the physics of hadrons craig d. roberts physics division argonne national laboratory & school of...

The Physics of Hadrons

Craig D. Roberts

Physics DivisionArgonne National Laboratory

&

School of PhysicsPeking University

Length-Scales of Physics

Craig Roberts, Physics Division: The Physics of Hadrons

2Northwestern University: 7 Jan '11

Hadron Physics


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“Hadron physics is unique at the cutting edge of modern science because Nature has provided us with just one instance of a fundamental strongly-interacting theory; i.e., Quantum Chromodynamics (QCD). The community of science has never before confronted such a challenge as solving this theory.”

Northwestern University: 7 Jan '11

Nuclear Science Advisory Committee

Long Range Plan


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“A central goal of (DOE Office of) Nuclear Physics is to understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD.”


Relativistic Quantum Gauge Theory: Interactions mediated by vector boson exchange Vector bosons are perturbatively-massless

Similar interaction in QED Special feature of QCD – gluon self-interactions, which

completely change the character of the theory

What is QCD?


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3-gluon vertex

4-gluon vertex


QED cf. QCD?


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2004 Nobel Prize in Physics : Gross, Politzer and Wilczek

e

QED

mQ

Qln

32

1)(

Q

NQ

f

QCD

ln)233(

6)(

fermionscreening

gluonantiscreening


Add 3-gluon self-interaction5 x10-5

Quarks and Nuclear Physics


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Standard Model of Particle Physics:Six quark flavours

Real WorldNormal matter – only two light-quark flavours are activeOr, perhaps, three

For numerous good reasons, much research also focuses on accessible heavy-quarks Nevertheless, I will focus on the light-quarks; i.e., u & d.


Ford Nucleon, 1958atomic powered car

Fermions – two static properties:proton electric charge = +1; and magnetic moment, μp

Magnetic Moment discovered by Stern & collaborators -1933; Awarded Nobel Prize in 1943Dirac (1928) – pointlike fermion: μp = e/[2 M]

Stern (1933) – μp = (1 + 1.79) e/[2 M]

Big Hint that Proton is not a point particleProton has constituentsThese are Quarks and GluonsQuark discovery via e− p-scattering at SLAC in 1968

– the elementary quanta of Quantum Chromo-dynamics



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Two Key Hadronsnucleon = neutron & proton

Electron is an excellent probe because it’s structurelessrelativistic current:

Nucleon’s relativistic current

Hadron structure exposedvia studies of form factors



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Point particle (Dirac): F2=0, hence μpGE=GM

Pre-2000 μpGE/GM



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Distribution of charge and magnetisation is identical

Strong support for simple s-wave models of nucleon structure

Simple picture- Proton


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Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchange


Simple picture- Pion


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Two quantum-mechanical constituent-quarks - particle+antiparticle -interacting via a potential, derived from one constituent-gluon exchange


Thomas Jefferson National Accelerator Facility (JLAB)



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Newport News, Virginia

1994 – JLab begins operation 1995 – Reaches design energy of 4GeV e– beams 2000 – Reaches energy of 6GeV e– beams 2009 – Construction begins on 12GeV upgrade

Annual budget in excess of $200-millionUpgrade is $310-million project

Underground target halls

Racecourse Accelerator

After-2000 μpGE/GM



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Data from JLab, using new method allowed by high-luminosity, changes picture completely

Charge distribution is markedly differtent from magnetisation distribution. Strong indication that nucleon has complicated internal structure.

Two puzzles:1. Reconcile the data2. If JLab correct, explain

Modern Miraclesin Hadron Physics


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o proton = three constituent quarks• Mproton ≈ 1GeV

• Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV

o pion = constituent quark + constituent antiquark• Guess Mpion ≈ ⅔ × Mproton ≈ 700MeV

o WRONG . . . . . . . . . . . . . . . . . . . . . . Mpion = 140MeVo Rho-meson

• Also constituent quark + constituent antiquark – just pion with spin of one constituent flipped

• Mrho ≈ 770MeV ≈ 2 × Mconstituent−quark

What is “wrong” with the pion?Northwestern University: 7 Jan '11

Dichotomy of the pion


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How does one make an almost massless particle from two massive constituent-quarks?

