craig roberts physics division. 1.rocio bermudez (u michoácan); 2.chen chen (anl, iit, ustc);...

Prospects for the physics of cold, sparse hadrons

Craig Roberts

Physics Division

Prospects for the physics of cold, sparse hadrons (72p)

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Collaborators: 2011-Present1. Rocio BERMUDEZ (U Michoácan);2. Chen CHEN (ANL, IIT, USTC);3. Xiomara GUTIERREZ-GUERRERO (U Michoácan);4. Trang NGUYEN (KSU);5. Khépani Raya (U Michoácan);6. Hannes ROBERTS (ANL, FZJ, UBerkeley);7. Chien-Yeah SENG (UW-Mad)8. Kun-lun WANG (PKU);9. J. Javier COBOS-MARTINEZ (U.Sonora);10. Mario PITSCHMANN (ANL & UW-Mad);11. Si-xue QIN (U. Frankfurt am Main);12. Jorge SEGOVIA (ANL);13. David WILSON (ODU);14. Lei CHANG (FZJ); 15. Ian CLOËT (ANL);16. Bruno EL-BENNICH (São Paulo);

Craig Roberts: U. Frankfurt: 8 July 2013

17. Adnan BASHIR (U Michoácan);18. Stan BRODSKY (SLAC);19. Gastão KREIN (São Paulo)20. Roy HOLT (ANL);21. Mikhail IVANOV (Dubna);22. Yu-xin LIU (PKU);23. Michael RAMSEY-MUSOLF (UW-Mad)24. Alfredo RAYA (U Michoácan);25. Sebastian SCHMIDT (IAS-FZJ & JARA);26. Robert SHROCK (Stony Brook);27. Peter TANDY (KSU);28. Tony THOMAS (U.Adelaide)29. Shaolong WAN (USTC)

StudentsPostdocsAsst. Profs.


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Science Challenges for the coming decade: 2013-2022

Exploit opportunities provided by new data on hadron elastic and transition form factors– Chart infrared evolution of QCD’s coupling and

dressed-masses – Reveal correlations that are key to nucleon structure– Expose the facts or fallacies in modern descriptions of

hadron structure



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Science Challenges for the coming decade: 2013-2022

Precision experimental study of valence region (Bjorken-x > 0.5), and theoretical computation of distribution functions and distribution amplitudes– Computation is critical, parametrisation is inadequate– Without computation, no amount of data will reveal

anything about the theory underlying the phenomena of strong interaction physics



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Overarching Science Challenges for the

coming decade: 2013-2022


Discover meaning of confinement, and its relationship to DCSB – the origin of visible mass


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What is QCD?Craig Roberts: U. Frankfurt: 8 July 2013

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QCD is a Theory 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 < 8000 GeV

Increasingly likely 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)

http://inspirehep.net/record/895220?ln=en


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Contrast: so-called Effective Field Theories

EFTs applicable over a very restricted energy domain; e.g., ChPT known to breakdown for E > 2mπ

Can be used to help explore how features of QCD influence observables



QCD appears valid at all energy scales that have been tested so far: no breakdown below

E ≈ 60000 mπ

Cannot 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 other

Can Cannot


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Strong-interaction: QCD

Asymptotically free– Perturbation theory is valid

and accurate tool at large-Q2

– Hence chiral limit is defined Essentially nonperturbative

for Q2 < 2 GeV2


Nature’s only (now known) example of a truly nonperturbative, fundamental theory A-priori, no idea as to what such a theory can produce


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



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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

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

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



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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

Confinement

complex-P2 complex-P2

o Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularitieso State described by rapidly damped wave & hence state cannot exist in observable spectrum

Normal particle Confined particle


timelike axis: P2<0

s ≈ 1/Im(m) ≈ 1/2ΛQCD ≈ ½fm

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In the study of hadrons, attention should turn from potential models toward the continuum bound-state problem in quantum field theory

Such approaches offer the possibility of posing simultaneously the questions – What is confinement?– What is dynamical chiral symmetry breaking?– How are they related?

Is it possible that two phenomena, so critical in the Standard Model and tied to the dynamical generation of a mass-scale in QCD, can have different origins and fates?



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Dynamical Chiral Symmetry Breaking



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Dynamical Chiral Symmetry BreakingDCSB is a fact in QCD

– Dynamical, not spontaneous• Add 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.



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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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Background Worth noting that nonzero vacuum expectation values of local

operators in QCD—the so-called vacuum condensates—are phenomenological parameters, which were introduced at a time of limited computational resources in order to assist with the theoretical estimation of essentially nonperturbative strong-interaction matrix elements.

A universality of these condensates was assumed, namely, that the properties of all hadrons could be expanded in terms of the same condensates. While this helps to retard proliferation, there are nevertheless infinitely many of them.

