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Quantum Chromodynamics:The Origin of Mass as We Know itCraig D. Roberts
Physics DivisionArgonne National Laboratory
&
School of PhysicsPeking University
Transition Region
Argonne National Laboratory
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
2IIT Physics Colloquium: 7 Oct 2010
Argonne National Laboratory
Physics DivisionATLAS Tandem Linac:
International User Facility for Low Energy Nuclear Physics
37 PhD Scientific StaffAnnual Budget:
$27million
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
3IIT Physics Colloquium: 7 Oct 2010
Length-Scales of Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
4IIT Physics Colloquium: 7 Oct 2010
Physics Division
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
5
Research sponsored primarily by Department of Energy: Office of Nuclear Physics Nuclear HadronTests of Standard Model
IIT Physics Colloquium: 7 Oct 2010
Physics Division
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
6
Research sponsored primarily by Department of Energy: Office of Nuclear Physics Nuclear HADRONTests of Standard Model
IIT Physics Colloquium: 7 Oct 2010
Hadron Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
7
“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.”
IIT Physics Colloquium: 7 Oct 2010
NSACLong Range Plan
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
8
“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.”
IIT Physics Colloquium: 7 Oct 2010
Quarks and Nuclear Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
9
Standard Model of Particle Physics:Six quark flavours
IIT Physics Colloquium: 7 Oct 2010
Quarks and Nuclear Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
10
Standard Model of Particle Physics:Six quark flavours
Real WorldNormal matter – only two light-quark flavours are active
IIT Physics Colloquium: 7 Oct 2010
Quarks and Nuclear Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
11
Standard Model of Particle Physics:Six quark flavours
Real WorldNormal matter – only two light-quark flavours are activeOr, perhaps, three
IIT Physics Colloquium: 7 Oct 2010
Quarks and Nuclear Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
12
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.
IIT Physics Colloquium: 7 Oct 2010
What is QCD?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
13IIT Physics Colloquium: 7 Oct 2010
What is QCD?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
14
Relativistic Quantum Gauge Theory: Interactions mediated by vector boson exchange Vector bosons are perturbatively-massless
IIT Physics Colloquium: 7 Oct 2010
What is QCD?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
15
Relativistic Quantum Gauge Theory: Interactions mediated by vector boson exchange Vector bosons are perturbatively-massless
Similar interaction in QED
IIT Physics Colloquium: 7 Oct 2010
What is QCD?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
16
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
3-gluon vertex
4-gluon vertex
IIT Physics Colloquium: 7 Oct 2010
QED cf. QCD? Running coupling
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
17
e
QED
mQ
Qln
32
1)(
IIT Physics Colloquium: 7 Oct 2010
QED cf. QCD? Running coupling
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
18
e
QED
mQ
Qln
32
1)(
Add 3-gluon self-interaction
IIT Physics Colloquium: 7 Oct 2010
QED cf. QCD?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
19
e
QED
mQ
Qln
32
1)(
Q
NQ
f
QCD
ln)233(
6)(
fermionscreening
gluonantiscreening
IIT Physics Colloquium: 7 Oct 2010
QED cf. QCD?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
20
2004 Nobel Prize in Physics : Gross, Politzer and Wilczek
e
QED
mQ
Qln
32
1)(
Q
NQ
f
QCD
ln)233(
6)(
fermionscreening
gluonantiscreening
IIT Physics Colloquium: 7 Oct 2010
Simple picture- Proton
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
21
Three quantum-mechanical constituent-quarks interacting via a potential, derived from one constituent-gluon exchange
IIT Physics Colloquium: 7 Oct 2010
Simple picture- Pion
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
22
Two quantum-mechanical constituent-quarks - particle+antiparticle -interacting via a potential, derived from one constituent-gluon exchange
IIT Physics Colloquium: 7 Oct 2010
Modern Miraclesin Hadron Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
23
o proton = three constituent quarks• Mproton ≈ 1GeV
• Therefore guess Mconstituent−quark ≈ ⅓ × GeV ≈ 350MeV
IIT Physics Colloquium: 7 Oct 2010
Modern Miraclesin Hadron Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
24
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
IIT Physics Colloquium: 7 Oct 2010
Modern Miraclesin Hadron Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
25
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 = 140MeV
IIT Physics Colloquium: 7 Oct 2010
Modern Miraclesin Hadron Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
26
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
IIT Physics Colloquium: 7 Oct 2010
Modern Miraclesin Hadron Physics
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
27
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?IIT Physics Colloquium: 7 Oct 2010
Dichotomy of the pion
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
28
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
However: current-algebra (1968) This is impossible in quantum mechanics, for which one
always finds:
mm 2
tconstituenstatebound mm
IIT Physics Colloquium: 7 Oct 2010
NSACLong Range Plan?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
29
What is a constituent quark, a constituent-gluon?
IIT Physics Colloquium: 7 Oct 2010
NSACLong Range Plan?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
30
What is a constituent quark, a constituent-gluon?
Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom?
