 [hep-ph]Valence quark distributions in the pion, M.B. Hecht, Craig D. Roberts, S.M. Schmidt, nucl-th/0008049, Phys.Rev. C63 (2001) 025213

.Slide30

DCSB on the light-front

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30Slide31

Pion’s valence-quark Distribution AmplitudeDeveloped DSE methods to compute φπ(x) = projection of the pion’s Poincaré-covariant wave-function onto the light-frontResults have been obtained with rainbow-ladder DSE kernel, simplest symmetry preserving form; and the best DCSB-improved kernel that is currently available.

xα (1-x)

α, with α

=0.31st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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Imaging dynamical

chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].Slide32

Pion’s valence-quark Distribution AmplitudeBoth kernels agree: marked broadening of φπ(x), which owes to DCSB 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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Asymptotic

RL

DB

This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB.Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result

Imaging dynamical

chiral

symmetry breaking:

pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].Slide33

Pion’s valence-quark Distribution AmplitudeBoth kernels agree: marked broadening of φπ(x), which owes to DCSB 1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

33

Asymptotic

RL

DB

This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB.Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result

These computations are the first to directly expose DCSB –

pointwise

– on the light-front; i.e., in the infinite momentum frame.

Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].Slide34

Pion’s valence-quark Distribution Amplitude1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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Established a one-to-one connection

between DCSB and the

pointwise

form of the pion’s wave function.Dilation measures the rate at which dressed-quark approaches the asymptotic bare-parton limitExperiments at JLab12 can empirically verify the behaviour of M(p), and hence chart the IR limit of QCDC.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50Dilation of pion’s wave function is measurable in pion’s electromagnetic

form factor at JLab12

A-rated:

E12-06-10Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].Slide35

Extracting information from lattice-QCD today

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

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35Slide36

Valence-quark Distribution Amplitudes of light-quark mesons from lattice-QCDPDA Moments from lattice-QCDBest available results show no distinction between pseudoscalar and vector, nor between light-front parallel and perpendicular polarisationsDSE studies underway: Shi-chao, Peter Tandy et al.1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

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R. Arthur

et al

.,

Phys.Rev. D83 (2011) 07450Slide37

Valence-quark Distribution Amplitudes of light-quark mesons from lattice-QCD1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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Reconstruct

PDAs using method described in

Pion

distribution amplitude from lattice-QCD,

I. C. Cloët, L. Chang, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1306.2645 [nucl-th], Phys. Rev. Lett. 111 (2013) 092001 [5 pages] SU(3) breaking is measured by shift in peak: ratio =1.09 xmax =0.545 for φK(xmax) cf. xmax=φπ(½) for φπ (x) cf. ratio of 1.15 for peak of [x svK(xmax)]/[x uv

K(

xmax

)]

φπ~ xα (1-x)α α=0.35+0.32 = 0.67- 0.24 = 0.11 φπ~ xα (1-x)β α=0.39±0.10 β=0.47 -/+ 0.16Lei Chang et al.In progress.Slide38

When is asymptotic PDA valid?PDA is a wave function  not directly observable but PDF is.φ

πasy(x) can only be a good approximation to the

pion's PDA when it is accurate to write

uvπ (x) ≈ δ(x) for the pion's

valence-quark distribution function.

This is far from valid at currently accessible scales

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)38Q2=27 GeV2This is not δ(x)!Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. RobertsSlide39

When is asymptotic PDA valid?When is asymptopia reached?If uvπ(x) ≈ δ(x),

then <x> = ∫

01

dx x uvπ

(x) = 0;

i.e., the light-front momentum fraction carried by valence-quarks is ZERO  Asymptopia is reached when <x> is “small”As usual, the computed valence-quark distribution produces (π = u+dbar) 2<x>2GeV = 44%When is <x> small?1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)39Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. RobertsNLO evolution of PDF, computation of <x>. Even at LHC energies, light-front fraction of the π momentum: <x>dressed valence-quarks = 25% <x>glue = 54%, <x>sea-quarks = 21%

LHC:

16TeV

Evolution in QCD is

LOGARITHMICJLab 2GeVSlide40

When is asymptotic PDA valid?When is asymptopia reached?If uvπ(x) ≈ δ(x), then <x> = ∫

01

dx

x uvπ(x) = 0; i.e.,

the light-front momentum

fraction carried by valence-quarks is ZERO  Asymptopia is reached when <x> is “small”As usual, the computed valence-quark distribution produces (π = u+dbar) 2<x>2GeV = 44%When is <x> small?1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)40Explanation and Prediction of Observables using Continuum Strong QCD, I.C. Cloët & C.D. RobertsNLO evolution of PDF, computation of <x>. Even at LHC energies, light-front fraction of the π momentum: <x>dressed valence-quarks = 25% <x>glue = 54%, <x>sea-quarks = 21%

LHC:

16TeV

Evolution in QCD is

LOGARITHMICJLab 2GeVEven at LHC energy scales, nonperturbative effects, such as DCSB, are playing a crucial role in setting the scales in PDAs and PDFs.Slide41

At the “Planck scale”1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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Explanation and Prediction of Observables using Continuum Strong QCD,

I.C

.

