Craig Roberts Physics Division. 1.Rocio BERMUDEZ (U Michoácan); 2.Xiomara GUTIERREZ-GUERRERO (U Michoácan); 3.S. HERNÁNDEZ (U Michoácan); 4.Trang NGUYEN

Images of theOrigin of Mass

Craig Roberts

Physics Division

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

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Collaborators: 2011-Present1. Rocio BERMUDEZ (U Michoácan);2. Xiomara GUTIERREZ-GUERRERO (U Michoácan);3. S. HERNÁNDEZ (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. Chen CHEN (USTC, ANL);10. J. Javier COBOS-MARTINEZ (U.Sonora);11. Mario PITSCHMANN (Vienna);12. Si-xue QIN (PKU, U. Frankfurt am Main);13. Jorge SEGOVIA (ANL);14. David WILSON (ODU);15. Lei CHANG (PKU, U.Adelaide); 16. Ian CLOËT (ANL);17. Bruno EL-BENNICH (São Paulo);

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

18. Adnan BASHIR (U Michoácan);19. Stan BRODSKY (SLAC);20. Gastão KREIN (São Paulo)21. Roy HOLT (ANL);22. Mikhail IVANOV (Dubna);23. Yu-xin LIU (PKU);24. Michael RAMSEY-MUSOLF (UW-Mad)25. Alfredo RAYA (U Michoácan);26. Sebastian SCHMIDT (IAS-FZJ & JARA);27. Robert SHROCK (Stony Brook);28. Peter TANDY (KSU);29. Tony THOMAS (U.Adelaide)30. Shaolong WAN (USTC)

StudentsPostdocsAsst. Profs.


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Ian Cloët


Pretend from now on that I am a vegetarian with a pony-tail, who was born in Australia and enjoys Belgian beer.

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Overarching Science Challenges for the coming

decade: 2013-2022 Discover the meaning of confinement Determine 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.




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Immediate 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 baryon structure– Expose facts & fallacies in modern descriptions of hadron structure

Precision experimental study of (far) valence region, and theoretical computation of distribution functions and distribution amplitudes– Computation is critical– Without it, no amount of data will reveal anything about the theory

underlying the phenomena of strong interaction physics



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What is QCD?


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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 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)QCD is a 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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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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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


complex-P2 complex-P2

o 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)o 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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Dynamical Chiral Symmetry Breaking



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Mass from Nothing1st Sino-Americas Workshop and School on the Bound-

State Problem in Continuum QCD, Hefei 2013: 22-26/Oct


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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.


Craig Roberts for Ian Cloët: Images of the Origin of Mass (66p)Confinement contains condensates, S.J. Brodsky, C.D. Roberts, R. Shrock and P.C. Tandy, arXiv:1202.2376 [nucl-th], Phys. Rev. C85 (2012) 065202




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




DCSB

1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct 18

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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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 diagrams Impossible to compute this in perturbation theory.

The standard algebraic manipulation tools are just inadequate



αS23

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Enigma of Mass1st Sino-Americas Workshop and School on the

Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct


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Bound-states in Quantum Field Theory

Mass and “Wave Function” are obtained from a Bethe-Salpeter equation– Generalisation of the Lippmann-Schwinger equation

The pion … Nature’s strong-interaction messenger … is a critical example



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

http://www.slac.stanford.edu/spires/find/hep/www?eprint=arXiv:0903.5461



http://link.aps.org/doi/10.1103/PhysRevLett.103.081601





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

Interaction model for the gap equationSi-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]




http://link.aps.org/doi/10.1103/PhysRevC.84.042202



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Parton structure of

hadrons1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct


Valence quarks

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Parton Structure of Hadrons

Valence-quark structure of hadrons– Definitive of a hadron.

After all, it’s how we distinguish 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?

Answers are essentially nonperturbative features of QCD



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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;



Valence quark distributions in the pion, M.B. Hecht, Craig D. Roberts, S.M. Schmidt, nucl-th/0008049, Phys.Rev. C63 (2001) 025213 .





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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



Soft-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 .

http://dx.doi.org/10.1103/PhysRevLett.105.252003









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DCSB on the light-front 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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Pion’s valence-quark Distribution Amplitude

Developed DSE methods to compute φπ(x) = 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=0.3



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



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












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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.












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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 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






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











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Extracting information from lattice-QCD today




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Valence-quark Distribution Amplitudes of light-quark mesons from lattice-QCD

PDA Moments from lattice-QCD

Best available results show no distinction between pseudoscalar and vector, nor between light-front parallel and perpendicular polarisations

DSE studies underway: Shi-chao, Peter Tandy et al.


R. Arthur et al., Phys.Rev. D83 (2011) 07450



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Valence-quark Distribution Amplitudes of light-quark mesons from lattice-QCD



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 -/+ 0.16

Lei Chang et al.In progress.