Naturally, one could always tune a potential in quantum mechanics so that the ground-state is massless – but some are still making this mistake

However: current-algebra (1968) This is impossible in quantum mechanics, for which one

always finds:

mm 2

tconstituenstatebound mm


NSACLong Range Plan?


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If not, with what should they be replaced?What is the meaning of the NSAC Challenge?

What is a constituent quark, a constituent-gluon?

Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom?


Under these circumstances: Can 12C be stable? Is the deuteron stable; can Big-Bang Nucleosynthesis occur?

(Many more existential questions …)

Probably not … but it wouldn’t matter because we wouldn’t be around to worry about it.

What is themeaning of all this?


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If mπ=mρ , thenRepulsive & attractive forces in the Nucleon-Nucleon potential have the SAME range … and …There is NO intermediate range attraction.


QCD’s Challenges

Dynamical Chiral Symmetry Breaking Very unnatural pattern of bound state masses;

e.g., Lagrangian (pQCD) quark mass is small but . . . no degeneracy between JP=+ and JP=− (parity partners)

Neither of these phenomena is apparent in QCD’s Lagrangian Yet they are the dominant determining characteristics

of real-world QCD.

QCD – Complex behaviour arises from apparently simple rules.


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Quark and Gluon ConfinementNo matter how hard one strikes the proton, one cannot liberate an individual quark or gluon


Understand emergent phenomena

Why don’t we juststop talking & solve the

problem? Emergent phenomena can’t be studied using perturbation theory So what? Same is true of bound-state problems in quantum

mechanics! Differences:

Here relativistic effects are crucial – virtual particlesQuintessence of Relativistic Quantum Field Theory

Interaction between quarks – the Interquark Potential – Unknown throughout > 98% of the pion’s/proton’s volume!

Understanding requires ab initio nonperturbative solution of fully-fledged interacting relativistic quantum field theory



Universal Truths

Spectrum of hadrons (ground, excited and exotic states), and hadron elastic and transition form factors provide unique information about long-range interaction between light-quarks and distribution of hadron's characterising properties amongst its QCD constituents.

Dynamical Chiral Symmetry Breaking (DCSB) is most important mass generating mechanism for visible matter in the Universe.

Higgs mechanism is (almost) irrelevant to light-quarks. Running of quark mass entails that calculations at even modest Q2 require a

Poincaré-covariant approach. Covariance requires existence of quark orbital angular momentum in hadron's rest-frame wave function.

Confinement is expressed through a violent change of the propagators for coloured particles & can almost be read from a plot of a states’ dressed-propagator.

It is intimately connected with DCSB.Craig Roberts, Physics Division: The Physics of Hadrons


Chiral symmetry

Craig Roberts, Physics Division: Much Ado About Nothing

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Feature of massless fermions in relativistic quantum field theory

Realised in the spectrum of the theory via the appearance of degenerate parity partners

Perturbative QCD: u- & d- quarks are very lightmu /md ≈ 0.5 & md ≈ 4 MeVH. Leutwyler, 0911.1416 [hep-ph]

However, splitting between parity partners is greater-than 100-times this mass-scale; e.g.,

Physics Division: 17 Dec 2010

JP ⅟₂+ (p) ⅟₂-

Mass 940 MeV 1535 MeV

http://inspirebeta.net/record/836368?ln=en



Universal Conventions

Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum)

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



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

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.



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103

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HG QCDNscondensateQCD

“The biggest embarrassment in theoretical physics.”

The Traditional Approach – Modelling

– has its problems.

How can we tackle the SM’sStrongly-interacting piece?




Lattice-QCD


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– Spacetime becomes an hypercubic lattice– Computational challenge, many millions of degrees of freedom



Lattice-QCD –


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– Spacetime becomes an hypercubic lattice– Computational challenge, many millions of degrees of freedom– Approximately 500 people worldwide & 20-30 people per collaboration.


A Compromise?Dyson-Schwinger Equations

1994 . . . “As computer technology continues to improve, lattice gauge theory [LGT] will become an increasingly useful means of studying hadronic physics through investigations of discretised quantum chromodynamics [QCD]. . . . .”




