Craig Roberts Physics Division Students Early-career scientists Published collaborations: 2010-present Rocio BERMUDEZ (U Michoácan); Chen CHEN (ANL, IIT,

N & N* Structure in Continuum Strong QCD

Craig Roberts

Physics Division

StudentsEarly-career scientists

Published collaborations: 2010-present Rocio BERMUDEZ (U Michoácan);

Chen CHEN (ANL, IIT, USTC);Xiomara GUTIERREZ-GUERRERO (U Michoácan);Trang NGUYEN (KSU);Si-xue QIN (PKU);Hannes ROBERTS (ANL, FZJ, UBerkeley);Lei CHANG (ANL, FZJ, PKU); Huan CHEN (BIHEP);Ian CLOËT (UAdelaide);Bruno EL-BENNICH (São Paulo);David WILSON (ANL);Adnan BASHIR (U Michoácan);Stan BRODSKY (SLAC);Gastão KREIN (São Paulo)Roy HOLT (ANL);Mikhail IVANOV (Dubna);Yu-xin LIU (PKU);Robert SHROCK (Stony Brook);Peter TANDY (KSU)Shaolong WAN (USTC)

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15.08.12: USC Summer Academy - 56

Craig Roberts: N & N* Structure in Continuum Strong QCD

Confinement


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Confinement Gluon and Quark Confinement

– Empirical Fact: No coloured states have yet been observed to reach a detectorX


However– There is no agreed, theoretical definition of light-quark

confinement– Static-quark confinement is irrelevant to real-world QCD

• There are no long-lived, very-massive quarks • But light-quarks are ubiquitous

Flux tubes, linear potentials and string tensions play no role in relativistic quantum field theory with light degrees of freedom.

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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"

http://inspirebeta.net/record/525949?ln=en





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Confinement QFT Paradigm: Confinement is expressed through a

dramatic change in the analytic structure of propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator– Gribov (1978); Munczek (1983); Stingl (1984); Cahill (1989);

Roberts, Williams & Krein (1992); Tandy (1994); …

complex-P2 complex-P2

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

o Spectral density no longer positive semidefinite & hence state cannot exist in observable spectrum

Normal particle Confined particle


timelike axis: P2<0

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Dynamical Chiral Symmetry Breaking




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Dynamical Chiral Symmetry Breaking

Whilst confinement is contentious …DCSB is a fact in QCD

– It is the most important mass generating mechanism for visible matter in the Universe. • Responsible for approximately 98% of the

proton’s mass.• Higgs mechanism is (almost) irrelevant to light-

quarks.



Frontiers of Nuclear Science:Theoretical Advances

In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.

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DSE prediction of DCSB confirmed

Mass from nothing!


C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227







Frontiers of Nuclear Science:Theoretical Advances

In QCD a quark's effective mass depends on its momentum. The function describing this can be calculated and is depicted here. Numerical simulations of lattice QCD (data, at two different bare masses) have confirmed model predictions (solid curves) that the vast bulk of the constituent mass of a light quark comes from a cloud of gluons that are dragged along by the quark as it propagates. In this way, a quark that appears to be absolutely massless at high energies (m =0, red curve) acquires a large constituent mass at low energies.

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Hint of lattice-QCD support for DSE prediction of violation of reflection positivity


C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227







12GeVThe Future of JLab

Jlab 12GeV: This region scanned by 2<Q2<9 GeV2 elastic & transition form factors.



The Future of Drell-Yan

Valence-quark PDFs and PDAs probe this critical and complementary region


π or K

N


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Science Challenges for the coming decade: 2013-2022

Search for exotic hadrons Exploit opportunities provided by new data on

nucleon elastic and transition form factors Precision experimental study of valence region, and

theoretical computation of distribution functions and distribution amplitudes

Develop QCD as a probe for physics beyond the Standard Model



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Overarching Science Challenges for the

coming decade: 2013-2022


Search for exotic hadrons Exploit opportunities provided by new data on

nucleon elastic and transition form factors Precision experimental study of valence region, and

theoretical computation of distribution functions and distribution amplitudes

Develop QCD as a probe for physics beyond the Standard Model

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

Charting the interaction between light-quarks

Confinement can be related to the analytic properties of QCD's Schwinger functions.

Question of light-quark confinement is thereby translated into the challenge of charting the infrared behavior of QCD's universal β-function

Through QCD's DSEs, the pointwise behaviour of the β-function determines the pattern of chiral symmetry breaking.