Cloët

& C.D. RobertsEvolution in QCD is LOGARITHMICIn the truly asymptotic domain, way, way beyond LHC energy scales, gluons and sea-quarks share the momentum of a hadron, each with roughly 50% of the momentumSlide42

Elastic Scattering1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

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e(p) + H(q)

→ e(p’) +

H(q

’)Slide43

Peter Tandy can now die

a happy man

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

43Slide44

Charged

pion

elastic form factor

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

44Single interaction kernel, determined by just 1 parameter and preserving the one-loop RG-behaviour of QCD, had unified Fπ(Q2) and φπ(x) (and many other quantities)However, using brute-force numerical techniques it was impossible to proceed reliably beyond Q2=4GeV2DSE 2013pQCD obtained with φπasy(x)

pQCD

obtained with

φ

π(x;2GeV), i.e., the PDA appropriate to the scale of the experiment15%DSE 2000Slide45

New Algorithm1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

45Slide46

Charged

pion

elastic form factor

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

46Single interaction kernel, determined by just 1 parameter and preserving the one-loop RG-behaviour of QCD, has unified Fπ(Q2) and φπ(x) (and many other quantities)Prediction of pQCD obtained when the pion valence-quark PDA has the form appropriate to the scale accessible in modern experiments is markedly different from the result obtained using the asymptotic PDAPion electromagnetic form factor at spacelike momenta, Lei Chang et al. arXiv:1307.0026 [nucl-th],  

Phys. Rev.

Lett. 111 (2013) 141802 [5 pages]

DSE 2013

pQCD obtained with φπasy(x)pQCD obtained with φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment15%Near agreement between the pertinent perturbative QCD prediction and DSE-2013 prediction is striking. Dominance of hard contributions to the pion form factor for Q2>8GeV2. Normalisation is fixed by a pion wave-function whose dilation with respect to φπasy(x) is a definitive signature of DCSBSlide47

Baryon Structure

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 the observation that an interaction which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channel1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)47R.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145SUc(3):Slide48

Baryon StructureRemarksDiquark correlations are not inserted by hand Such correlations are a dynamical consequence of strong-coupling in Q

CDThe same mechanism that produces an almost

massless pion

from two dynamically-massive quarks; i.e., DCSB, forces a strong correlation between two quarks in colour-antitriplet channels within a baryon – an indirect consequence of Pauli-Gürsey symmetryDiquark correlations are not

pointlike

Typically,

r0+ ~ rπ & r1+ ~ rρ (actually 10% larger)They have soft form factors1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)48SU(2) isospin symmetry of hadrons might emerge from mixing half-integer spin particles with their antiparticles.Faddeev EquationSlide49

Nucleon StructureProbed in scattering experimentsElectron is a good probe because it is structureless Electron’s relativistic current isProton’s electromagnetic current1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

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49

F

1

= Dirac form factor

F2 = 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, F1

=1 & F

2

=0, so that G

E=GM and hence distribution of charge and magnetisation within this fermion are identicalSlide50

Structure of HadronsElastic form factorsProvide vital information about the structure and composition of the most basic elements of nuclear physics. They are a measurable and physical manifestation of the nature of the hadrons' constituents and the dynamics that binds them together. Accurate form factor data are driving paradigmatic shifts in our pictures of hadrons and their structure; e.g., role of orbital angular momentum and nonpointlike diquark correlationsscale at which p-

QCD

effects become evidentstrangeness content

meson-cloud effectsetc.1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

50Slide51

Flavor separation of proton form factorsVery different behavior for u & d quarks

Means apparent scaling in proton F2/F1 is purely accidental

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)51

Cates, de

Jager

, Riordan, Wojtsekhowski, PRL 106 (2011) 252003Q4F2q/kQ4 F1qSlide52

Diquark correlations!Poincaré covariant Faddeev equation Predicts scalar and axial-vector diquarks Proton's singly-represented d-quark more likely to be struck in association with 1+ diquark than with 0

