Craig Roberts, Physics Division. 1.Rocio BERMUDEZ (U Michoácan); 2.Shi CHAO (Nanjing U) ;...

Strong coupling QCD – the ins and outs of

bound-statesCraig Roberts, Physics Division

Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states

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Collaborators: 2012-Present1. Rocio BERMUDEZ (U Michoácan);2. Shi CHAO (Nanjing U) ;3. Ming-hui DING (PKU);4. Fei GAO (PKU) ;5. S. HERNÁNDEZ (U Michoácan);6. Cédric MEZRAG (CEA, Saclay) ;7. Trang NGUYEN (KSU);8. Khépani RAYA (U Michoácan);9. Hannes ROBERTS (ANL, FZJ, UBerkeley);10. Chien-Yeah SENG (UM-Amherst) ;11. Kun-lun WANG (PKU);12. Shu-sheng XU (Nanjing U) ;13. Chen CHEN (USTC);14. J. Javier COBOS-MARTINEZ (U.Sonora);15. Mario PITSCHMANN (Vienna);16. Si-xue QIN (U. Frankfurt am Main, PKU);17. Jorge SEGOVIA (ANL);18. David WILSON (ODU);

574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp

22. Adnan BASHIR (U Michoácan);23. Stan BRODSKY (SLAC);24. Gastão KREIN (São Paulo) ;25. Roy HOLT (ANL);26. Yu-xin LIU (PKU);27. Hervé Moutarde (CEA, Saclay) ;28. Michael RAMSEY-MUSOLF (UM-Amherst) ;29. Alfredo RAYA (U Michoácan);30. Jose Rodriguez Qintero (U. Huelva) ;31. Sebastian SCHMIDT (IAS-FZJ & JARA);32. Robert SHROCK (Stony Brook);33. Peter TANDY (KSU);34. Tony THOMAS (U.Adelaide) ;35. Shaolong WAN (USTC) ;36. Hong-Shi ZONG (Nanjing U)

Students, Postdocs, Asst. Profs.

19. Lei Chang (U. Adelaide) ;20. Ian Cloet (ANL) ;21. Bruno El-Bennich (São Paulo);

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Physics is an

empirical science



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It’s not physics unless it can be tested

empirically.



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It’s not proven

unless it’s verified

experimentally.574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC

ERA. 79pp


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Top Open Questions in

Physics574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp


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Understand the 4% of material that we know

exists 574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp



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Key Questions for the Future

What is confinement? Where is the mass of the nucleon? Where is the nucleon's magnetic moment? What is the nucleon? What is a hadron? …


Examples of Emergent Phenomena in QCD, the strong-interaction sector of

the Standard Model


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Key Questions for the Future

What is confinement? Where is the mass of the nucleon? Where is the nucleon's magnetic moment? What is the nucleon? What is a hadron? …


One cannot properly know what lies beyond the Standard Model unless one first knows what is in the Standard Model

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Jefferson Lab574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp



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Thomas Jefferson National Accelerator Facility (JLab) One of the primary reasons for building CEBAF/JLab

Prediction: at energy-scales greater than some a priori unknown minimum value, Λ, cross-sections and form factors will behave as

power = ( number valence-quarks – 1 + Δλ ) Δλ=0,1, depending on whether helicity is conserved

or flipped … prediction of 1/k2 vector-boson exchange

logarithm = distinctive feature & concrete prediction of QCD Initially imagined that Λ = 1GeV! So, JLab was initially built to reach 4GeV.


Parton model scaling

QCD scaling violations

e.g. S. J. Brodsky and G. R. Farrar, Phys. Rev. Lett. 31, 1153 (1973)


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Thomas Jefferson National Accelerator Facility (JLab) 1994 – 2004

o An enormous number of fascinating experimental results

o Including an empirical demonstration that the distribution of charge and magnetisation within the proton are completely different,

o Suggesting that quark-quark correlations play a crucial role in nucleon structure

But no sign of parton model scaling and certainly not of scaling violations


Particle physics paradigm

Particle physics paradigm


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Thomas Jefferson National Accelerator Facility (JLab)