DSEs connect β-function to experimental observables. Hence, comparison between computations and observations ofo Hadron spectrum, Elastic & transition form factors, Parton distribution fnscan be used to chart β-function’s long-range behaviour.


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This is a well-posed problem whose solution is an elemental goal of modern hadron physics.The answer provides QCD’s running coupling.


Process-independent αS(Q2) → unified description of observables

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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

Dichotomy of the pionGoldstone mode and bound-state



fπ Eπ(p2) = B(p2)



Looking deeply

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Empirical status of the Pion’s valence-quark distributions

Owing to absence of pion targets, the pion’s valence-quark distribution functions are measured via the Drell-Yan process: π p → μ+ μ− X

Three experiments: CERN (1983 & 1985)and FNAL (1989). No more recent experiments because theory couldn’t even explain these!

ProblemConway et al. Phys. Rev. D 39, 92 (1989)Wijesooriya et al. Phys.Rev. C 72 (2005) 065203

PDF behaviour at large-x inconsistent with pQCD; viz, expt. (1-x)1+ε cf. QCD (1-x)2+γ



Pion








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Models of the Pion’s valence-quark distributions

(1−x)β with β=0 (i.e., a constant – any fraction is equally probable! )– AdS/QCD models using light-front holography – Nambu–Jona-Lasinio models, when a translationally invariant

regularization is used (1−x)β with β=1

– Nambu–Jona-Lasinio NJL models with a hard cutoff– Duality arguments produced by some theorists

(1−x)β with 0<β<2– Relativistic constituent-quark models, with power-law depending on

the form of model wave function (1−x)β with 1<β<2

– Instanton-based models, all of which have incorrect large-k2 behaviour



Pion

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Models of the Pion’s valence-quark distributions

(1−x)β with β=0 (i.e., a constant – any fraction is equally probable! )– AdS/QCD models using light-front holography – Nambu–Jona-Lasinio models, when a translationally invariant

regularization is used (1−x)β with β=1

– Nambu–Jona-Lasinio NJL models with a hard cutoff– Duality arguments produced by some theorists

(1−x)β with 0<β<2– Relativistic constituent-quark models, depending on the form of

model wave function (1−x)β with 1<β<2

– Instanton-based models



Pion

Completely unsatisfactory. Impossible to suggest that there’s even qualitative agreement!

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DSE prediction of the Pion’s valence-quark distributions

Consider a theory in which quarks scatter via a vector-boson exchange interaction whose k2>>mG

2 behaviour is (1/k2)β, Then at a resolving scale Q0

uπ(x;Q0) ~ (1-x)2β

namely, the large-x behaviour of the quark distribution function is a direct measure of the momentum-dependence of the underlying interaction.

In QCD, β=1 and hence QCD uπ(x;Q0) ~ (1-x)2



Pion

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Consider a theory in which quarks scatter via a vector-boson exchange interaction whose k2>mG

2 behaviour is (1/k2)β, Then at a resolving scale Q0

uπ(x;Q0) ~ (1-x)2β

namely, the large-x behaviour of the quark distribution function is a direct measure of the momentum-dependence of the underlying interaction.

In QCD, β=1 and hence QCD uπ(x;Q0) ~ (1-x)2

Completely unambigous!Direct connection between experiment and theory, empowering both as tools of discovery.

DSE prediciton of the Pion’s valence-quark distributions



Pion

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“Model Scale” At what scale Q0 should the

prediction be valid? Hitherto, PDF analyses within

models have used the resolving scale Q0 as a parameter, to be chosen by requiring agreement between the model and low-moments of the PDF that are determined empirically.



Pion

Modern DSE studies have exposed a natural value for the model scale; viz., the gluon mass

Q0 ≈ mG ≈ 0.6 GeV ≈ 1/0.33 fmwhich is the location of the inflexion point in the chiral-limit dressed-quark mass function

Esse

ntial

ly n

onpe

rtur

bativ

e do

mai

n

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QCD-based DSE calculation = (1-

x)2+γ 15.08.12: USC Summer Academy - 56


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Reanalysis of qvπ(x)

After first DSE computation, the “Conway et al.” data were reanalysed, this time at next-to-leading-order (Wijesooriya et al. Phys.Rev. C 72 (2005) 065203)

The new analysis produced a much larger exponent than initially obtained; viz., β=1.87, but now it disagreed equally with model results and the DSE prediction NB. Within pQCD, one can readily understand why adding a higher-order

correction leads to a suppression of qvπ(x) at large-x.