+form factor contributions involving 1

+ diquark are softer

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

52

Cloët

, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36Wilson, Cloët, Chang, Roberts, PRC 85 (2012) 045205Doubly-represented u-quark is predominantly linked with harder 0+ diquark contributions Interference produces zero in Dirac form factor of d

-quark in proton

Location of the zero depends on the relative probability of finding

1+ & 0+ diquarks in protonCorrelated, e.g., with valence d/u ratio at x=1du=Q2/M2Slide53

Visible Impacts of DCSB1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)53

Apparently small changes in M(p) within the domain 1<p(

GeV

)<3

have striking effect on the proton’s electric form factor

The possible existence and location of the zero is determined by

behaviour of Q2F2p(Q2)Like the pion’s PDA, Q2F2p(Q2) measures the rate at which dressed-quarks become parton-like:F2p=0 for bare quark-partonsTherefore, GEp can’t be zero on the bare-parton domainI.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution, arXiv:1304.0855 [nucl-th], Phys. Rev. Lett. 111 (2013) 101803Slide54

Visible Impacts of DCSB1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)54

Follows that the

possible existence

and location

of a zero in the ratio of proton elastic form factors

[

μpGEp(Q2)/GMp(Q2)] are a direct measure of the nature of the quark-quark interaction in the Standard Model.Leads to Prediction neutron:protonGEn(Q2) > GEp(Q2) at Q2 > 4GeV2I.C. Cloët, C.D. Roberts, A.W. Thomas:

Revealing dressed-quarks via the proton's charge distribution, arXiv:1304.0855 [nucl-th

], Phys. Rev.

Lett. 111 (2013) 101803Slide55

Far valence domain x≃

1

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

55Slide56

Far valence domain x≃1Endpoint of the far valence domain: x ≃ 1, is especially significantAll familiar PDFs vanish at x=1; but ratios of any two need notUnder DGLAP evolution, the value of such a ratio is invariant.Thus, e.g., limx→1

dv(x)/uv

(x) is unambiguous, scale invariant, nonperturbative

feature of QCD.  keen discriminator between frameworks that claim to explain nucleon structure. Furthermore,

Bjorken

-

x=1 corresponds strictly to the situation in which the invariant mass of the hadronic final state is precisely that of the target; viz., elastic scattering.  Structure functions inferred experimentally on x≃1 are determined theoretically by target's elastic form factors.1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)56Nucleon spin structure at very high-xCraig D. Roberts, Roy J. Holt and Sebastian M. SchmidtarXiv:1308.1236 [nucl-th], Phys. Lett. B in pressSlide57

Neutron Structure Function at high-xValence-quark distributions at x=1Fixed point under DGLAP evolutionStrong discriminator between theoriesAlgebraic formulaP1p,s

= contribution to the proton's charge arising from diagrams with a scalar diquark component in both the initial and final state

P1p,a

= kindred axial-vector diquark contributionP1p,m = contribution to the proton's charge arising from diagrams with a different diquark component in the initial and final state.

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

57I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36D. J. Wilson, I. C. Cloët, L. Chang and C. D. RobertsarXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages] Measures relative strength of axial-vector/scalar diquarks in protonSlide58

Neutron StructureFunction at high-x1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

58

d/u=1/2

SU(6

) symmetry

pQCD

, uncorrelated Ψ0+ qq only, d/u=0Deep inelastic scattering – the Nobel-prize winning quark-discovery experimentsReviews: S. Brodsky et al. NP B441 (1995) W. Melnitchouk &

A.W.Thomas

PL B377 (1996) 11

N. Isgur, PRD 59 (1999) R.J. Holt & C.D. Roberts RMP (2010)d/u=0.28DSE: “realistic”Distribution of neutron’s momentum amongst quarks on the valence-quark domainDSE: “contact”d/u=0.18Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) 117501

x>0.9

Melnitchouk

, Arrington

et al

.

Phys.Rev.Lett

. 108 (2012) 252001

I.C.

Cloët

, C.D. Roberts,

et al

.

arXiv:0812.0416 [

nucl-th

]

,

Few Body Syst. 46 (2009) 1-36

D. J. Wilson, I. C.

Cloët

, L. Chang and C. D. Roberts

arXiv:1112.2212 [

nucl-th

]

, 

Phys. Rev. C

85

 (2012) 025205 [21 pages]

Slide59

Neutron StructureFunction at high-x1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

59

d/u=1/2

SU(6

) symmetry

pQCD

, uncorrelated Ψ0+ qq only, d/u=0Deep inelastic scattering – the Nobel-prize winning quark-discovery experimentsReviews: S. Brodsky et al. NP B441 (1995) W. Melnitchouk &

A.W.Thomas

PL B377 (1996) 11

N. Isgur, PRD 59 (1999) R.J. Holt & C.D. Roberts RMP (2010)d/u=0.28DSE: “realistic”Distribution of neutron’s momentum amongst quarks on the valence-quark domainDSE: “contact”d/u=0.18Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) 117501

x>0.9

Melnitchouk

, Arrington

et al

.