1994 . . . “However, it is equally important to develop other complementary nonperturbative methods based on continuum descriptions. In particular, with the advent of new accelerators such as CEBAF (VA) and RHIC (NY), there is a need for the development of approximation techniques and models which bridge the gap between short-distance, perturbative QCD and the extensive amount of low- and intermediate-energy phenomenology in a single covariant framework. . . . ”




1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.”




1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.”

C. D. Roberts and A. G. Williams, “Dyson-Schwinger equations and their application to hadronic physics,” Prog. Part. Nucl. Phys. 33, 477 (1994) [arXiv:hep-ph/9403224].(473 citations)






A Compromise?DSEs


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Dyson (1949) & Schwinger (1951) . . . One can derive a system of coupled integral equations relating all the Green functions for a theory, one to another.Gap equation:

o fermion self energy o gauge-boson propagatoro fermion-gauge-boson vertex

These are nonperturbative equivalents in quantum field theory to the Lagrange equations of motion.

Essential in simplifying the general proof of renormalisability of gauge field theories.

)(

1)(

ppipS


Dyson-SchwingerEquations

Well suited to Relativistic Quantum Field Theory Simplest level: Generating Tool for Perturbation

Theory . . . Materially Reduces Model-Dependence … Statement about long-range behaviour of quark-quark interaction

NonPerturbative, Continuum approach to QCD Hadrons as Composites of Quarks and Gluons Qualitative and Quantitative Importance of:

Dynamical Chiral Symmetry Breaking– Generation of fermion mass from

nothing Quark & Gluon Confinement

– Coloured objects not detected, Not detectable?Craig Roberts, Physics Division: The Physics of Hadrons

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Approach yields Schwinger functions; i.e., propagators and verticesCross-Sections built from Schwinger FunctionsHence, method connects observables with long- range behaviour of the running couplingExperiment ↔ Theory comparison leads to an understanding of long- range behaviour of strong running-coupling


QCD is asymptotically-free (2004 Nobel Prize) Chiral-limit is well-defined;

i.e., one can truly speak of a massless quark. NB. This is nonperturbatively impossible in QED.

Dressed-quark propagator: Weak coupling expansion of

gap equation yields every diagram in perturbation theory In perturbation theory:

If m=0, then M(p2)=0Start with no mass,Always have no mass.

Mass from Nothing?!Perturbation Theory


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...ln1)(2

22 p

mpM


Spontaneous(Dynamical)Chiral Symmetry Breaking

The 2008 Nobel Prize in Physics was divided, one half awarded to Yoichiro Nambu

"for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics"



Gell-Mann – Oakes – RennerRelation (1968)

Pion’s leptonic decay constant, mass-dimensioned observable which describes rate of process π+→μ+ν

Vacuum quark condensate

How is this expression modified and interpreted in a theory with confinement?



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!





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


12GeVThe Future of JLab

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


Universal Conventions

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



What does this approach tell us?

?

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

Building on the concepts and theory that produces the features that have been described, one can derive numerous exact results in QCD.

One of them explains the peculiar nature of the pion’s mass; i.e., it’s relationship to the Lagrangian current-quark mass m(ς):

Dichotomy of the pion


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This is an almost-familiar relation, a peculiar, non-quantum-mechanicalIdentity – looks like the GMOR

What are the constants of proportionality, physically?

P. Maris, C.D. Roberts & P.C. Tandynucl-th/9707003




In-meson condensate


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Maris & Robertsnucl-th/9708029

Pseudoscalar projection of pion’s Bethe-Salpeter wave-function onto the origin in configuration space: |Ψπ

PS(0)|

– or the pseudoscalar pion-to-vacuum matrix element

Rigorously defined in QCD – gauge-independent, cutoff-independent, etc. For arbitrary current-quark masses For any pseudoscalar meson




In-meson condensate


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Pseudovector projection of pion’s Bethe-Salpeter wave-function onto the origin in configuration space: |Ψπ

AV(0)|

– or the pseudoscalar pion-to-vacuum matrix element – or the pion’s leptonic decay constant

Rigorously defined in QCD – gauge-independent, cutoff-independent, etc. For arbitrary current-quark masses For any pseudoscalar meson





In-meson condensate


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Define

Then, using the pion Goldberger-Treiman relations, one derives, in the chiral limit

Namely, the so-called vacuum quark condensate is the chiral-limit value of the in-pion condensate

The in-pion condensate is the only well-defined function of current-quark mass in QCD that is smoothly connected to the vacuum quark condensate.