Hecht, Roberts, Schmidt Phys.Rev. C 63 (2001) 025213

New experiments were proposed … for accelerators that do not yet exist but the situation remained otherwise unchanged

Until the publication of Distribution 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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Reanalysis of qvπ(x)

This article emphasised and explained the importance of the persistent discrepancy between the DSE result and experiment as a challenge to QCD

It prompted another reanalysis of the data, which accounted for a long-overlooked effect: viz., “soft-gluon resummation,” – Compared to previous analyses, we include next-to-leading-

logarithmic threshold resummation effects in the calculation of the Drell-Yan cross section. As a result of these, we find a considerably softer valence distribution at high momentum fractions x than obtained in previous next-to-leading-order analyses, in line with expectations based on perturbative-QCD counting rules or Dyson-Schwinger equations.



Distribution 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

Aicher, Schäfer, Vogelsang, “Soft-Gluon Resummation and the Valence Parton Distribution Function of the Pion,” Phys. Rev. Lett. 105 (2010) 252003










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Current status of qv

π(x) Data as reported byE615

DSE prediction (2001)



Trang, Bashir, Roberts & Tandy, “Pion and kaon valence-quark parton distribution functions,” arXiv:1102.2448 [nucl-th], Phys. Rev. C 83, 062201(R) (2011) [5 pages]




http://link.aps.org/doi/10.1103/PhysRevC.83.062201





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Current status of qv

π(x) Data after inclusion of soft-gluon resummation

DSE prediction andmodern representation of the data are

indistinguishable on the valence-quark domain

Emphasises the value of using a single internally-consistent, well-constrained framework to correlate and unify the description of hadron observables



Trang, Bashir, Roberts & Tandy, “Pion and kaon valence-quark parton distribution functions,” arXiv:1102.2448 [nucl-th], Phys. Rev. C 83, 062201(R) (2011) [5 pages]









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Pion’s Light-Front Distribution Amplitude15.08.12: USC Summer Academy - 56



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Reconstruct φπ(x) from moments:

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 valence-quark Distribution Amplitude


Pion’s Bethe-Salpeter wave function

Work now underway with sophisticated rainbow-ladder interaction: Chang, Cloët, Roberts, Schmidt & Tandy

Expression exact in QCD – no corrections


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Using simple parametrisations of solutions to the gap and Bethe-Salpeter equations, rapid and semiquantitatively reliable estimates can be made for φπ(x)

– (1/k2)ν=0

– (1/k2)ν =½

– (1/k2)ν =1

Again, unambiguous and direct mapping between behaviour of interaction and behaviour of distribution amplitude


Leading pQCD φπ(x)=6 x (1-x)


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Preliminary results: rainbow-ladder QCD analyses of renormalisation-group-improved (1/k2)ν =1 interaction – humped disfavoured but modest flattening


Such behaviour is only obtained with (1) Running mass in dressed-quark propagators (2) Pointwise expression of Goldstone’s theorem

Chang, Cloët, Roberts, Schmidt & Tandy, in progress;Si-xue Qin, Lei Chang, Yu-xin Liu, Craig Roberts and David Wilson, arXiv:1108.0603 [nucl-th], Phys. Rev. C 84 042202(R) (2011)


Reconstructed from 100 moments

Eπ(k2) but constant mass quark

a2<0

a2>0








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x ≈ 0 & x ≈ 1 correspond to maximum relative momentum within bound-state– expose pQCD physics

x ≈ ½ corresponds to minimum possible relative momentum– behaviour of

distribution around midpoint is strongly influence by DCSB



Preliminary results, rainbow-ladder QCD analyses of (1/k2)ν =1 interaction humped disfavoured but modest flattening


33


x ≈ 0 & x ≈ 1 correspond to maximum relative momentum within bound-state– expose pQCD physics

x ≈ ½ corresponds to minimum possible relative momentum– behaviour of

distribution around midpoint is strongly influence by DCSB



Preliminary results, rainbow-ladder QCD analyses of (1/k2)ν =1 interaction humped disfavoured but modest flattening

These computations are the first to offer the possibility of directly exposing DCSB – pointwise – in the light-front frame.

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Grand Unification15.08.12: USC Summer Academy - 56


Unification of Meson & Baryon Properties

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

single, symmetry-preserving framework Symmetry-preserving means:

Poincaré-covariant Guarantee Ward-Takahashi identities Express accurately the pattern by which symmetries are broken




Faddeev Equation

Linear, Homogeneous Matrix equationYields wave function (Poincaré Covariant Faddeev Amplitude)

that describes quark-diquark relative motion within the nucleon Scalar and Axial-Vector Diquarks . . .