Phys.Rev.Lett

. 108 (2012) 252001

I.C.

Cloët

, C.D. Roberts,

et al

.

arXiv:0812.0416 [

nucl-th

]

,

Few Body Syst. 46 (2009) 1-36

D. J. Wilson, I. C.

Cloët

, L. Chang and C. D. Roberts

arXiv:1112.2212 [

nucl-th

]

, 

Phys. Rev. C

85

 (2012) 025205 [21 pages]

NB.

d/

u|

x

=1

= 0

means there are no valence d-quarks

in the proton!

JLab12 can solve this enigmaSlide60

Neutron StructureFunction at high-x“While it is quite hazardous to extrapolate from our limited xB

range all the way to x

B = 1, these results appear to disfavor models of the proton with d/u=0 at

xB = 1”

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

60Short Range Correlations and the EMC Effect, L.B. Weinstein et al., Phys.Rev.Lett. 106 (2011) 052301, arXiv:1009.5666 [hep-ph]Figure courtesy of D.W. HiginbothamObservation: EMC effect measured in electron DIS at 0.35 < xB < 0.7, is linearly related to the Short Range Correlation (SRC) scale factor obtained from electron inclusive scattering at xB > 1.Slide61

Nucleon spin structure at very high x1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

61

Similar formulae for nucleon longitudinal structure functions.

Plainly, existing data cannot distinguish between modern pictures of nucleon structure

Empirical results for nucleon longitudinal spin asymmetries on

x

≃ 1 promise to add greatly to our capacity for discriminating between contemporary pictures of nucleon structure. NB. pQCD is actually model-dependent: assumes SU(6) spin-flavour wave function for the proton's valence-quarks and the corollary that a hard photon may interact only with a quark that possesses the same helicity as the target.Nucleon spin structure at very high-xCraig D. Roberts, Roy J. Holt and Sebastian M. SchmidtarXiv:1308.1236 [nucl-th], Phys. Lett. B in pressSlide62

Tensor Charge: σμν currenth1T = distribution of transversely polarized quarks inside a transversely polarised protonδq = Light-front number-density of quarks with transverse polarisation parallel to that of the proton

minus that of quarks with transverse polarisation antiparallel

Bias in quark polarisation

induced by polarisation of parent protonValue of tensor charge places constraints on some extensions of the Standard Model <PRD85 (2012) 054512> Current knowledge of transversity: SIDIS @HERMES, COMPASS, JLab

No gluon

transversity

distribution => transversity is suppressed at low-x, so large-x behavior important => JLab12 a useful tool. So, transversity will be measured at JLab12 (Hall-A E12-09-018-SIDIS; CLAS12; and SoLID)1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)62Direction of motionSlide63

Tensor Charge: σμν currentJlab 12 ProjectionAnselmino et al., 1303.3822 [hep-ph]

Pitschmann et al. (DSE) (2013) [including axial-vector diquarks

but contact interaction]Hecht

et al. (DSE), PRC64 (2001) 025204 [only scalar diquarks]Cloët et al., PLB659 (2008) 214

Pasquini

et al

., PRD76 (2007) 034020Wakamatsu, PLB653 (2007) 398Gockeler et al., PLB627 (2005) 113Gamberg et al., PRL 87 (2001) 242001 He et al., PRD52 (1995) 2960Bacchetta et al., JHEP 1303 (2013) 1191st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)63Direction of motionBig shift from including axial-vector diquark correlations? d-quark can now be unpaired.Slide64

TheoryLattice-QCDSignificant progress in the last five yearsThis must continueBound-state problem in continuum quantum field theorySignificant progress, tooThis must continue

First Sino-Americas School & Workshop on the Continuum Bound-State Problem, Hefei, China.

22-26/Oct./2013

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)64Slide65

Epilogue1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

65Slide66

EpilogueThe Physics of Hadrons is Unique:Confronting a fundamental theory in which the elementary degrees-of-freedom are intangible and only composites reach detectorsConfinement in real-world is NOT understoodBut DCSB is understood, and is crucial to any understanding of

hadron phenomena

They

must

have a common origin

Experimental and theoretical study of the Bound-state problem in continuum QCD promises to provide many more

predictions, insights and answers.1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)66Slide67

This is not the end1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

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67Slide68

Lattice comparisonPion’s valence-quark PDAEmploy the generalised-Gegenbauer method described previously (and in Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages])

.