2004 … Mission Need Agreed on upgrade of CEBAF (JLab's accelerator) to 12GeV

2014 … 12GeV commissioning beams now being delivered to the experimental halls

Final cost of upgrade isapproximately $370-Million

Physics of JLab at 12GeV arXiv:1208.1244 [hep-ex]


http://arxiv.org/abs/arXiv:1208.1244

http://arxiv.org/abs/arXiv:1208.1244

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Critical Theory Needs for JLab12 Experiment – Goal: accurate measurement of pion form factor

to 6 GeV2; and it can produce a 10% measurement at 9 GeV2

Experiment – Goal: Accurate measurement of nucleon elastic and transition form factors to 15 GeV2

Experiment – Goal: Hadron tomography in momentum and configuration space

Critical need for success of Laboratory’s programme – Insightful computational framework

• Capable of computing hadron wave functions• Capable of predicting and unifying meson & nucleon

elastic and transition form factors on 0<Q2<15 GeV2

• Possessing direct connection to QCD, so that connection with established predictions of (perturbative) QCD can be established




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Contemporary Theory

Dyson-Schwinger equations– Insightful computational framework – Established connection

with predictions of (perturbative) QCD– Capable of predicting and unifying meson & nucleon

elastic and transition form factors on 0<Q2<20 GeV2

… and beyond– Capable of predicting pointwise behaviour of hadronic

parton distribution functions/amplitudes… valence-quark domain is understood



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Significant Progress on All Fronts


Novel understanding of gluon and quarkconfinement and its consequencesis emerging from quantum field theory

Arriving at a clear picture of how hadron masses emerge dynamically in a universe with light quarks

Dynamical Chiral Symmetry Breaking (DCSB) Realistic computations of ground-state hadron wave functions

with a direct connection to QCD are now available Quark-quark correlations are crucial in hadron structure

and accumulating empirical evidence in support of this prediction


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What is Confinement?


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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.”



Folklore … JLab Hall-D Conceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes.

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Problem: Pions … They’re unnaturally light16 tonnes of force makes a lot of them.



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Problem: 16 tonnes of force makes a lot of pions.



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Light quarks & Confinement In the presence of

light quarks, pair creation seems to occur non-localized and instantaneously



G. Bali et al., PoS LAT2005 (2006) 308

http://inspirebeta.net/record/694488?ln=en


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Light quarks & Confinement In the presence of

light quarks, pair creation seems to occur non-localized and instantaneously

No flux tube in a theory with light-quarks.

Flux-tube is not the correct paradigm for confinement in hadron physics



G. Bali et al., PoS LAT2005 (2006) 308




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What is Dressing?574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE

LHC ERA. 79pp


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Quark Gap Equation574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC

ERA. 79pp

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Dynamical Chiral Symmetry Breaking



DCSB is a fact in QCD– Dynamical, not spontaneous

• Add nothing to QCD , No Higgs field, nothing! Effect achieved purely throughquark+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.

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In QCD: Gluons alsobecome massive! Not just quarks …

Gluons also have a gap equation …

Gluons are cannibals – a particle species whose members become massive by eating each other!



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422 )(

kkm

g

gg

Present level of uncertainty using phenomenology and theory ∼ 30%

Power-law suppressed in ultraviolet, so invisible in perturbation theory

Gluon mass-squared function


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Massive Gauge Bosons! Gauge boson cannibalism

… a new physics frontier … within the Standard Model Asymptotic freedom means

… ultraviolet behaviour of QCD is controllable Dynamically generated masses for gluons and quarks means

that QCD dynamically generates its own infrared cutoffs– Gluons and quarks with

wavelength λ > 2/mass ≈ 1 fm decouple from the dynamics … Confinement?!

How does that affect observables?– It will have an impact in

any continuum study– Must play a role in gluon saturation ...

In fact, perhaps it’s a harbinger of gluon saturation?574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp


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Confinement is dynamical!


Confinement QFT Paradigm: – Confinement is expressed through a dramatic

change in the analytic structure of propagators for coloured states

– It can almost be read from a plot of the dressed-propagator for a coloured state



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Normal particleConfined particle

σ ≈ 1/Im(m) ≈ 1/2ΛQCD ≈ ½fm

Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities, (or qualitatively analogous structures chracterised by a dynamically generated mass-scale)

Propagation described by rapidly damped wave & hence state cannot exist in observable spectrum


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Quark Fragmentation A quark begins to

propagate in spacetime But after each “step” of

length σ, on average, an interaction occurs, so that the quark loses its identity, sharing it with other partons

Finally, a cloud of partons is produced, which coalesces into colour-singlet final states


meson

meson

meson

meson

Baryon

σ

Real-world confinement is a dynamical phenomenon, surrounded by mystery!