Both have “correct” parity and “right” masses In Nucleon’s Rest Frame Amplitude has

s−, p− & d−wave correlations36

diquark

quark

quark exchangeensures Pauli statistics

composed of strongly-dressed quarks bound by dressed-gluons


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


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ContactInteraction



Symmetry-preserving treatment of vector×vector contact interaction is useful tool for the study of phenomena characterised by probe momenta less-than the dressed-quark mass, M. Because: For experimental observables determined by probe momenta Q2<M2, contact interaction results are not realistically distinguishable from those produced by the most sophisticated renormalisation-group-improved kernels.

Symmetry-preserving regularisation of the contact interaction serves as a useful surrogate, opening domains which analyses using interactions that more closely resemble those of QCD are as yet unable to enter.

They’re critical in attempts to use data as tool for charting nature of the quark-quark interaction at long-range; i.e., identifying signals of the running of couplings and masses in QCD.


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Contact Interaction arXiv:1204.2553 [nucl-th]

Spectrum of hadrons with strangenessChen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson

arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages] Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts

arXiv:1102.4376 [nucl-th], Phys. Rev. C 83, 065206 (2011) [12 pages] , π- and ρ-mesons, and their diquark partners, from a contact interaction, H.L.L. Roberts, A. Bashir, L.X. Gutierrez-Guerrero, C.D. Roberts and David J. Wilson

arXiv:1101.4244 [nucl-th], Few Body Syst. 51 (2011) pp. 1-25Masses of ground and excited-state hadronsH.L.L. Roberts, Lei Chang, Ian C. Cloët and Craig D. Roberts

arXiv:1009.0067 [nucl-th], Phys. Rev. C82 (2010) 065202 [10 pages]Abelian anomaly and neutral pion productionHannes L.L. Roberts, C.D. Roberts, A. Bashir, L. X. Gutiérrez-Guerrero & P. C. Tandy

arXiv:1002.1968 [nucl-th], Phys. Rev. C 81 (2010) 065202 (5 pages)Pion form factor from a contact interaction L. Xiomara Gutiérrez-Guerrero, Adnan Bashir, Ian C. Cloët and C. D. Roberts


Symmetry-preserving treatment of vector-vector contact-interaction: series of papers establishes strengths & limitations.

http://inspirehep.net/record/1110694?ln=en






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












http://www.springerlink.com/content/l277662502362386/















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Spectrum of Hadronswith Strangeness

Solve gap equation for u & s-quarks

Input ratio ms /mu = 24 is consistent with modern estimates Output ratio Ms /Mu = 1.43 shows dramatic impact of DCSB, even on

the s-quark: Ms-ms = 0.36 GeV = M0

… This is typical of all DSE and lattice studies κ = in-hadron condensate rises slowly with mass of hadron



arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson




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Spectrum of Mesonswith Strangeness

Solve Bethe-Salpeter equations for mesons and diquarks







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Spectrum of Mesonswith Strangeness




Computed values for ground-states are greater than the empirical masses, where they are known.

Typical of DCSB-corrected kernels that omit resonant contributions; i.e., do not contain effects that mayphenomenologically be associated with a meson cloud.

Perhaps underestimate radial-ground splitting by 0.2GeV





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Spectrum of Diquarkswith Strangeness








43

Spectrum of Diquarkswith Strangeness





Level ordering of diquark correlations is same as that for mesons. In all diquark channels, except scalar, mass of diquark’s partner meson is a fair guide to the diquark’s mass: o Meson mass bounds the diquark’s mass from below;o Splitting always less than 0.13GeV and decreases with

increasing meson massScalar channel “special” owing to DCSB




44

Bethe-Salpeter amplitudes

Bethe-Salpeter amplitudes are couplings in Faddeev Equation

Magnitudes for diquarks follow precisely the meson pattern




Owing to DCSB, FE couplings in ½- channels are 25-times weaker than in ½+ !




45

Spectrum of Baryonswith Strangeness

Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons.







46

Spectrum of Baryonswith Strangeness





As with mesons, computed baryon masses lie uniformly above the empirical values.

Success because our results are those for the baryons’ dressed-quark cores, whereas empirical values include effects associated with meson-cloud, which typically produce sizable reductions.

JülichEBAC




47

Structure of Baryonswith Strangeness Baryon structure is flavour-blind




Diquark content




48

Structure of Baryonswith Strangeness Baryon structure is flavour-blind



arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen, Chang, Roberts, Wan and Wilson & Nucleon and Roper em elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts, arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]

Diquark content

Jqq=0 content of J=½ baryons is almost independent of their flavour structure

Radial excitation of ground-state octet possess zero scalar diquark content!

