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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
Craig Roberts, Physics Division: The Physics of Hadrons
3
“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
Craig Roberts, Physics Division: The Physics of Hadrons
4
“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.”
Northwestern University: 7 Jan '11
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?
Craig Roberts, Physics Division: The Physics of Hadrons
5
3-gluon vertex
4-gluon vertex
Northwestern University: 7 Jan '11
QED cf. QCD?
Craig Roberts, Physics Division: The Physics of Hadrons
6
2004 Nobel Prize in Physics : Gross, Politzer and Wilczek
e
QED
mQ
Qln
32
1)(
Q
NQ
f
QCD
ln)233(
6)(
fermionscreening
gluonantiscreening
Northwestern University: 7 Jan '11
Add 3-gluon self-interaction5 x10-5
Quarks and Nuclear Physics
Craig Roberts, Physics Division: The Physics of Hadrons
7
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.
Northwestern University: 7 Jan '11
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
Northwestern University: 7 Jan '11
Craig Roberts, Physics Division: The Physics of Hadrons
8
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
Northwestern University: 7 Jan '11
Craig Roberts, Physics Division: The Physics of Hadrons
9
Point particle (Dirac): F2=0, hence μpGE=GM
Pre-2000 μpGE/GM
Northwestern University: 7 Jan '11
Craig Roberts, Physics Division: The Physics of Hadrons
10
Distribution of charge and magnetisation is identical
Strong support for simple s-wave models of nucleon structure
Simple picture- Proton
Craig Roberts, Physics Division: The Physics of Hadrons
11
Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchange
Northwestern University: 7 Jan '11
Simple picture- Pion
Craig Roberts, Physics Division: The Physics of Hadrons
12
Two quantum-mechanical constituent-quarks - particle+antiparticle -interacting via a potential, derived from one constituent-gluon exchange
Northwestern University: 7 Jan '11
Thomas Jefferson National Accelerator Facility (JLAB)
Northwestern University: 7 Jan '11
Craig Roberts, Physics Division: The Physics of Hadrons
13
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
Northwestern University: 7 Jan '11
Craig Roberts, Physics Division: The Physics of Hadrons
14
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
Craig Roberts, Physics Division: The Physics of Hadrons
15
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
Craig Roberts, Physics Division: The Physics of Hadrons
16
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
Northwestern University: 7 Jan '11
NSACLong Range Plan?
Craig Roberts, Physics Division: The Physics of Hadrons
17
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?
Northwestern University: 7 Jan '11
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?
Craig Roberts, Physics Division: The Physics of Hadrons
18
If mπ=mρ , thenRepulsive & attractive forces in the Nucleon-Nucleon potential have the SAME range … and …There is NO intermediate range attraction.
Northwestern University: 7 Jan '11
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.
Craig Roberts, Physics Division: The Physics of Hadrons
19
Quark and Gluon ConfinementNo matter how hard one strikes the proton, one cannot liberate an individual quark or gluon
Northwestern University: 7 Jan '11
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
Craig Roberts, Physics Division: The Physics of Hadrons
20Northwestern University: 7 Jan '11
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
21Northwestern University: 7 Jan '11
Chiral symmetry
Craig Roberts, Physics Division: Much Ado About Nothing
22
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
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.”
Craig Roberts, Physics Division: The Physics of Hadrons
23Northwestern University: 7 Jan '11
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.
Craig Roberts, Physics Division: The Physics of Hadrons
24Northwestern University: 7 Jan '11
4620
4
103
8
HG QCDNscondensateQCD
“The biggest embarrassment in theoretical physics.”
The Traditional Approach – Modelling
– has its problems.
How can we tackle the SM’sStrongly-interacting piece?
Craig Roberts, Physics Division: The Physics of Hadrons
25Northwestern University: 7 Jan '11
How can we tackle the SM’sStrongly-interacting piece?
Lattice-QCD
Craig Roberts, Physics Division: The Physics of Hadrons
26
– Spacetime becomes an hypercubic lattice– Computational challenge, many millions of degrees of freedom
Northwestern University: 7 Jan '11
How can we tackle the SM’sStrongly-interacting piece?