IIT Physics Colloquium: 7 Oct 2010
NSACLong Range Plan?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
31
If not, with what should they be replaced?
What is a constituent quark, a constituent-gluon?
Do they – can they – correspond to well-defined quasi-particle degrees-of-freedom?
IIT Physics Colloquium: 7 Oct 2010
NSACLong Range Plan?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
32
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?
IIT Physics Colloquium: 7 Oct 2010
What is themeaning of all this?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
33
If mπ=mρ , then repulsive and attractive forces in the Nucleon-Nucleon potential have the SAME range and there is NO intermediate range attraction.
IIT Physics Colloquium: 7 Oct 2010
What is themeaning of all this?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
34
Under these circumstances: Can 12C be stable? Is the deuteron stable; can Big-Bang Nucleosynthesis occur? Many more existential questions …
If mπ=mρ , then repulsive and attractive forces in the Nucleon-Nucleon potential have the SAME range and there is NO intermediate range attraction.
IIT Physics Colloquium: 7 Oct 2010
What is themeaning of all this?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
35
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.
If mπ=mρ , then repulsive and attractive forces in the Nucleon-Nucleon potential have the SAME range and there is NO intermediate range attraction.
IIT Physics Colloquium: 7 Oct 2010
QCD’s Challenges
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
36
Quark and Gluon ConfinementNo matter how hard one strikes the proton, one cannot liberate an individual quark or gluon
IIT Physics Colloquium: 7 Oct 2010
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)
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
37
Quark and Gluon ConfinementNo matter how hard one strikes the proton, one cannot liberate an individual quark or gluon
IIT Physics Colloquium: 7 Oct 2010
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.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
38
Quark and Gluon ConfinementNo matter how hard one strikes the proton, one cannot liberate an individual quark or gluon
IIT Physics Colloquium: 7 Oct 2010
QCD’s ChallengesUnderstand emergent phenomena
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: QCD - Origin of Mass as We Know It
39
Quark and Gluon ConfinementNo matter how hard one strikes the proton, one cannot liberate an individual quark or gluon
IIT Physics Colloquium: 7 Oct 2010
Why don’t we juststop talking & solve the
problem? Emergent phenomena can’t be studied using perturbation theory
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
40IIT Physics Colloquium: 7 Oct 2010
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!
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
41IIT Physics Colloquium: 7 Oct 2010
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!
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
42IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
43IIT Physics Colloquium: 7 Oct 2010
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.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
44IIT Physics Colloquium: 7 Oct 2010
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.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
45IIT Physics Colloquium: 7 Oct 2010
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.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
46IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
47IIT Physics Colloquium: 7 Oct 2010
How can we tackle the SM’sStrongly-interacting piece?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
48IIT Physics Colloquium: 7 Oct 2010
How can we tackle the SM’sStrongly-interacting piece?
The Traditional Approach – Modelling
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
49IIT Physics Colloquium: 7 Oct 2010
How can we tackle the SM’sStrongly-interacting piece?
The Traditional Approach – Modelling
– has its problems.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
50IIT Physics Colloquium: 7 Oct 2010
How can we tackle the SM’sStrongly-interacting piece?
Lattice-QCD
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
51
– Spacetime becomes an hypercubic lattice– Computational challenge, many millions of degrees of freedom
IIT Physics Colloquium: 7 Oct 2010
How can we tackle the SM’sStrongly-interacting piece?
Lattice-QCD –
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
52
– Spacetime becomes an hypercubic lattice– Computational challenge, many millions of degrees of freedom– Approximately 500 people worldwide & 20-30 people per collaboration.
IIT Physics Colloquium: 7 Oct 2010
A Compromise?Dyson-Schwinger Equations
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
53IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
54IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
55IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
56IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
57IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
58IIT Physics Colloquium: 7 Oct 2010
A Compromise?DSEs
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
59
Dyson (1949) & Schwinger (1951) . . . One can derive a system of coupled integral equations relating all the Green functions for a theory, one to another.
IIT Physics Colloquium: 7 Oct 2010
A Compromise?DSEs
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
60
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
)(
1)(
ppipS
IIT Physics Colloquium: 7 Oct 2010
A Compromise?DSEs
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
61
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
IIT Physics Colloquium: 7 Oct 2010
Dyson-SchwingerEquations
Well suited to Relativistic Quantum Field Theory Simplest level: Generating Tool for Perturbation
Theory . . . Materially Reduces Model-Dependence
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: QCD - Origin of Mass as We Know It
62IIT Physics Colloquium: 7 Oct 2010
Dyson-SchwingerEquations
Well suited to Relativistic Quantum Field Theory Simplest level: Generating Tool for Perturbation
Theory . . . Materially Reduces Model-Dependence
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: QCD - Origin of Mass as We Know It
63
In doing this, arrive at understanding of long- range behaviour of strong running-coupling
Approach yields Schwinger functions; i.e., propagators and vertices
Cross-Sections built from Schwinger Functions
Hence, method connects observables with long- range behaviour of the running coupling
IIT Physics Colloquium: 7 Oct 2010
Mass from Nothing?!Perturbation Theory
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.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
64IIT Physics Colloquium: 7 Oct 2010
Mass from Nothing?!Perturbation Theory
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:
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
65
...ln1)(2
22 p
mpM
IIT Physics Colloquium: 7 Oct 2010
Mass from Nothing?!Perturbation Theory
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)=0
Start with no mass,Always have no mass.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
66
...ln1)(2
22 p
mpM
IIT Physics Colloquium: 7 Oct 2010
Dynamical (Spontaneous)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: QCD - Origin of Mass as We Know It
67IIT Physics Colloquium: 7 Oct 2010
Mass from Nothing?!Nonperturbative DSEs
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
68
Gap equation is a nonlinear integral equationModern computers enable it to be solved, self-consistently,
with ease In the last ten years, we have learnt a great deal
about the nature of its kernelWhat do the self-consistent,
nonperturbative solutions tell us?
IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
69IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
70
DSE prediction of DCSB confirmed
Mass from nothing!
IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
71
Hint of lattice-QCD supportfor DSE prediction of violation of reflection positivity IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
72
Jlab 12GeV: Scanned by 2<Q2<9 GeV2 elastic & transition form factors.
IIT Physics Colloquium: 7 Oct 2010
Dichotomy of the pion
Building on the concepts and theory that produces the features that have been described, one can derive numerous exact results in QCD.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
73IIT Physics Colloquium: 7 Oct 2010
Dichotomy of the pion
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):
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
74
P. Maris, C.D. Roberts & P.C. Tandynucl-th/9707003
IIT Physics Colloquium: 7 Oct 2010
Dichotomy of the pion
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):
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
75
This is the promised, peculiar,non-quantum-mechanical relationship.
What are the constants of proportionality, physically?
P. Maris, C.D. Roberts & P.C. Tandynucl-th/9707003
IIT Physics Colloquium: 7 Oct 2010
Gell-Mann – Oakes – RennerRelation (1968)
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
76IIT Physics Colloquium: 7 Oct 2010
Gell-Mann – Oakes – RennerRelation (1968)
Pion’s leptonic decay constant, mass-dimensioned observable which describes rate of process π+→μ+ν
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
77IIT Physics Colloquium: 7 Oct 2010
Gell-Mann – Oakes – RennerRelation (1968)
Pion’s leptonic decay constant, mass-dimensioned observable which describes rate of process π+→μ+ν
Vacuum quark condensate
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
78IIT Physics Colloquium: 7 Oct 2010
Gell-Mann – Oakes – RennerRelation (1968)
Pion’s leptonic decay constant, mass-dimensioned observable which describes rate of process π+→μ+ν
Vacuum quark condensate With the GMOR, without the authors’ intention, began the story of
vacuum condensates Through the intervening years it became commonplace to believe
that condensates are “REAL”; Namely, spacetime-independent mass-dimensioned vacuum expectation values, which have measurable consequences.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
79IIT Physics Colloquium: 7 Oct 2010
Universal “Truths”
Suppose, as is widely held, that vacuum condensates are spacetime-independent, mass-dimensioned physical quantities
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
80IIT Physics Colloquium: 7 Oct 2010
Universal “Truths”
Suppose, as is widely held, that vacuum condensates are spacetime-independent, mass-dimensioned physical quantities
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: QCD - Origin of Mass as We Know It
81IIT Physics Colloquium: 7 Oct 2010
Universal Misapprehensions
Suppose, as is widely held, that vacuum condensates are spacetime-independent, mass-dimensioned physical quantities
Then they couple to gravity in general relativity and make an enormous contribution to the cosmological constant
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
82
4520
4
103
8
HG QCDNscondensateQCD
IIT Physics Colloquium: 7 Oct 2010
Universal Misapprehensions
Suppose, as is widely held, that vacuum condensates are spacetime-independent, mass-dimensioned physical quantities
Then they couple to gravity in general relativity and make anenormous contribution to the cosmological constant
Experimentally, the answer is
Ωcosm. const. = 0.76
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
83
4520
4
103
8
HG QCDNscondensateQCD
IIT Physics Colloquium: 7 Oct 2010
Universal Misapprehensions
Suppose, as is widely held, that vacuum condensates are spacetime-independent, mass-dimensioned physical quantities
Then they couple to gravity in general relativity and make anenormous contribution to the cosmological constant
Experimentally, the answer is
Ωcosm. const. = 0.76
This appalling mismatch is a bit of a problem.Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
84
4520
4
103
8
HG QCDNscondensateQCD
IIT Physics Colloquium: 7 Oct 2010
Paradigm shift:In-Hadron Condensates
B Resolution
– Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
85
Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201
IIT Physics Colloquium: 7 Oct 2010
QCD
Paradigm shift:In-Hadron Condensates
B Resolution
– Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
86
Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201
IIT Physics Colloquium: 7 Oct 2010
QCD
Paradigm shift:In-Hadron Condensates
B Resolution
– Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
87
Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201
IIT Physics Colloquium: 7 Oct 2010
Paradigm shift:In-Hadron Condensates
B Resolution
– Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
88
Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201
IIT Physics Colloquium: 7 Oct 2010
Paradigm shift:In-Hadron Condensates
B Resolution
– Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
89
Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201
IIT Physics Colloquium: 7 Oct 2010
Paradigm shift:In-Hadron Condensates
B Resolution
– Whereas it might sometimes be convenient in computational truncation schemes to imagine otherwise, “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
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
90
Brodsky, Roberts, Shrock, Tandy, Phys. Rev. C82 (Rapid Comm.) (2010) 022201
0);0( qq
Chiral limit
IIT Physics Colloquium: 7 Oct 2010
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.”