An EIC will enable “3D” measurements relating to fragmentation and insight into real-world confinement

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Symmetry preserving analyses in continuum

QCD574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp


Pion’s Goldberger-Treiman relation


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Pion’s Bethe-Salpeter amplitudeSolution of the Bethe-Salpeter equation

Dressed-quark propagator

Axial-vector Ward-Takahashi identity entails

Owing to DCSB& Exact inChiral QCD


Miracle: two body problem solved, almost completely, once solution of one body problem is known

Maris, Roberts and Tandynucl-th/9707003, Phys.Lett. B420 (1998) 267-273

B(k2)



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This is the most fundamental

expression of Goldstone’s Theorem and DCSB574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE

LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states

fπ Eπ(p2) = B(p2)

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Enigma of mass

The 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 QCD

Hence, 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.



fπ Eπ(p2) = B(p2)

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Dynamical Chiral Symmetry Breaking

Vacuum Condensates?574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp


Universal Conventions

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



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http://en.wikipedia.org/wiki/QCD_vacuum

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“Orthodox Vacuum”

Vacuum = “frothing sea” Hadrons = bubbles in that “sea”,

containing nothing but quarks & gluonsinteracting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!



u

u

ud

u ud

du


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However, just like gluons and quarks, and for the same reasons:Condensates are confined within hadrons. There are no in-vacuum condensates.

Historically, DCSB has come to be associated with the presumed existence of spacetime-independent condensates that permeate the Universe.


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Confinement contains

condensates574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp


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“Orthodox Vacuum”

Vacuum = “frothing sea” Hadrons = bubbles in that “sea”,

containing nothing but quarks & gluonsinteracting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!



u

u

ud

u ud

du

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New Paradigm Vacuum = perturbative hadronic fluctuations

but no nonperturbative condensates Hadrons = complex, interacting systems

within which perturbative behaviour is restricted to just 2% of the interior



u

u

ud

u ud

du

“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.”



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“Void that is truly empty solves dark energy puzzle”Rachel Courtland, New Scientist 4th Sept. 2010

Cosmological Constant: Putting QCD condensates back into hadrons reduces the mismatch between experiment and theory by a factor of 1046

Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard Model

experiment*103

8 4620

4

HG QCDNscondensateQCD

Paradigm shift:In-Hadron Condensates

“The biggest embarrassment in

theoretical physics.”

http://www.newscientist.com/article/mg19325911.700-dark-energy-seeking-the-heart-of-darkness.html

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Pion’s Wave Function574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC

ERA. 79pp


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Pion’s valence-quark Distribution Amplitude

Last two years, methods have been developed that enable direct computation of meson light-front wave functions

φπ(x) = twist-two parton distribution amplitude = projection of the pion’s Poincaré-covariant wave-function onto the light-front

Results have been obtained with rainbow-ladder DSE kernel, simplest symmetry preserving form; and the best DCSB-improved kernel that is currently available.

xα (1-x)α, with α≈0.5574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp


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].

http://inspirehep.net/record/1209281?ln=en



http://prl.aps.org/abstract/PRL/v110/i13/e132001







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Pion’s valence-quark Distribution Amplitude

Continuum-QCD prediction: marked broadening of φπ(x), which owes to DCSB



Asymptotic

RL

DB

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].












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Features of Ground-state PDAs

A diverse array of studies since Caraguatatuba (2012) have shown that ground-state meson PDAs are broad, concave functions

Camel-humped distributions – popular with some for many years – are physically unreasonable because they correspond to bound-state amplitudes that disfavour equal momentum partitioning between valence-quark degrees of freedom


Concave function: no line segment lies above any point on the graph

arXiv:1301.0324 [nucl-th], arXiv:1306.2645 [nucl-th], arXiv:1311.1390 [nucl-th], arXiv:1405.0289 [nucl-th], arXiv:1406:3353 [nucl-th]

















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Pion electromagnetic form factor

2013: existing data and theory – no hint of a trend toward the so-called asymptotic pQCD prediction?