Lattice-QCD –
Craig Roberts, Physics Division: The Physics of Hadrons
27
– Spacetime becomes an hypercubic lattice– Computational challenge, many millions of degrees of freedom– Approximately 500 people worldwide & 20-30 people per collaboration.
Northwestern University: 7 Jan '11
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]. . . . .”
Craig Roberts, Physics Division: The Physics of Hadrons
28Northwestern University: 7 Jan '11
A Compromise?Dyson-Schwinger Equations
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. . . . ”
Craig Roberts, Physics Division: The Physics of Hadrons
29Northwestern University: 7 Jan '11
A Compromise?Dyson-Schwinger Equations
1994 . . . “Cross-fertilisation between LGT studies and continuum techniques provides a particularly useful means of developing a detailed understanding of nonperturbative QCD.”
Craig Roberts, Physics Division: The Physics of Hadrons
30Northwestern University: 7 Jan '11
A Compromise?Dyson-Schwinger Equations
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)
Craig Roberts, Physics Division: The Physics of Hadrons
31Northwestern University: 7 Jan '11
A Compromise?DSEs
Craig Roberts, Physics Division: The Physics of Hadrons
32
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
Northwestern University: 7 Jan '11
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
33
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
Northwestern University: 7 Jan '11
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
Craig Roberts, Physics Division: The Physics of Hadrons
34
...ln1)(2
22 p
mpM
Northwestern University: 7 Jan '11
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"
Craig Roberts, Physics Division: The Physics of Hadrons
35Northwestern University: 7 Jan '11
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?
Craig Roberts, Physics Division: The Physics of Hadrons
36Northwestern University: 7 Jan '11
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.
Craig Roberts, Physics Division: The Physics of Hadrons
37Northwestern University: 7 Jan '11
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.
Craig Roberts, Physics Division: The Physics of Hadrons
38
DSE prediction of DCSB confirmed
Mass from nothing!
Northwestern University: 7 Jan '11
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.
Craig Roberts, Physics Division: The Physics of Hadrons
39
Hint of lattice-QCD support for DSE prediction of violation of reflection positivity
Northwestern University: 7 Jan '11
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.
Craig Roberts, Physics Division: The Physics of Hadrons
40
Jlab 12GeV: Scanned by 2<Q2<9 GeV2 elastic & transition form factors.
Northwestern University: 7 Jan '11
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.”
Craig Roberts, Physics Division: The Physics of Hadrons
41Northwestern University: 7 Jan '11
What does this approach tell us?
?
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
Craig Roberts, Physics Division: The Physics of Hadrons
42
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
Northwestern University: 7 Jan '11
In-meson condensate
Craig Roberts, Physics Division: The Physics of Hadrons
43
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
Northwestern University: 7 Jan '11
In-meson condensate
Craig Roberts, Physics Division: The Physics of Hadrons
44
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
Northwestern University: 7 Jan '11
Maris & Robertsnucl-th/9708029
In-meson condensate
Craig Roberts, Physics Division: The Physics of Hadrons
45
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.
Northwestern University: 7 Jan '11
0);0( qq
Chiral limit
Maris & Robertsnucl-th/9708029
|ΨπPS(0)|*|Ψπ
AV(0)|
Nature of the Pion:QCD’s Goldstone Mode
Craig Roberts, Physics Division: The Physics of Hadrons
46Northwestern University: 7 Jan '11
Nature of the Pion:QCD’s Goldstone Mode
Craig Roberts, Physics Division: The Physics of Hadrons
47
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
Northwestern University: 7 Jan '11
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
Craig Roberts, Physics Division: The Physics of Hadrons
48
Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201Brodsky and Shrock, arXiv:0905.1151 [hep-th], to appear in PNAS
Northwestern University: 7 Jan '11
Paradigm shift:In-Hadron Condensates
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.