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)68

Lattice-QCD

=> one nontrivial moment: <(2x-1)2> = 0.27 ± 0.04LegendSolid = DB (Best) DSEDashed = RL DSEDotted (black) = 6 x (1-x)Dot-dashed = midpoint lattice; and the yellow shading exhibits band allowed by lattice errorsφπ~ xα

(1-x)α

α

=0.35

+0.32 = 0.67- 0.24 = 0.11DB α=0.31 but 10% a2<0RL α=0.29 and 0% a2V. Braun et al., PRD 74 (2006) 074501Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th],  Phys. Rev. Lett. 111 (2013) 092001 [5 pages]Slide69

When is asymptotic PDA valid?Under leading-order evolution, the PDA remains broad to Q2>100 GeV2Feature signals persistence of the influence of dynamical chiral symmetry breaking.

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

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69

Consequently, the asymptotic distribution,

φπasy(x), is a poor approximation to the pion's PDA at all such scales that are either currently accessible or foreseeable in experiments on pion elastic and transition form factors. Thus, related expectations based on φπasy(x) should be revised.

asymptotic

4 GeV

2

100 GeV2Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th],  Phys. Rev. Lett. 111 (2013) 092001 [5 pages]Slide70

Flavor separation of proton form factorsVisible Impacts of DCSB1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

70

Effect driven primarily by electric form factor of doubly-represented

u

-quark

u

-quark is 4-times more likely than d-quark to be involved in hard interactionSo … GEpu ≈ GEpSingly-represented d-quark is usually sequestered inside a soft diquark correlationSo, although it also becomes parton-like more quickly as α increases, that is hidden from viewd-quarku-quarkI.C. Cloët & C.D. Roberts … continuingSlide71

Confinement contains condensates

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

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71Slide72

“Orthodox Vacuum”Vacuum = “frothing sea” Hadrons = bubbles in that “sea”, containing nothing but quarks & gluons interacting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

72

u

u

u

d

u

u

d

duSlide73

New ParadigmVacuum = hadronic fluctuations but no condensates Hadrons = complex, interacting systems within which perturbative behaviour is restricted to just 2% of the interior1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

73

u

u

u

d

u

u

d

duSlide74

Regge Trajectories?Martinus Veltmann, “Facts and Mysteries in Elementary Particle Physics” (World Scientific, Singapore, 2003): In time the Regge trajectories thus became the cradle of string theory. Nowadays the Regge

trajectories have largely disappeared, not in the least because these higher spin bound states are hard to find experimentally. At the peak of the Regge fashion (around 1970) theoretical physics produced many papers containing families of

Regge trajectories, with the various (hypothetically straight) lines based on one or two points only!

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

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74

Phys.Rev. D 62 (2000) 016006 [9 pages]1993: "for elucidating the quantum structure of electroweak interactions in physics"Systematics of radial and angular-momentum Regge trajectories of light non-strange qqbar-states“ P. Masjuan, E. Ruiz Arriola, W. Broniowski. arXiv:1305.3493 [hep-ph] Slide75

Hybrid Hadrons & Lattice QCD – Robert Edwards, Baryons13Heavy pions … so, naturally, constituent-quark like spectraTo which potential does it correspond?1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)

75

arXiv:1104.5152, 1201.2349Slide76

Hybrid meson models – Robert Edwards, Baryons13With minimal quark content, , gluonic field can in a color singlet or octet

`constituent’ gluon

in S-wave

`constituent’ gluon

in P-wave

bag model

flux-tube model

arXiv:1104.5152, 1201.2349

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct

76

Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)Slide77

Hybrid baryon models – Robert Edwards, Baryons13Minimal quark content, , gluonic field can be in color singlet, octet or decuplet

bag model

flux-tube model

Now must take into account

permutation

symmetry of quarks and gluonic field

arXiv:1104.5152, 1201.23491st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct77Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)Slide78

Table of ContentsIntroductionPion valence-quark distribution

Pion

valence-quark parton

distribution amplitudeWhen is the asymptotic PDA a good approximation?Charged pion

elastic form factor

Nucleon form factors

Nucleon structure functions at large-xEpilogueDSE cf. Lattice PDA & PDA evolutionGE/GM flavour separationConfinement contains condensatesRegge Trajectories?1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/OctCraig Roberts for Ian Cloët: Images of the Origin of Mass (66p)78