As qualities associated with an unmeasurable state (the vacuum), such condensates do not admit direct measurement. Practitioners have attempted to assign values to them via an internally consistent treatment of many separate empirical observables.

However, only one, the so-called quark condensate, is attributed a value with any confidence.



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Confinement contains

condensatesCraig Roberts: U. Frankfurt: 8 July 2013


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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 = hadronic fluctuations but no condensates

Hadrons = complex, interacting systemswithin 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

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4

103

8

HG QCDNscondensateQCD

Paradigm shift:In-Hadron Condensates

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


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Relevant References arXiv:1202.2376, Phys. Rev. C 85 (2012) 065202

Confinement contains condensatesStanley J. Brodsky, Craig D. Roberts, Robert Shrock, Peter C. Tandy

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

arXiv:1005.4610 [nucl-th], Phys. Rev. C82 (2010) 022201(RapCom.) New perspectives on the quark condensate, Brodsky, Roberts, Shrock, Tandy

arXiv:0905.1151 [hep-th], PNAS 108, 45 (2011) Condensates in Quantum Chromodynamics and the Cosmological Constant , Brodsky and Shrock,

hep-th/0012253 The Quantum vacuum and the cosmological constant problem, Svend Erik Rugh and Henrik Zinkernagel.


http://arxiv.org/abs/1202.2376

http://dx.doi.org/10.1103/PhysRevC.85.065202






http://prc.aps.org/abstract/PRC/v85/i1/e012201






















DCSB

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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) 225-227 In 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.






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Enigma of MassCraig Roberts: U. Frankfurt: 8 July 2013


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

Pseudovector componentsnecessarily nonzero.

Cannot be ignored!

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



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Dichotomy of the pionGoldstone mode and bound-state

Goldstone’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



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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In QCD, Gluons, too, become massive

Not just quarks … Gluons also have a

gap equation …1/k2 behaviour signals essential singularity in the running coupling:

Impossible to reach in perturbation theory



22

422 )(

kkm

g

gg

)( 2k

const

e

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Parton structure of

hadronsCraig Roberts: U. Frankfurt: 8 July 2013


Valence quarks

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Deep inelastic scattering

Quark discovery experiment at SLAC (1966-1978, Nobel Prize in 1990)

Completely different to elastic scattering– Blow the target to pieces instead of keeping only

those events where it remains intact. Cross-section is interpreted as a measurement of

the momentum-fraction probability distribution for quarks and gluons within the target hadron: q(x), g(x)



Probability that a quark/gluon within the target will carry a fraction x of the bound-state’s light-front momentumDistribution Functions of the Nucleon and Pion in the

Valence Region, Roy J. Holt and Craig D. Roberts, arXiv:1002.4666 [nucl-th], Rev. Mod. Phys. 82 (2010) pp. 2991-3044




http://rmp.aps.org/abstract/RMP/v82/i4/p2991_1



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Parton Structure of Hadrons

Valence-quark structure of hadrons– Definitive of a hadron – it’s how we tell a proton from

a neutron– Expresses charge; flavour; baryon number; and other

Poincaré-invariant macroscopic quantum numbers– Via evolution, determines background at LHC

Sea-quark distributions– Flavour content, asymmetry, intrinsic: yes or no?

Any nontrivial answers are essentially nonperturbative features of QCD



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Parton Structure of Hadrons Light front provides a link with quantum mechanics

– If a probability interpretation is ever valid, then it’s in the infinite-momentum frame

Enormous amount of intuitively expressive information about hadrons & processes involving them is encoded in – Parton distribution functions – Generalised parton distribution functions – Transverse-momentum-dependent parton distribution

functions Information will be revealed by the measurement of

these functions – so long as they can be calculatedSuccess of programme demands very close collaboration between experiment and theory



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Need for calculation is emphasised by Saga of pion’s valence-quark distribution:o 1989: uv

π ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD;

o 2001: DSE- QCD predictsuv

π ~ (1-x)2 argues that distribution inferred from data can’t be correct;



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Need for calculation is emphasised by Saga of pion’s valence-quark distribution:o 1989: uv

π ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD;

o 2001: DSE- QCD predicts uv

π ~ (1-x)2 argues that distribution inferred from data can’t be correct;

o 2010: NLO reanalysis including soft-gluon resummation, inferred distribution agrees with DSE and QCD




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Exact expression in QCD for the pion’s valence-quark parton distribution amplitude

Expression is Poincaré invariant but a probability interpretation is only valid in the light-front frame because only therein does one have particle-number conservation.

Probability that a valence-quark or antiquark carries a fraction x=k+ / P+

of the pion’s light-front momentum { n2=0, n.P = -mπ}

Pion’s valence-quark Distribution Amplitude


Pion’s Bethe-Salpeter wave function

Whenever a nonrelativistic limit is realistic, this would correspond to the Schroedinger wave function.