0);0( qq

Chiral limit


|ΨπPS(0)|*|Ψπ

AV(0)|



Nature of the Pion:QCD’s Goldstone Mode



Nature of the Pion:QCD’s Goldstone Mode


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2 → many or infinitely many

Nature and number of constituents depends on the wavelengthof the probe

Constituent-quarks are replaced by thedressed-quarksand –gluons of QCD


Resolution– Whereas it might sometimes be convenient in computational

truncation schemes to imagine otherwise, owing to confinement “condensates” do not exist as spacetime-independent mass-scales that fill all spacetime.

– So-called vacuum condensates can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions.

– GMOR cf.

QCD

Paradigm shift:In-Hadron Condensates


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Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201Brodsky and Shrock, arXiv:0905.1151 [hep-th], to appear in PNAS






– No qualitative difference between fπ and ρπ

– Both are equivalent order parameters for DCSB




And |π> →|0> matrix elements




– No qualitative difference between fπ and ρπ

– And



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0);0( qq

Chiral limit



ONLY expression related to the condensate that is rigorously defined in QCD for nonzero current-quark mass


“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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103

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HG QCDNscondensateQCD

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

Gap EquationGeneral Form

Dμν(k) – dressed-gluon propagator Γν(q,p) – dressed-quark-gluon vertex Suppose one has in hand – from anywhere – the exact

form of the dressed-quark-gluon vertex

What is the associated symmetry-preserving Bethe-Salpeter kernel?!



Bethe-Salpeter EquationBound-State DSE

K(q,k;P) – fully amputated, two-particle irreducible, quark-antiquark scattering kernel

Textbook material. Compact. Visually appealing. Correct

Blocked progress for more than 60 years.



Bethe-Salpeter EquationGeneral Form

Equivalent exact bound-state equation but in this form K(q,k;P) → Λ(q,k;P)

which is completely determined by dressed-quark self-energy Enables derivation of a Ward-Takahashi identity for Λ(q,k;P)


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Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601





Ward-Takahashi IdentityBethe-Salpeter Kernel

Now, for first time, it’s possible to formulate an Ansatz for Bethe-Salpeter kernel given any form for the dressed-quark-gluon vertex by using this identity

This enables the identification and elucidation of a wide range of novel consequences of DCSB


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Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601

iγ5 iγ5





Dressed-quark anomalousmagnetic moments

Schwinger’s result for QED: pQCD: two diagrams

o (a) is QED-likeo (b) is only possible in QCD – involves 3-gluon vertex

Analyse (a) and (b)o (b) vanishes identically: the 3-gluon vertex does not contribute to

a quark’s anomalous chromomag. moment at leading-ordero (a) Produces a finite result: “ – ⅙ αs/2π ”

~ (– ⅙) QED-result But, in QED and QCD, the anomalous chromo- and electro-

magnetic moments vanish identically in the chiral limit!Craig Roberts, Physics Division: The Physics of Hadrons



Interaction term that describes magnetic-moment coupling to gauge fieldo Straightforward to show that it mixes left ↔ righto Thus, explicitly violates chiral symmetry

Follows that in fermion’s e.m. current γμF1 does cannot mix with σμνqνF2

No Gordon Identityo Hence massless fermions cannot not possess a measurable

chromo- or electro-magnetic moment But what if the chiral symmetry is dynamically

broken, strongly, as it is in QCD?Craig Roberts, Physics Division: The Physics of Hadrons



Three strongly-dressed and essentially-

nonperturbative contributions to dressed-quark-gluon vertex:


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DCSB

Ball-Chiu term•Vanishes if no DCSB•Appearance driven by STI

Anom. chrom. mag. mom.contribution to vertex•Similar properties to BC term•Strength commensurate with lattice-QCD