Cosmological Constant: – Putting QCD condensates back into hadrons reduces the mismatch
between experiment and theory by a factor of 1045
– Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard Model
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
91
“Void that is truly empty solves dark energy puzzle”Rachel Courtland, New Scientist 4th Sept. 2010
IIT Physics Colloquium: 7 Oct 2010
Nature of the Pion:QCD’s Goldstone Mode
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
92IIT Physics Colloquium: 7 Oct 2010
Nature of the Pion:QCD’s Goldstone Mode
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
93
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
IIT Physics Colloquium: 7 Oct 2010
Charting the interaction between light-quarks
We’ve covered Dynamical Chiral Symmetry Breaking in detail. It’s the origin of 98% of all the visible matter in the Universe
What about confinement, the other and probably most fundamental of the emergent phenomena?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
94IIT Physics Colloquium: 7 Oct 2010
Charting the interaction between light-quarks
Confinement can be related to the analytic properties of QCD's Schwinger functions.
Question of light-quark confinement can be translated into the challenge of charting the infrared behavior of QCD's universal β-function– This function may depend on the scheme chosen to renormalise
the quantum field theory but it is unique within a given scheme.Of course, the behaviour of the β-function on the perturbative domain is well known.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
95IIT Physics Colloquium: 7 Oct 2010
Charting the interaction between light-quarks
Confinement can be related to the analytic properties of QCD's Schwinger functions.
Question of light-quark confinement can be translated into the challenge of charting the infrared behavior of QCD's universal β-function– This function may depend on the scheme chosen to renormalise
the quantum field theory but it is unique within a given scheme.Of course, the behaviour of the β-function on the perturbative domain is well known.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
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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.
IIT Physics Colloquium: 7 Oct 2010
Charting the interaction between light-quarks
Through QCD's Dyson-Schwinger equations (DSEs) the pointwise behaviour of the β-function determines pattern of chiral symmetry breaking.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
97IIT Physics Colloquium: 7 Oct 2010
Charting the interaction between light-quarks
Through QCD's Dyson-Schwinger equations (DSEs) the pointwise behaviour of the β-function determines pattern of chiral symmetry breaking.
DSEs connect β-function to experimental observables. Hence, comparison between computations and observations ofo Hadron mass spectrumo Elastic and transition form factorscan be used to chart β-function’s long-range behaviour.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
98IIT Physics Colloquium: 7 Oct 2010
Charting the interaction between light-quarks
Through QCD's Dyson-Schwinger equations (DSEs) the pointwise behaviour of the β-function determines pattern of chiral symmetry breaking.
DSEs connect β-function to experimental observables. Hence, comparison between computations and observations ofo Hadron mass spectrumo Elastic and transition form factorscan be used to chart β-function’s long-range behaviour.
Extant studies of mesons show that the properties of hadron excited states are a great deal more sensitive to the long-range behaviour of the β-function than those of the ground states.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
99IIT Physics Colloquium: 7 Oct 2010
Charting the interaction between light-quarks
Through QCD's Dyson-Schwinger equations (DSEs) the pointwise behaviour of the β-function determines pattern of chiral symmetry breaking.
DSEs connect β-function to experimental observables. Hence, comparison between computations and observations can be used to chart β-function’s long-range behaviour.
To realise this goal, a nonperturbative symmetry-preserving DSE truncation is necessary:o Steady quantitative progress is being made with a scheme that is
systematically improvable (Bender, Roberts, von Smekal – nucl-th/9602012)o Leading-order is called the rainbow-ladder truncation.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
100IIT Physics Colloquium: 7 Oct 2010
Charting the interaction between light-quarks
Through QCD's Dyson-Schwinger equations (DSEs) the pointwise behaviour of the β-function determines pattern of chiral symmetry breaking.
DSEs connect β-function to experimental observables. Hence, comparison between computations and observations can be used to chart β-function’s long-range behaviour.
To realise this goal, a nonperturbative symmetry-preserving DSE truncation is necessary:o On the other hand, at significant qualitative advances are possible with
symmetry-preserving kernel Ansätze that express important additional nonperturbative effects – M(p2) – difficult/impossible to capture in any finite sum of contributions.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
101
Can’t walk beyond the rainbow, but must leap!