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Moments method is ideal for φπ(x):

entails

Contact interaction(1/k2)ν , ν=0Straightforward exercise to show∫0

1 dx xm φπ(x) = fπ 1/(1+m) , hence φπ(x)= fπ Θ(x)Θ(1-x)



Pion’s Bethe-Salpeter wave function

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The distribution amplitude φπ(x) is actually dependent on the momentum-scale at which a particular interaction takes place; viz., φπ(x)= φπ(x,Q)

One may show in general that φπ(x) has an expansion in terms of Gegenbauer–α=3/2 polynomials:

Only even terms contribute because the neutral pion is an eigenstate of charge conjugation, so φπ(x)=φπ(1-x)

Evolution, analogous to that of the parton distribution functions, is encoded in the coefficients an(Q)



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However, practically, in reconstructing φπ(x) from its moments, it is better to use Gegenbauer–α polynomials and then rebuild the Gegenbauer–α=3/2 expansion from that.– Better means – far more rapid convergence because

Gegenbauer–α=3/2 is only accurate near ΛQCD/Q=0.– One nontrivial Gegenbauer–α polynomial provides converged

reconstruction cf. more than SEVEN Gegenbauer–α=3/2 polynomials

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=0.3



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







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Both kernels agree: marked broadening of φπ(x), which owes to DCSB



Asymptoticφπ(x)=6 x (1-x)

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












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Both kernels agree: marked broadening of φπ(x), which owes to DCSB



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.












44Craig Roberts: U. Frankfurt: 8 July 2013


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 limit

Experiments at JLab12 can empirically verify the behaviour of M(p), and hence chart the IR limit of QCD

C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50

Dilation of pion’s wave function is measurable in

pion’s electromagnetic form factor at JLab12

A-rated: E12-06-10

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]. Pion’s valence-quark

Distribution Amplitude





http://www.jlab.org/exp_prog/proposals/06/PR12-06-101.pd











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Lattice comparisonPion’s valence-quark PDA

Employ the generalised-Gegenbauer method described previously (and in Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]).



Lattice-QCD => one nontrivial moment:

<(2x-1)2> = 0.27 ± 0.04 Legend

• Solid = DB (Best) DSE• Dashed = RL DSE• Dotted (black) = 6 x (1-x)• Dot-dashed = midpoint

lattice; and the yellow shading exhibits band allowed by lattice errors

φπ~ xα (1-x)α

α=0.35+0.32 = 0.67- 0.24 = 0.11

DB α=0.31 but 10% a2<0RL α=0.29 and 0% a2

V. Braun et al., PRD 74 (2006) 074501

Pion distribution amplitude from lattice-QCD, I.C. Cloët et al. arXiv:1306.2645 [nucl-th]








http://prd.aps.org/abstract/PRD/v74/i7/e074501






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Lattice comparisonPion’s valence-quark PDA

Establishes that contemporary DSE- and lattice-QCD computations, at the same scale, agree on the pointwise form of the pion's PDA, φπ(x).

This unification of DSE- and lattice-QCD results expresses a deeper equivalence between them, expressed, in particular, via the common behaviour they predict for the dressed-quark mass-function, which is both – a definitive signature of dynamical chiral symmetry breaking – and the origin of the distribution amplitude's dilation.







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When is asymptotic PDA valid?

Under leading-order evolution, the PDA remains broad to Q2>100 GeV2

Feature signals persistence of the influence of dynamical chiral symmetry breaking.



Consequently, the asymptotic distribution, φπ

asy(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 GeV2

100 GeV2





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When is asymptotic PDA valid?

φπasy(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)!






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Elastic Scattering




Charged pion elastic form factor

P. Maris & P.C. Tandy, Phys.Rev. C62 (2000) 055204: numerical procedure is practically useless for Q2>4GeV2, so prediction ends!

Algorithm developed for pion PDA overcomes this obstacle

Solves the practical problem of continuing from Euclidean metric formulation to Minkowski space

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]









Improved DSE interaction kernel, based on DSE and lattice-QCD studies of gluon sectorS.-x. Qin, L. Chang et al. Phys.Rev. C84 (2011) 042202(R)

New prediction in better agreement with available data than old DSE result

Prediction extends from Q2=0 to arbitrarily large Q2, without interruption, unifying both domains

DSE 2000 … Breakdown here










Unlimited domain of validity emphasised in this figure

Depict prediction on domain 0<Q2<20GeV2 but have computed the result to Q2=100GeV2.

If it were necessary, reliable results could readily be obtained at even higher values.

DSE 2013








Predict a maximum at 6-GeV2, which lies within domain that is accessible to JLab12

Difficult, however, to distinguish DSE prediction from Amendolia-1986 monopole

What about comparison with perturbative QCD?

Amendolia et al.