This is a consequence of DCSB Ground-state (1/2)+ possess unnaturally

large scalar diquark content Orthogonality forces radial excitations to

possess (almost) none at all!

80%

50%

50%

0%










49






(1/2)+

(1/2)+

(1/2)-




50






(1/2)+

(1/2)+

(1/2)-

This level ordering has long been a problem in CQMs with linear or HO confinement potentials

Correct ordering owes to DCSB Positive parity diquarks have

Faddeev equation couplings 25-times greater than negative parity diquarks

Explains why approaches within which DCSB cannot be realised (CQMs) or simulations whose parameters suppress DCSB will both have difficulty reproducing experimental ordering





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Neutron Structure Function at high x

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”

I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]D. J. Wilson, I. C. Cloët, L. Chang and C. D. RobertsarXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]

Distribution of neutron’s momentum amongst quarks on the valence-quark domain15.08.12: USC Summer Academy - 56

DSE: “contact”

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













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Nucleon to Roper Transition Form Factors Extensive CLAS @ JLab Programme has produced the first

measurements of nucleon-to-resonance transition form factors

Theory challenge is toexplain the measurements

Notable result is zero in F2p→N*,

explanation of which is a realchallenge to theory.

First observation of a zero in a form factor


I. Aznauryan et al., Results of the N* Program at JLabarXiv:1102.0597 [nucl-ex]





53

Nucleon to Roper Transition Form Factors Extensive CLAS @ JLab Programme has produced the first

measurements of nucleon-to-resonance transition form factors

Theory challenge is toexplain the measurements

Notable result is zero in F2p→N*,

explanation of which is a realchallenge to theory.

DSE study connects appearanceof zero in F2

p→N* with axial-vector-diquark dominance in Roper resonance and structure of form factors of J=1 state


I. Aznauryan et al., Results of the N* Program at JLabarXiv:1102.0597 [nucl-ex]

Γμ,αβNucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts, Phys. Rev. C85 (2012) 025205 [21 pages]

Solid – DSEDashed – EBAC Quark CoreNear match supports picture of Roper as quark core plus meson cloud










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Nucleon to Roper Transition Form Factors

Tiator and Vanderhaeghen – in progress– Empirically-inferred light-front-transverse

charge density– Positive core plus negative annulus

Readily explained by dominance of axial-vector diquark configuration in Roper– Considering isospin and charge

Negative d-quark twice as likely to bedelocalised from the always-positive core than the positive u-quark


{uu}

d

2 {ud}

u

1+



Epilogue


56

Epilogue Confinement with light-quarks is not connected in any known

way with a linear potential; not with a potential of any kind. Confinement with light-quarks is associated with a dramatic

change in the infrared structure of the parton propagators. Dynamical chiral symmetry breaking, the origin of 98% of

visible matter in universe, is manifested unambiguously and fundamentally in an equivalence between the one- and two-body problem in QCD

Working together to chart the behaviour of the running masses in QCD, experiment and theory can potentially answer the questions of confinement and dynamical chiral symmetry breaking; a task that currently each alone find hopeless.


QCD is the most interesting part of the standard model - Nature’s only example of an essentially nonperturbative fundamental theory,

57

This is not the end



Universal Misapprehensions

Since 1979, DCSB has commonly been associated literally with a spacetime-independent mass-dimension-three “vacuum condensate.”

Under this assumption, “condensates” couple directly to gravity in general relativity and make an enormous contribution to the cosmological constant

Experimentally, the answer is

Ωcosm. const. = 0.76 This mismatch is a bit of a problem.



58

4620

4

103

8

HG QCDNscondensateQCD

59

New Paradigm“in-hadron condensates”



60

“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


62

Some Relevant References arXiv:1202.2376, Phys. Rev. C85, 065202 (2012) [9 pages]

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





























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Contents

Confinement Dynamical chiral symmetry breaking Dichotomy of the pion Pion valence-quark distribution Pion’s Distribution Amplitude Grand Unification - Mesons and Baryons Neutron Structure Function at high x Nucleon to Roper Transition Form Factors Epilogue New Paradigm “in-hadron condensates”


Documents

Craig Roberts Physics Division Students Early-career scientists Published collaborations: 2010-present Rocio BERMUDEZ (U Michoácan); Chen CHEN (ANL, IIT,