Jlab 12 will allow an extension of the Fπ measurement up to a value of Q2 of about 6 (GeV/c)2

& 10% measurement at 9 GeV2


Projected JLab reach

Result imagined by many to be QCD prediction

Evaluated with φπ = 6x(1-x)

E12-06-101 and E12-07-105


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Pion electromagnetic form factor Understanding – Part 1

– Compare data with the real QCD prediction; i.e. the result calculated using the broad pion PDA predicted by modern analyses of continuum QCD

Understanding – Part 2– Algorithm used to

compute the PDA can also be employed to compute Fπ(Q2) directly, to arbitrarily large Q2


Real QCD prediction – obtained with realistic, computed PDA

Predictions: JLab will see maximum Experiments to 8GeV2 will see

parton model scaling and QCD scaling violations for the first time in a hadron form factor

Pion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013)

maximum

Agreement within 15%







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When is asymptotic PDA valid?

PDA is a wave function not directly observable

but PDF is. φπ

asy(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



Q2=27 GeV2

This is not δ(x)!

Explanation and Prediction of Observables using Continuum Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv:1310.2651 [nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line]

Basic features of the pion valence-quark distribution function, L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29




http://dx.doi.org/10.1016/j.ppnp.2014.02.001

http://dx.doi.org/10.1016/j.physletb.2014.08.009




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When is asymptotic PDA valid? When is asymptopia reached?

If uvπ(x) ≈ δ(x), then

<x> = ∫01 dx x uv

π(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?


NLO evolution of PDF, computation of <x>. Even at LHC energies, light-front fraction of

the π momentum:<x>dressed valence-quarks = 21%

<x>glue = 54%, <x>sea-quarks = 25%

LHC: 16TeV

Evolution in QCD is LOGARITHMIC

JLab 2GeV







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At the “Planck scale”


Evolution in QCD is LOGARITHMIC

In 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 momentum


EIC Reach





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GPDs & TMDs574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp



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PDFs … only describe hadron light-front structure incompletely because inclusive deep inelastic scattering (DIS) measurements do not yield information about the distribution of partons in the plane perpendicular to the bound-state's total momentum; i.e., within the light front.

Generalised Parton Distributions (GPDs)– Spatial tomography of hadrons– Measured in DVCS

Transverse Momentum-dependent Distributions (TMDs)– Momentum tomography of hadrons– Measured in SIDIS

A new generation of experiments – more than ½ beam time at JLab – aims to provide the empirical information necessary to develop a phenomenology of nucleon Wigner distributions.

GPDs & TMDs



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Principal problem with phenomenology– If one wishes to use measured GPDs as a means by which to

validate our basic perception of strong interactions in the Standard Model, then data fitting is inadequate.

Instead, it is necessary to compute GPDs using a framework that possesses a direct connection with QCD.

This observation is highlighted by experience drawn from the simpler case of the pion's valence-quark PDF (L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29)– Phenomenology contradicted QCD predictions– Many claimed QCD was challenged– Until nonperturbative continuum-QCD predictions appeared …– Data reanalysed … now the PDF is seen as a success for QCD

GPDs & TMDs






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GPDs unify PDFs and elastic form factors, and extend both into a new domain

GPDs – unify & extend



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Rainbow-ladder (RL) truncation– δn

xP(ℓ):= δ(n ℓ - x n P)⋅ ⋅ , ℓ+R =ηbar ℓ++η ℓP, ℓ-

R= η ℓ- + ηbarℓP,

ℓ± = ℓ ± Δ/2, ℓP = ℓ - P. Triangle corresponds to the textbook handbag diagram

– Certainly guarantees connection between H(x,ξ,t) and Fπ(t), at same order of truncation

However, handbag diagram is not complete set of diagrams in RL truncation of valence-quark PDF and hence it’s not adequate for H(x,ξ,t)

Correction for PDF is known … Extension of Hπ(x,ξ,t) to all ξ ≠ 0 is not yet known but ξ =0 can be handled

Pion valence-quark GPD


Basic features of the pion valence-quark distribution function, L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29





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Completely general expression:

Use fact that H(x,ξ,t) can be written as a Radon transform, owing to its general properties:

Then … compute handbag diagram plus first-guess correction … inspect the result … read off the surviving Radon amplitude, F(α,β,t) … obtain

Hπ(x,ξ,t) is then completely determined … not just a limited number of moments but the entire function



Sketching the pion's valence-quark generalised parton distribution, C. Mezrag, L. Chang, H. Moutarde, C.D. Roberts, J. Rodriguez-Quintero, F. Sabatié, S.M. Schmidt in progress

ξ =0

uvπ(x)

computed directly from triangle diagram


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GPD in impact parameter space:

A true quantum mechanics density …… describes the probability of finding a parton within the light-front at a transverse position |bperp| from the hadron's centre of transverse momentum (CoTM)

Computed result … … not a guess




qπ(x


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GPD in impact parameter space:

Peaked at (xVm, |bperp|=0) … peak

becomes sharper as resolving scale, ζ, increases

Broad at |bperp| =0, becomes even broader as ζ increases

Narrowing as x → 1 … increasing ζ: xV

m → 0; GPD becomes even narrower … there can’t be many partons carrying x 1; i.e., all the ≃hadron’s light-front momentum




qπ(x

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Baryon Bound-States




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Baryon Structure

Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarks

Confinement and DCSB are readily expressed Prediction: strong diquark correlations exist within baryons as

a dynamical consequence of DCSB in QCD– The same mechanism that produces an almost massless pion from

two dynamically-massive quarks forces a strong correlation between two quarks in colour-antitriplet channels within a baryon

Diquark correlations are not pointlike– Typically, r0+ ~ rπ & r1+ ~ rρ

(actually 10% larger)– They have soft form factors



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Baryon Structure

Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarks

Confinement and DCSB are readily expressed Prediction: strong diquark correlations exist within baryons as

a dynamical consequence of DCSB in QCD– The same mechanism that produces an almost massless pion from

two dynamically-massive quarks forces a strong correlation between two quarks in colour-antitriplet channels within a baryon

Diquark correlations are not pointlike– Typically, r0+ ~ rπ & r1+ ~ rρ

(actually 10% larger)– They have soft form factors


Nucleon wave function can be calculated …

prediction of nucleon properties is possible


Visible Impacts of DCSB


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Apparently small changes in M(p) within the domain 1<p(GeV)<3have striking effect on the proton’s electric form factor

The possible existence and location of the zero is determined by behaviour of Q2F2

p(Q2), proton’s Pauli form factor Like the pion’s PDA, Q2F2

p(Q2) measures the rate at which dressed-quarks become parton-like: F2

p=0 for bare quark-partons Therefore, GE

p can’t be zero on the bare-parton domain

I.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) 101803










Visible Impacts of DCSB

574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp 64

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.

I.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) 101803









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Electric Charge Proton: if one accelerates the

rate at which the dressed-quark sheds its cloud of gluons to become a parton, then zero in Gep is pushed to larger Q2

Opposite for neutron! Explained by presence of

diquark correlations



J. Segovia, I.C. Cloët, C.D. Roberts, S.M. Schmidt: Nucleon and Δ Elastic and Transition Form Factors, arXiv:1408.2919 [nucl-th], Few Body Systems (in press)

These features entail that at x≈ 5 the electric form factor of the neutral neutron will become larger than that of the unit-charge proton!

JLab12 will probe this prediction

Leads to Prediction neutron:protonGEn(Q2) > GEp(Q2) at Q2 > 4GeV2





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Far valence domain x≃1



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Far valence domain x≃1

Endpoint of the far valence domain: x 1, is especially significant≃– All familiar PDFs vanish at x=1; but ratios of any two need not– Under 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.


Nucleon spin structure at very high-xCraig D. Roberts, Roy J. Holt and Sebastian M. SchmidtarXiv:1308.1236 [nucl-th], Phys. Lett. B 727 (2013) pp. 249–254





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Neutron Structure Function at high-x

Valence-quark distributions at x=1– Fixed point under DGLAP evolution– Strong discriminator between theories

Algebraic formula

– P1p,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 contribution

– P1p,m = contribution to the proton's charge arising from diagrams

with a different diquark component in the initial and final state.