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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, I.C. Cloët & C.D. Roberts


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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 = 25%

<x>glue = 54%, <x>sea-quarks = 21%

LHC: 16TeV

Evolution in QCD is LOGARITHMIC

JLab 2GeV


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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 = 25%

<x>glue = 54%, <x>sea-quarks = 21%

LHC: 16TeV


JLab 2GeV

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


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At the “Planck scale”




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


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Elastic Scattering1st Sino-Americas Workshop and School on the Bound-State

Problem in Continuum QCD, Hefei 2013: 22-26/Oct

e(p) + H(q) → e(p’) + H(q’)

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Peter Tandy can now die

a happy man1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct


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Charged pion elastic form factor



Single 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=4GeV2

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%DSE 2000


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New Algorithm1st Sino-Americas Workshop and School on the Bound-State


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Charged pion elastic form factor



Single 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 PDA

Pion 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 experiment

15%

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 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


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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Nucleon StructureProbed in scattering experiments

Electron is a good probe because it is structurelessElectron’s relativistic current is

Proton’s electromagnetic current



F1 = Dirac form factor F2 = Pauli form factor

GE = Sachs Electric form factorIf a nonrelativistic limit exists, this relates to the charge density

GM = Sachs Magntic form factorIf a nonrelativistic limit exists, this relates to the magnetisation density

Structureless fermion, or simply structured fermion, F1=1 & F2=0, so that GE=GM and hence distribution of charge and magnetisation within this fermion are identical

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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.




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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 1st Sino-Americas Workshop and School on the Bound-State


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

Q4F2q/k

Q4 F1q


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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




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 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












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 > 4GeV2

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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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 in press




57

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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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
















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“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.







61

Nucleon spin structure at very high x


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 press




62

Tensor Charge: σμν current

h1T = distribution of transversely polarized quarks inside a transversely polarised proton

δq = 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 proton

Value 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)



Direction of motion


63

Tensor Charge: σμν current

1. Jlab 12 Projection2. Anselmino et al., 1303.3822 [hep-ph]3. Pitschmann et al. (DSE) (2013) [including

axial-vector diquarks but contact interaction]4. Hecht et al. (DSE), PRC64 (2001) 025204

[only scalar diquarks]5. Cloët et al., PLB659 (2008) 2146. Pasquini et al., PRD76 (2007) 0340207. Wakamatsu, PLB653 (2007) 3988. Gockeler et al., PLB627 (2005) 1139. Gamberg et al., PRL 87 (2001) 242001 10. He et al., PRD52 (1995) 296011. Bacchetta et al., JHEP 1303 (2013) 119



Direction of motion

Big shift from including axial-vector diquark correlations? d-quark can now be unpaired.




http://arxiv.org/abs/hep-ph/0612094






64

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/

65

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


66

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 But 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/Oct


67

This is not the end1st Sino-Americas Workshop and School on the Bound-State



68

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], Phys. Rev. Lett. 111 (2013) 092001 [5 pages]








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













69

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

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











70

Flavor separation of proton form factors




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 interaction

So … GEpu ≈ GEp

Singly-represented d-quark is usually sequestered inside a soft diquark correlation

So, although it also becomes parton-like more quickly as α increases, that is hidden from view

d-quark

u-quark

I.C. Cloët & C.D. Roberts … continuing

71

Confinement contains

condensates1st Sino-Americas Workshop and School on the Bound-State Problem in Continuum QCD, Hefei 2013: 22-26/Oct


72

“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

73

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

74

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!



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]





http://inspirehep.net/record/1233541/export/hx




75

Hybrid Hadrons & Lattice QCD – Robert Edwards, Baryons13

Heavy pions … so, naturally, constituent-quark like spectra To which potential does it correspond?


arXiv:1104.5152, 1201.2349


76

Hybrid meson models – Robert Edwards, Baryons13

With minimal quark content, , gluonic field can in a color singlet or octet

`constituent’ gluonin S-wave

`constituent’ gluonin P-wave

bag model

flux-tube model

arXiv:1104.5152, 1201.2349



77

Hybrid baryon models – Robert Edwards, Baryons13

Minimal 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, 1201.2349


78

Table of ContentsI. IntroductionII. Pion valence-quark distributionIII. Pion valence-quark parton distribution amplitudeIV. When is the asymptotic PDA a good approximation?V. Charged pion elastic form factorVI. Nucleon form factorsVII. Nucleon structure functions at large-xVIII. Epilogue

A. DSE cf. Lattice PDA & PDA evolutionB. GE/GM flavour separationC. Confinement contains condensatesD. Regge Trajectories?



Documents

Craig Roberts Physics Division. 1.Rocio BERMUDEZ (U Michoácan); 2.Xiomara GUTIERREZ-GUERRERO (U Michoácan); 3.S. HERNÁNDEZ (U Michoácan); 4.Trang NGUYEN