– No qualitative difference between fπ and ρπ
– Both are equivalent order parameters for DCSB
Craig Roberts, Physics Division: The Physics of Hadrons
49Northwestern University: 7 Jan '11
Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201Brodsky and Shrock, arXiv:0905.1151 [hep-th], to appear in PNAS
And |π> →|0> matrix elements
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.
– No qualitative difference between fπ and ρπ
– And
Paradigm shift:In-Hadron Condensates
Craig Roberts, Physics Division: The Physics of Hadrons
50
0);0( qq
Chiral limit
Northwestern University: 7 Jan '11
Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201Brodsky and Shrock, arXiv:0905.1151 [hep-th], to appear in PNAS
ONLY expression related to the condensate that is rigorously defined in QCD for nonzero current-quark mass
Paradigm shift:In-Hadron Condensates
“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.”
Craig Roberts, Physics Division: The Physics of Hadrons
51
“Void that is truly empty solves dark energy puzzle”Rachel Courtland, New Scientist 4th Sept. 2010
Northwestern University: 7 Jan '11
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
4520
4
103
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HG QCDNscondensateQCD
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?!
Craig Roberts, Physics Division: The Physics of Hadrons
52Northwestern University: 7 Jan '11
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.
Craig Roberts, Physics Division: The Physics of Hadrons
53Northwestern University: 7 Jan '11
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)
Craig Roberts, Physics Division: The Physics of Hadrons
54
Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601
Northwestern University: 7 Jan '11
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
Craig Roberts, Physics Division: The Physics of Hadrons
55
Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601
iγ5 iγ5
Northwestern University: 7 Jan '11
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
56Northwestern University: 7 Jan '11
Dressed-quark anomalousmagnetic moments
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
57Northwestern University: 7 Jan '11
Dressed-quark anomalousmagnetic moments
Three strongly-dressed and essentially-
nonperturbative contributions to dressed-quark-gluon vertex:
Craig Roberts, Physics Division: The Physics of Hadrons
58
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.
Northwestern University: 7 Jan '11
Dressed-quark anomalousmagnetic moments
Craig Roberts, Physics Division: The Physics of Hadrons
59
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 ?
Northwestern University: 7 Jan '11
DSEs and Baryons
Craig Roberts, Physics Division: The Physics of Hadrons
60
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
Northwestern University: 7 Jan '11
rqq ≈ rπ
Faddeev Equation
Craig Roberts, Physics Division: The Physics of Hadrons
61
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
Northwestern University: 7 Jan '11
Spectrum of some known u- & d-quark baryons
Craig Roberts, Physics Division: The Physics of Hadrons
62
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)?
Northwestern University: 7 Jan '11
Nucleon ElasticForm Factors
Craig Roberts, Physics Division: The Physics of Hadrons
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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
Northwestern University: 7 Jan '11
Craig Roberts, Physics Division: The Physics of Hadrons
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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.
Northwestern University: 7 Jan '11
DSE result Dec 08
DSE result – including the anomalous magnetic moment distribution
I.C. Cloët, C.D. Roberts, et al.In progress
Craig Roberts, Physics Division: The Physics of Hadrons
65
New JLab data: S. Riordan et al., arXiv:1008.1738 [nucl-ex]
DSE-prediction
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]
)(
)(2
2
QG
QGnM
nEn
This evolution is very sensitive to momentum-dependence of dressed-quark propagator
Northwestern University: 7 Jan '11
Measurement of GEn at nonzero Q2
is extremely difficult
Craig Roberts, Physics Division: The Physics of Hadrons
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New JLab data: S. Riordan et al., arXiv:1008.1738 [nucl-ex]
DSE-prediction
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]
)(
)(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
Northwestern University: 7 Jan '11
Craig Roberts, Physics Division: The Physics of Hadrons
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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
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]
Distribution of neutron’s momentum amongst quarks on the valence-quark domain
Northwestern University: 7 Jan '11
Related measure of 1+/0+ strength
Craig Roberts, Physics Division: The Physics of Hadrons
68
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”
Northwestern University: 7 Jan '11