I.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 proton




http://www.springerlink.com/content/d0r372483080w110/




http://prc.aps.org/abstract/PRC/v85/i2/e025205




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Neutron StructureFunction at high-x


d/u=1/2

SU(6) symmetry

pQCD, uncorrelated Ψ

0+ qq only, d/u=0

Deep inelastic scattering – the Nobel-prize winning quark-discovery experiments

Reviews: 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=0.28

DSE: “realistic”

Distribution of neutron’s momentum amongst quarks on the valence-quark domain

DSE: “contact”d/u=0.18

Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) 117501

x>0.9

Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) 252001


















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Neutron StructureFunction at high-x


d/u=1/2

SU(6) symmetry

pQCD, uncorrelated Ψ

0+ qq only, d/u=0

Deep inelastic scattering – the Nobel-prize winning quark-discovery experiments

Reviews: 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=0.28

DSE: “realistic”

Distribution of neutron’s momentum amongst quarks on the valence-quark domain

DSE: “contact”d/u=0.18

Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) 117501

x>0.9

Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) 252001


NB. d/u|x=1= 0 means there are

no valence d-quarks in the proton!

JLab12 can solve this enigma















71

Spin structure on x≃1574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp



72

Quark helicity at large Bjorken-x

Correlations between dressed-quarks within the proton have an enormous impact on nucleon spin structure







73

Quark helicity at large Bjorken-x



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.







74

TMDs Eight leading-twist TMDs Three of these are nonzero in the collinear limit



75

TMDs … Transversity … Tensor Charge

Intrinsic, defining property of the nucleon … just as significant as axial-charge

No gluon transversity distribution Value of tensor charge places constraints on some extensions of

the Standard Model <PRD85 (2012) 054512> Current knowledge of transversity:

SIDIS @HERMES, COMPASS, JLab Future SIDIS at JLab (SoLId), EIC, …


Direction of motion



76

TMDs … Transversity … Tensor Charge

Presence of diquark correlations in the proton wave function suppresses δu by 50% cf. SU(6) quark model prediction

Axial-vector correlation is crucial, e.g.: δd is only nonzero because the proton wave function contains axial-vector correlations; and axial-vector suppresses δu


Direction of motion

DSE latticemodels

Data fits

Pitschmann et al., arXiv:1411.xxxx – Nucleon tensor charges and electric dipole moments


77

Future574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp


78


79

Future Strong self-interactions amongst gluons are a unique feature of QCD

– Plausibly, they make QCD the only known nonperturbatively well-defined theory in Nature

Gluon cannibalism produces nonperturbatively massive gauge bosons and dressed-quarks– It is responsible for 98% of the mass of visible matter in the Universe

In this Universe, all readily accessible matter is defined by light quarks– Confinement is therefore a complex, dynamical phenomenon

unrelated to static potentials in quantum mechanical models This is the Standard Model Frontier:

– Predict– Measure – Explain



All the phenomena driven by the gluons that bind us all


80

Index Key Questions for the Future Critical Theory Needs for JLab12 QCD is a Theory Light quarks & Confinement Quark Gap Equation In QCD: Gluons also become massive! Confinement What is an hadron? Enigma of mass Confinement contains condensates Pion’s valence-quark Distribution Am

plitude Pion electromagnetic form factor When is asymptotic PDA valid? Pion valence -quark GPD Baryon Structure Visible Impacts of DCSB


Electric Charge Flavor separation of proton form facto

rs Far valence domain x 1≃ TMDs … Transversity … Tensor Charge Future


81

What is QCD?


82

Very likely a self-contained, nonperturbatively renormalisable and hence well defined Quantum Field TheoryThis is not true of QED – cannot be defined nonperturbatively

No confirmed breakdown over an enormous energy domain: 0 GeV < E < 8 TeV

Increasingly probable that any extension of the Standard Model will be based on the paradigm established by QCD – Extended Technicolour: electroweak symmetry breaks via a

fermion bilinear operator in a strongly-interacting non-Abelian theory. (Andersen et al. “Discovering Technicolor” Eur.Phys.J.Plus 126 (2011) 81)

– Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg-Landau theory of superconductivity



(not an effective theory)QCD is a Theory

wikipedia.org/wiki/Technicolor_(physics)



http://en.wikipedia.org/wiki/Technicolor_(physics)


83

Calories for quarks One of the most important figures in the Standard Model of Particle Physics

98% of the mass in this room & visible mass in the Universe owes to the phenomenon that produces this behaviour


84

Just one of the terms that are summed in a solution of the simplest, sensible 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 diagrams Impossible to compute this in perturbation theory.