IIT Physics Colloquium: 7 Oct 2010
Gap EquationGeneral Form
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
102IIT Physics Colloquium: 7 Oct 2010
Gap EquationGeneral Form
Dμν(k) – dressed-gluon propagator Γν(q,p) – dressed-quark-gluon vertex
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
103IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
104IIT Physics Colloquium: 7 Oct 2010
Bethe-Salpeter EquationBound-State DSE
K(q,k;P) – fully amputated, two-particle irreducible, quark-antiquark scattering kernel
Textbook material. Compact. Visually appealing. Correct
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
105IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
106IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
107
Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601
IIT Physics Colloquium: 7 Oct 2010
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
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
108
Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601
iγ5 iγ5
IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
109
Lei Chang and C.D. Roberts0903.5461 [nucl-th]Phys. Rev. Lett. 103 (2009) 081601
iγ5 iγ5
IIT Physics Colloquium: 7 Oct 2010
Dressed-quark anomalousmagnetic moments
Schwinger’s result for QED:
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
110IIT Physics Colloquium: 7 Oct 2010
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
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
111IIT Physics Colloquium: 7 Oct 2010
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
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
112IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
113IIT Physics Colloquium: 7 Oct 2010
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
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
114IIT Physics Colloquium: 7 Oct 2010
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
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
115IIT Physics Colloquium: 7 Oct 2010
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: QCD - Origin of Mass as We Know It
116IIT Physics Colloquium: 7 Oct 2010
Dressed-quark anomalousmagnetic moments
Three strongly-dressed and essentially-
nonperturbative contributions to dressed-quark-gluon vertex:
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
117
DCSB
Lei Chang, Yu-Xin Liu and Craig D. RobertsarXiv:1009.3458 [nucl-th]
IIT Physics Colloquium: 7 Oct 2010
Dressed-quark anomalousmagnetic moments
Three strongly-dressed and essentially-
nonperturbative contributions to dressed-quark-gluon vertex:
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
118
DCSB
Ball-Chiu term•Vanishes if no DCSB•Appearance driven by STI
Lei Chang, Yu-Xin Liu and Craig D. RobertsarXiv:1009.3458 [nucl-th]
IIT Physics Colloquium: 7 Oct 2010
Dressed-quark anomalousmagnetic moments
Three strongly-dressed and essentially-
nonperturbative contributions to dressed-quark-gluon vertex:
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
119
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
Lei Chang, Yu-Xin Liu and Craig D. RobertsarXiv:1009.3458 [nucl-th]
IIT Physics Colloquium: 7 Oct 2010
Dressed-quark anomalousmagnetic moments
Three strongly-dressed and essentially-
nonperturbative contributions to dressed-quark-gluon vertex:
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
120
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]
IIT Physics Colloquium: 7 Oct 2010
Dressed-quark anomalousmagnetic moments
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
121
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]
IIT Physics Colloquium: 7 Oct 2010
Dressed-quark anomalousmagnetic moments
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
122
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]
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 transition form factors, etc.o Muon g-2 ?
IIT Physics Colloquium: 7 Oct 2010
Dressed Vertex & Meson Spectrum
Splitting known experimentally for more than 35 years Hitherto, no explanation
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
123
Experiment Rainbow-ladder
One-loop corrected
Ball-Chiu Full vertex
a1 1230
ρ 770
Mass splitting 455
IIT Physics Colloquium: 7 Oct 2010
Dressed Vertex & Meson Spectrum
Splitting known experimentally for more than 35 years Hitherto, no explanation Systematic symmetry-preserving, Poincaré-covariant DSE
truncation scheme of nucl-th/9602012.o Never better than ⅟₄ of splitting∼
Constructing kernel skeleton-diagram-by-diagram, DCSB cannot be faithfully expressed:
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
124
Experiment Rainbow-ladder
One-loop corrected
Ball-Chiu Full vertex
a1 1230 759 885
ρ 770 644 764
Mass splitting 455 115 121
Full impact of M(p2) cannot be realised!
IIT Physics Colloquium: 7 Oct 2010
Dressed Vertex & Meson Spectrum
Fully consistent treatment of Ball-Chiu vertexo Retain λ3 – term but ignore Γ4 & Γ5
o Some effects of DCSB built into vertex & Bethe-Salpeter kernel Big impact on σ – π complex But, clearly, not the complete answer.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
125
Experiment Rainbow-ladder
One-loop corrected
Ball-Chiu Full vertex
a1 1230 759 885 1066
ρ 770 644 764 924
Mass splitting 455 115 121 142
IIT Physics Colloquium: 7 Oct 2010
Dressed Vertex & Meson Spectrum
Fully consistent treatment of Ball-Chiu vertexo Retain λ3 – term but ignore Γ4 & Γ5
o Some effects of DCSB built into vertex & Bethe-Salpeter kernel Big impact on σ – π complex But, clearly, not the complete answer.