Skullerud, Bowman, Kizilersu et al.hep-ph/0303176

Role and importance isNovel discovery•Essential to recover pQCD•Constructive interference with Γ5

Lei Chang, Yu-Xin Liu and Craig D. RobertsarXiv:1009.3458 [nucl-th], to appear in Phys. Rev. Lett.


http://inspirebeta.net/record/868745





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Formulated and solved general Bethe-Salpeter equation Obtained dressed electromagnetic vertex Confined quarks don’t have a mass-shello Can’t unambiguously define

magnetic momentso But can define

magnetic moment distribution

Lei Chang, Yu-Xin Liu and Craig D. RobertsarXiv:1009.3458 [nucl-th],to appear in Phys. Rev. Lett.

ME κACM κAEM

Full vertex 0.44 -0.22 0.45

Rainbow-ladder 0.35 0 0.048

AEM is opposite in sign but of roughly equal magnitude as ACMo Potentially important for elastic & transition form factors, etc.o Muon g-2 ?





DSEs and Baryons


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M(p2) – effects have enormous impact on meson properties.Must be included in description and prediction of baryon

properties. M(p2) 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 founded on 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


rqq ≈ rπ


Faddeev Equation


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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 correlations

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

diquark

quark

quark exchangeensures Pauli statistics



Spectrum of some known u- & d-quark baryons


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H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. RobertsIn progress; H.L.L. Roberts, L. Chang and C.D. RobertsarXiv:1007.4318 [nucl-th];H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts arXiv:1007.3566 [nucl-th];

Baryons: ground-states and 1st radial exciations

mN mN* mN(⅟₂) mN*(⅟₂-) mΔ mΔ* mΔ(3⁄₂-) mΔ*(3⁄₂-)

DSE 1.14 1.73 1.86 2.09 1.39 1.85 1.98 2.16

EBAC 1.76 1.80 1.39 1.98

mean-|relative-error| = 2%-Agreement DSE dressed-quark-core masses cf. Excited Baryon Analysis Center bare masses is significant because no attempt was made to ensure this.

1st radialExcitation ofN(1535)?








Nucleon ElasticForm Factors


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Photon-baryon vertexOettel, Pichowsky and von Smekal, nucl-th/9909082

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

“Survey of nucleon electromagnetic form factors” – unification of meson and baryon observables; and prediction of nucleon elastic form factors to 15 GeV2






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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

I.C. Cloët, C.D. Roberts, et al.In progress





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New JLab data: S. Riordan et al., arXiv:1008.1738 [nucl-ex]

DSE-prediction


)(

)(2

2

QG

QGnM

nEn

This evolution is very sensitive to momentum-dependence of dressed-quark propagator


Measurement of GEn at nonzero Q2

is extremely difficult








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New JLab data: S. Riordan et al., arXiv:1008.1738 [nucl-ex]

DSE-prediction


)(

)(2,

1

2,1

QF

QFup

dp

Location of zero measures relative strength of scalar and axial-vector qq-correlations

Brooks, Bodek, Budd, Arrington fit to data: hep-ex/0602017









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Neutron Structure Function at high x

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 R.J. Holt & C.D. Roberts

RMP (2010) 2991

SU(6) symmetry

pQCD

0+ qq only

DSE: 0+ & 1+ qq


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


Related measure of 1+/0+ strength





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Epilogue

Dynamical chiral symmetry breaking (DCSB) – mass from nothing for 98% of visible matter – is a realityo Expressed in M(p2), with observable signals in experiment

Poincaré covarianceo Crucial in description of contemporary datao Quantum mechanics is inadequate as a tool in hadron physics

Fully-self-consistent treatment of an interaction Essential if experimental data is truly to be understood.

Hadron internal structure is far from simple o Distribution of charge, magnetisation, momentum, spin amongst

constituents is wavelength (and frame) dependent o Correlations between constituents are key

– Confinement is almost certainly the origin of DCSB– DCSB is a property of hadrons, not the “vacuum”


the physics of hadrons craig d. roberts physics division argonne national laboratory & school of...

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