DSE 2013

ρ-meson pole VMD

maximum

A-rated: E12-06-10


http://www.jlab.org/exp_prog/proposals/06/PR12-06-101.pd






Charged pion elastic form factor 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 PDA

Near agreement between the pertinent perturbative QCD prediction and DSE-2013 prediction is striking.

DSE 2013

pQCD obtained with φπasy(x)

pQCD obtained with φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment

15%

Single DSE interaction kernel, determined fully by just one parameter and preserving the one-loop renormalisation group behaviour of QCD, has unified the Fπ(Q2) and φπ(x) (and numerous other quantities)







Charged pion elastic form factor Leading-order, leading-twist

QCD prediction, obtained with φπ(x) evaluated at a scale appropriate to the experiment underestimates DSE-2013 prediction by merely an approximately uniform 15%.

Small mismatch is explained by a combination of higher-order, higher-twist corrections & and shortcomings in the rainbow-ladder truncation.

DSE 2013

pQCD obtained with φπasy(x)

pQCD obtained φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment

15%

Hence, one should expect dominance of hard contributions to the pion form factor for Q2>8GeV2.

Nevertheless, the normalisation of the form factor is fixed by a pion wave-function whose dilation with respect to φπ

asy(x) is a definitive signature of DCSB






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 Equation Nucleon 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-quarks Tractable 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 channel

Craig Roberts: U. Frankfurt: 8 July 2013 56

R.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145

6333 SUc(3):


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Baryon Structure

Remarks Diquark correlations are not inserted by hand

Such correlations are a dynamical consequence of strong-coupling in QCD

The 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 symmetry

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

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



SU(2) isospin symmetry of hadrons might emerge from mixing half-integer spin particles with their antiparticles.

Faddeev Equation

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Structure of Hadrons Elastic form factors

– Provide 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

correlations– scale at which p-QCD effects become evident– strangeness content– meson-cloud effects– etc.



59

Jlab Highlights



)(

)(

2

2

QG

QG

pM

pEp

http://www.jlab.org/highlights/phys.html

Distribution of charge is different from distribution of magnetisation

http://www.jlab.org/highlights/phys.html


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Photon-nucleon current

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

DSE → BSE → Faddeev equation plus current → nucleon form factors

Vertex must contain the dressed-quark anomalous magnetic moment

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


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

In a realistic calculation, the last three diagrams represent 8-dimensional integrals, which can be evaluated using Monte-Carlo techniques



http://inspirebeta.net/record/868745



http://link.aps.org/doi/10.1103/PhysRevLett.106.072001






61

I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]

)(

)(

2

2

QG

QG

pM

pEp

Highlights again the critical importance of DCSB in explanation of real-world observables.

DSE result Dec 08

DSE result – including the anomalous magnetic moment distribution


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













Visible Impacts of DCSB


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) Like the pion’s PDA, Q2F2

p(Q2) measures the rate at which dress-ed-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]






Visible Impacts of DCSB


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]






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Flavor separation of proton form factors

Very different behavior for u & d quarks Means apparent scaling in proton F2/F1 is purely accidental


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

Q4F2q/k

Q4 F1q


65

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

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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/








67

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

















68


SU(6) symmetry

pQCD, uncorrelated Ψ

0+ qq only

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)

DSE: “realistic”

Distribution of neutron’s momentum amongst quarks on the valence-quark domainCraig Roberts: U. Frankfurt: 8 July 2013

DSE: “contact”

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 resolve this conundrum
















69


“While it is quite hazardous to extrapolate from our limited xB range all the way to xB = 1, these results appear to disfavor models of the proton with d/u=0 at xB = 1”


Short 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. Higinbotham

Observation: 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.

http://dx.doi.org/10.1103/PhysRevLett.106.052301

http://dx.doi.org/10.1103/PhysRevLett.106.052301




70

Theory Lattice-QCD

– Significant progress in the last five years

– This must continue Bound-state problem in

continuum quantum field theory– Significant progress, too– This must continue

First Sino-Americas School & Workshop on the Continuum Bound-State Problem, Hefei, China. 22-26/Oct./2013



http://hepg-work.ustc.edu.cn/dse2013/

http://hepg-work.ustc.edu.cn/dse2013/



Epilogue

72

Epilogue The Physics of Hadrons is Unique:

– Confronting a fundamental theory in which the elementary degrees-of-freedom are intangible and only composites reach detectors

Confinement in real-world is NOT understood DCSB 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 insights and answers.



73

This is not the end



74

Table of Contents

I. IntroductionII. Pion valence-quark distributionIII. Pion valence-quark parton distribution amplitudeIV. Charged pion elastic form factorV. Baryon StructureVI. Nucleon form factorsVII. Nucleon structure functions at large-xVIII.Epilogue



craig roberts physics division. 1.rocio bermudez (u michoácan); 2.chen chen (anl, iit, ustc);...

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