The standard algebraic manipulation tools are just inadequate



αS23

85

GMOR Relation




86

GMOR Relation

Valuable to highlight the precise form of the Gell-Mann–Oakes–Renner (GMOR) relation: Eq. (3.4) in Phys.Rev. 175 (1968) 2195

o mπ is the pion’s mass o Hχsb is that part of the hadronic Hamiltonian density which

explicitly breaks chiral symmetry. The operator expectation value in this equation is evaluated

between pion states. Un-approximated form of the GMOR relation doesn’t make

any reference to a vacuum condensate574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp

Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)









87

GMOR is synonymous with “Vacuum Quark

Condensate”574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp


88

GMOR Relation

Demonstrated algebraically that the so-called Gell-Mann – Oakes – Renner relation is the following statement

Namely, the mass of the pion is completely determined by the pion’s scalar form factor at zero momentum transfer Q2 = 0. viz., by the pion’s scalar charge



Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)







89

Hadron Charges

Matrix elements associated with hadron form factors Scalar charge of a hadron is an intrinsic property of

that hadron … no more a property of the vacuum than the hadron’s electric charge, axial charge, tensor charge, etc. …



90

What is a hadron?574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC

ERA. 79pp



91

What is an hadron? Answer depends on your frame of reference,

even though truly observable quantities do not! Light-front (infinite momentum frame)

– Hadron is viewed as collection of infinitely many weakly interacting partons

– Bound-state complexity is “factorised off” and parametrised in nonperturbative distribution amplitudes

– Wave functions are complex but operators are simple “Human” frames

– Hadron structure is expressed in Schwinger functions • propagators and bound-state wave functions

– Computable using known methods in quantum field theory and expressed in terms of dressed-gluons and quarks, each of which is a complex, coherent collections of partons.

– Wave functions are simple but operators are complex



92

What is an hadron? Answer depends on your frame of reference,

even though truly observable quantities do not! Light-front (infinite momentum frame)

– Hadron is viewed as collection of infinitely many weakly interacting partons

– Bound-state complexity is “factorised off” and parametrised in nonperturbative distribution amplitudes

– Wave functions are complex but operators are simple “Human” frames

– Hadron structure is expressed in Schwinger functions • propagators and bound-state wave functions

– Computable using known methods in quantum field theory and expressed in terms of dressed-gluons and quarks, each of which is a complex, coherent collections of partons.

– Wave functions are simple but operators are complex


Descriptions are completely equivalent and hence one can choose whichever is most practical/useful/insightful, so long as frame-dependence of numerous interpretations is not forgotten.


93

Kinematics: – k, n are light-like four-vectors, satisfying k2=0=n2, k n=1⋅ ;– zperp represents that two-component part of z annihilated by both k, n; – P± = P ± Δ/2– ξ = -n Δ/2n P⋅ ⋅ = skewness: -1 ≤ ξ ≤ 1– t=-Δ2 is the momentum transfer– P2 = t/4-mπ

2, P Δ=0⋅

Poincaré invariance: – Support -1 ≤ x ≤ 1

GPD also depends on renormalisation scale ζ. Evolution equations are known: ERBL for |x|<ξ ; DGLAP for |x|>ξ (ξ >0)



94

Discovering Diquarks574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp



95

Flavor separation of proton form factors

Very different behavior for u & d quarks Means apparent scaling in proton F2/F1 is purely accidental 574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE

LHC ERA. 79pp

Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 (2011) 252003

Q4F2q/k

Q4 F1q


96

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


Cloët, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36Wilson, Cloët, Chang, Roberts, PRC 85 (2012) 045205

Doubly-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 proton– Correlated, e.g., with valence d/u ratio at x=1

d

u

=Q2/M2

Craig Roberts, Physics Division. 1.Rocio BERMUDEZ (U Michoácan); 2.Shi CHAO (Nanjing U) ;...

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Transcript of Craig Roberts, Physics Division. 1.Rocio BERMUDEZ (U Michoácan); 2.Shi CHAO (Nanjing U) ;...