Fully-consistent treatment of complete vertex Ansatz
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
126
Experiment Rainbow-ladder
One-loop corrected
Ball-Chiu Full vertex
a1 1230 759 885 1066 1230
ρ 770 644 764 924 745
Mass splitting 455 115 121 142 485
IIT Physics Colloquium: 7 Oct 2010
Dressed Vertex & Meson Spectrum
Fully-consistent treatment of complete vertex Ansatz Subtle interplay between competing effects, which can only
now be explicated Promise of first reliable prediction of light-quark hadron
spectrum, including the so-called hybrid and exotic states.
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
127
Experiment Rainbow-ladder
One-loop corrected
Ball-Chiu Full vertex
a1 1230 759 885 1066 1230
ρ 770 644 764 924 745
Mass splitting 455 115 121 142 485
IIT Physics Colloquium: 7 Oct 2010
Pion’s Goldberger-Treiman relation
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
128
Maris, Roberts and Tandynucl-th/9707003
Pion’s Bethe-Salpeter amplitude
Dressed-quark propagator
IIT Physics Colloquium: 7 Oct 2010
Pion’s Goldberger-Treiman relation
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
129
Maris, Roberts and Tandynucl-th/9707003
Pion’s Bethe-Salpeter amplitude
Dressed-quark propagator
Axial-vector Ward-Takahashi identity entails
Exact inChiral QCD
IIT Physics Colloquium: 7 Oct 2010
Pion’s Goldberger-Treiman relation
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
130
Maris, Roberts and Tandynucl-th/9707003
Pion’s Bethe-Salpeter amplitude
Dressed-quark propagator
Axial-vector Ward-Takahashi identity entails
Pseudovector componentsnecessarily nonzero.
Cannot be ignored!
Exact inChiral QCD
IIT Physics Colloquium: 7 Oct 2010
Pion’s GT relationImplications for observables?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
131
Maris and Robertsnucl-th/9804062
IIT Physics Colloquium: 7 Oct 2010
Pion’s GT relationImplications for observables?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
132
Maris and Robertsnucl-th/9804062
Pseudovector componentsdominate in ultraviolet:(Q/2)2 = 2 GeV2
pQCD point for M(p2)→ pQCD at Q2 = 8GeV2
IIT Physics Colloquium: 7 Oct 2010
Pion’s GT relationImplications for observables?
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
133
Maris and Robertsnucl-th/9804062
Pseudovector componentsdominate in ultraviolet:(Q/2)2 = 2 GeV2
pQCD point for M(p2)→ pQCD at Q2 = 8GeV2
IIT Physics Colloquium: 7 Oct 2010
Pion’s GT relation
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
134
Guttierez, Bashir, Cloët, RobertsarXiv:1002.1968 [nucl-th]
Pion’s Bethe-Salpeter amplitude
Dressed-quark propagator
IIT Physics Colloquium: 7 Oct 2010
Pion’s GT relationContact interaction
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
135
Guttierez, Bashir, Cloët, RobertsarXiv:1002.1968 [nucl-th]
Pion’s Bethe-Salpeter amplitude
Dressed-quark propagator
Bethe-Salpeter amplitude can’t depend on relative momentum; propagator can’t be momentum-dependent
1 MQ
IIT Physics Colloquium: 7 Oct 2010
Pion’s GT relationContact interaction
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
136
Guttierez, Bashir, Cloët, RobertsarXiv:1002.1968 [nucl-th]
Pion’s Bethe-Salpeter amplitude
Dressed-quark propagator
Bethe-Salpeter amplitude can’t depend on relative momentum; propagator can’t be momentum-dependent
Solved gap and Bethe-Salpeter equationsP2=0: MQ=0.4GeV, Eπ=0.098, Fπ=0.5MQ
1 MQ
IIT Physics Colloquium: 7 Oct 2010
Pion’s GT relationContact interaction
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
137
Guttierez, Bashir, Cloët, RobertsarXiv:1002.1968 [nucl-th]
Pion’s Bethe-Salpeter amplitude
Dressed-quark propagator
Bethe-Salpeter amplitude can’t depend on relative momentum; propagator can’t be momentum-dependent
Solved gap and Bethe-Salpeter equationsP2=0: MQ=0.4GeV, Eπ=0.098, Fπ=0.5MQ
1 MQ
Nonzero and significant
IIT Physics Colloquium: 7 Oct 2010
Pion’s GT relationContact interaction
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
138
Guttierez, Bashir, Cloët, RobertsarXiv:1002.1968 [nucl-th]
Pion’s Bethe-Salpeter amplitude
Dressed-quark propagator
Asymptotic form of Fπ(Q2)Eπ
2(P)→ Fπem(Q2) = MQ
2/Q2
1 MQ
For 20+ years it was imagined that contact-interaction produced a result that’s indistinguishable From pQCD counting rule
IIT Physics Colloquium: 7 Oct 2010
Pion’s GT relationContact interaction
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
139
Guttierez, Bashir, Cloët, RobertsarXiv:1002.1968 [nucl-th]
Pion’s Bethe-Salpeter amplitude
Dressed-quark propagator
Asymptotic form of Fπ(Q2)Eπ
2(P)→ Fπem(Q2) = MQ
2/Q2
Eπ(P) Fπ(P) – cross-term
→ Fπem(Q2) = (Q2/MQ
2) * [Eπ(P)/Fπ(P)] * Eπ2(P)-term = CONSTANT!
1 MQ
For 20+ years it was imagined that contact-interaction produced a result that’s indistinguishable From pQCD counting rule
IIT Physics Colloquium: 7 Oct 2010
Pion’s ElectromagneticForm Factor
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
140
Guttierez, Bashir, Cloët, RobertsarXiv:1002.1968 [nucl-th]
QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2
cf. contact-interaction: produces M(p2)=constant
)(2
1
yx
)(~)(4
yxyxD
IIT Physics Colloquium: 7 Oct 2010
Pion’s ElectromagneticForm Factor
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
141
Guttierez, Bashir, Cloët, RobertsarXiv:1002.1968 [nucl-th]
QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2
cf. contact-interaction: produces M(p2)=constant
)(2
1
yx
)(~)(4
yxyxD
IIT Physics Colloquium: 7 Oct 2010
Pion’s ElectromagneticForm Factor
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
142
Guttierez, Bashir, Cloët, RobertsarXiv:1002.1968 [nucl-th]
QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2
cf. contact-interaction: produces M(p2)=constant
)(2
1
yx
)(~)(4
yxyxD
Single mass parameter in both studies Same predictions for Q2=0 observables Disagreement >20% for Q2>MQ
2
IIT Physics Colloquium: 7 Oct 2010
BaBar Anomalyγ* γ → π0
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
143
H.L.L. Roberts, C.D. Roberts, Bashir, Guttierez, TandyarXiv:1009.0067 [nucl-th]
QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2
cf. contact-interaction: produces M(p2)=constant
)(2
1
yx
)(~)(4
yxyxD
IIT Physics Colloquium: 7 Oct 2010
BaBar Anomalyγ* γ → π0
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
144
H.L.L. Roberts, C.D. Roberts, Bashir, Guttierez, TandyarXiv:1009.0067 [nucl-th]
QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2
cf. contact-interaction: produces M(p2)=constant
)(2
1
yx
)(~)(4
yxyxD
pQCD
IIT Physics Colloquium: 7 Oct 2010
BaBar Anomalyγ* γ → π0
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
145
H.L.L. Roberts, C.D. Roberts, Bashir, Guttierez, TandyarXiv:1009.0067 [nucl-th]
QCD-based DSE prediction: D(x-y) = produces M(p2)~1/p2
cf. contact-interaction: produces M(p2)=constant
)(2
1
yx
)(~)(4
yxyxD
No fully-self-consistent treatment of the pion can reproduce the BaBar data. All produce monotonically- increasing concave functions. BaBar data not a true measure of γ* γ → π0
Likely source of error is misidentification of π0 π0
events where 2nd π0 isn’t seen.
pQCD
IIT Physics Colloquium: 7 Oct 2010
Unifying Baryonsand Mesons
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
146
M(p2) – effects have enormous impact on meson properties.Must be included in description and prediction of baryon
properties.
IIT Physics Colloquium: 7 Oct 2010
Unifying Baryonsand Mesons
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
147
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.
IIT Physics Colloquium: 7 Oct 2010
Unifying Baryonsand Mesons
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
148
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
IIT Physics Colloquium: 7 Oct 2010
Faddeev Equation
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
149
Linear, Homogeneous Matrix equation
R.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145
diquark
quark
IIT Physics Colloquium: 7 Oct 2010
Faddeev Equation
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
150
Linear, Homogeneous Matrix equationYields wave function (Poincaré Covariant Faddeev Amplitude)
that describes quark-diquark relative motion within the nucleon
R.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145
diquark
quark
quark exchangeensures Pauli statistics
IIT Physics Colloquium: 7 Oct 2010
Faddeev Equation
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
151
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
IIT Physics Colloquium: 7 Oct 2010
Spectrum of some known u- & d-quark baryons
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
152
Mesons & Diquarks
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]
m0+ m1
+ m0- m1
- mπ mρ mσ ma1
0.72 1.01 1.17 1.31 0.14 0.80 1.06 1.23
IIT Physics Colloquium: 7 Oct 2010
Spectrum of some known u- & d-quark baryons
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
153
Mesons & DiquarksCahill, Roberts, Praschifka: Phys.Rev. D36 (1987) 2804
Proof of mass ordering: diquark-mJ+ > meson-mJ-
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]
m0+ m1
+ m0- m1
- mπ mρ mσ ma1
0.72 1.01 1.17 1.31 0.14 0.80 1.06 1.23
IIT Physics Colloquium: 7 Oct 2010
Spectrum of some known u- & d-quark baryons
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
154
Mesons & DiquarksCahill, Roberts, Praschifka: Phys.Rev. D36 (1987) 2804
Proof of mass ordering: diquark-mJ+ > meson-mJ-
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]
m0+ m1
+ m0- m1
- mπ mρ mσ ma1
0.72 1.01 1.17 1.31 0.14 0.80 1.06 1.23
Baryons: ground-states and 1st radial exciationsmN mN* mN(⅟₂) mN*(⅟₂-) mΔ mΔ* mΔ(3⁄₂-) mΔ*(3⁄₂-)
DSE 1.05 1.73 1.86 2.09 1.33 1.85 1.98 2.16
EBAC 1.76 1.80 1.39 1.98
IIT Physics Colloquium: 7 Oct 2010
Spectrum of some known u- & d-quark baryons
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
155
Mesons & DiquarksCahill, Roberts, Praschifka: Phys.Rev. D36 (1987) 2804
Proof of mass ordering: diquark-mJ+ > meson-mJ-
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]
m0+ m1
+ m0- m1
- mπ mρ mσ ma1
0.72 1.01 1.17 1.31 0.14 0.80 1.06 1.23
Baryons: ground-states and 1st radial exciationsmN mN* mN(⅟₂) mN*(⅟₂-) mΔ mΔ* mΔ(3⁄₂-) mΔ*(3⁄₂-)
DSE 1.05 1.73 1.86 2.09 1.33 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 (JLab) bare masses is significant ’cause no attempt was made to ensure this.
IIT Physics Colloquium: 7 Oct 2010
Spectrum of some known u- & d-quark baryons
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
156
Mesons & DiquarksCahill, Roberts, Praschifka: Phys.Rev. D36 (1987) 2804
Proof of mass ordering: diquark-mJ+ > meson-mJ-
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]
m0+ m1
+ m0- m1
- mπ mρ mσ ma1
0.72 1.01 1.17 1.31 0.14 0.80 1.06 1.23
Baryons: ground-states and 1st radial exciationsmN mN* mN(⅟₂) mN*(⅟₂-) mΔ mΔ* mΔ(3⁄₂-) mΔ*(3⁄₂-)
DSE 1.05 1.73 1.86 2.09 1.33 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 (JLab) bare masses is significant ’cause no attempt was made to ensure this.
1st radialExcitation ofN(1535)?
IIT Physics Colloquium: 7 Oct 2010
Nucleon ElasticForm Factors
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
157
Photon-baryon vertexOettel, Pichowsky and von Smekal, nucl-th/9909082
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]
Form factors reveal how the observable properties of the nucleon – charge and magnetisation – are shared amongst its constituents
IIT Physics Colloquium: 7 Oct 2010
Nucleon ElasticForm Factors
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
158
Photon-baryon vertexOettel, Pichowsky and von Smekal, nucl-th/9909082
I.C. Cloët, C.D. Roberts, 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
IIT Physics Colloquium: 7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
159
New JLab data: S. Riordan et al., arXiv:1008.1738 [nucl-ex]
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]
)(
)(2
2
QG
QGnM
nEn
IIT Physics Colloquium: 7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
160
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
IIT Physics Colloquium: 7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
161
New JLab data: S. Riordan et al., arXiv:1008.1738 [nucl-ex]
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]
)(
)(2,
1
2,1
QF
QFup
dp
IIT Physics Colloquium: 7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
162
New JLab data: S. Riordan et al., arXiv:1008.1738 [nucl-ex]
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th]
)(
)(2,
1
2,1
QF
QFup
dp
Brooks, Bodek, Budd, Arrington fit to data: hep-ex/0602017
IIT Physics Colloquium: 7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
163
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
IIT Physics Colloquium: 7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
164
Neutron Structure Function at high x
SU(6) symmetry
pQCD
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) 11N. Isgur, PRD 59 (1999)R.J. Holt & C.D. Roberts
RMP (2010)
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 domainIIT Physics Colloquium:
7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
165
Neutron Structure Function at high x
SU(6) symmetry
pQCD
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) 11N. Isgur, PRD 59 (1999)R.J. Holt & C.D. Roberts
RMP (2010)
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 domainIIT Physics Colloquium:
7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
166
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
Confinement is almost Certainly the origin of DCSB
IIT Physics Colloquium: 7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
167
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 covarianceCrucial in description of contemporary data
Confinement is almost Certainly the origin of DCSB
IIT Physics Colloquium: 7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
168
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 covarianceCrucial in description of contemporary data
Fully-self-consistent treatment of an interaction Essential if experimental data is truly to be understood.
Confinement is almost Certainly the origin of DCSB
IIT Physics Colloquium: 7 Oct 2010
Craig Roberts, Physics Division: QCD - Origin of Mass as We Know It
169
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 covarianceCrucial in description of contemporary data
Fully-self-consistent treatment of an interaction Essential if experimental data is truly to be understood.
Dyson-Schwinger equations: o single framework, with IR model-input turned to advantage,
“almost unique in providing unambiguous path from a defined interaction → Confinement & DCSB → Masses → radii → form factors → distribution functions → etc.”
McLerran & PisarskiarXiv:0706.2191 [hep-ph]
Confinement is almost Certainly the origin of DCSB
IIT Physics Colloquium: 7 Oct 2010