Craig Roberts
Physics Division
 The 2013 Nobel Prize in Physics was awarded to Higgs
and Englert following discovery of the Higgs boson at
the Large Hadron Collider.
 The Higgs boson is often said to give mass to
everything. However, that is wrong. It only gives
mass to some very simple particles, accounting for
only one or two percent of the mass of more complex
things like atoms, molecules and everyday objects,
from your mobile phone to your pet llama. The vast
majority of mass comes from the energy needed to
hold quarks together inside nuclei.
 I will explain this remarkable emergent phenomenon, contained in Nambu's share
of the 2008 Nobel Prize, and discuss its connection with the peculiar feature of
confinement in QCD; viz., the fact that quarks are forever imprisoned, never
reaching the freedom of a particle detector. I will also describe why confinement
guarantees that condensates, quantities that were once commonly viewed as
constant mass-scales that fill all spacetime, are instead wholly contained within
hadrons; and show how contemporary and future terrestrial experiments can help
complete the book on the Standard Model
Craig Roberts: Calories for Quarks: The Origin of Mass
23.Sep.2014: ECT* (89p)
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Students, Postdocs,
Asst. Profs.
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Rocio BERMUDEZ (U Michoácan);
Shi CHAO (Nanjing U)
Ming-hui DING (PKU);
Fei GAO (PKU)
S. HERNÁNDEZ (U Michoácan);
Cédric MEZRAG (CEA, Saclay)
Trang NGUYEN (KSU);
Khépani RAYA (U Michoácan);
Hannes ROBERTS (ANL, FZJ, UBerkeley);
Chien-Yeah SENG (UM-Amherst)
Kun-lun WANG (PKU);
Shu-sheng XU (Nanjing U)
Chen CHEN (USTC);
J. Javier COBOS-MARTINEZ (U.Sonora);
Mario PITSCHMANN (Vienna);
Si-xue QIN (U. Frankfurt am Main, PKU);
Jorge SEGOVIA (ANL);
David WILSON (ODU);
Craig Roberts: Calories for Quarks: The Origin of Mass
19. Lei Chang (U. Adelaide)
20. Ian Cloet (ANL)
21. Bruno El-Bennich (São Paulo);
22.
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Adnan BASHIR (U Michoácan);
Stan BRODSKY (SLAC);
Gastão KREIN (São Paulo)
Roy HOLT (ANL);
Yu-xin LIU (PKU);
Hervé Moutarde (CEA, Saclay)
Michael RAMSEY-MUSOLF (UM-Amherst)
Alfredo RAYA (U Michoácan);
Jose Rodriguez Qintero (U. Huelva)
Sebastian SCHMIDT (IAS-FZJ & JARA);
Robert SHROCK (Stony Brook);
Peter TANDY (KSU);
Tony THOMAS (U.Adelaide)
Shaolong WAN (USTC)
Hong-Shi ZONG (Nanjing U)
23.Sep.2014: ECT* (89p)
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Students, Postdocs,
Asst. Profs.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Rocio BERMUDEZ (U Michoácan);
Shi CHAO (Nanjing U)
Ming-hui DING (PKU);
Fei GAO (PKU)
S. HERNÁNDEZ (U Michoácan);
Cédric MEZRAG (CEA, Saclay)
Trang NGUYEN (KSU);
Khépani RAYA (U Michoácan);
Hannes ROBERTS (ANL, FZJ, UBerkeley);
Chien-Yeah SENG (UM-Amherst)
Kun-lun WANG (PKU);
Shu-sheng XU (Nanjing U)
Chen CHEN (USTC);
J. Javier COBOS-MARTINEZ (U.Sonora);
Mario PITSCHMANN (Vienna);
Si-xue QIN (U. Frankfurt am Main, PKU);
Jorge SEGOVIA (ANL);
David WILSON (ODU);
Craig Roberts: Calories for Quarks: The Origin of Mass
19. Lei Chang (U. Adelaide)
20. Ian Cloet (ANL)
21. Bruno El-Bennich (São Paulo);
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
Adnan BASHIR (U Michoácan);
Stan BRODSKY (SLAC);
Gastão KREIN (São Paulo)
Roy HOLT (ANL);
Yu-xin LIU (PKU);
Hervé Moutarde (CEA, Saclay)
Michael RAMSEY-MUSOLF (UW-Mad)
Alfredo RAYA (U Michoácan);
Jose Rodriguez Qintero (U. Huelva)
Sebastian SCHMIDT (IAS-FZJ & JARA);
Robert SHROCK (Stony Brook);
Peter TANDY (KSU);
Tony THOMAS (U.Adelaide)
Shaolong WAN (USTC)
Hong-Shi ZONG (Nanjing U)
23.Sep.2014: ECT* (89p)
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Craig Roberts: Calories for Quarks: The Origin of Mass
23.Sep.2014: ECT* (89p)
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Standard Model
- Formulation
 The Standard Model of Particle Physics
is a local gauge field theory, which can
be completely expressed in a very compact form
 Lagrangian possesses UY(1)xSUL(2)xSUc(3) gauge symmetry
– 19 parameters, which must be determined through comparison
with experiment
• Physics is an empirical science
– UY(1)xSUL(2) represents the electroweak theory
• 17 of the parameters are here, most of them tied to the Higgs boson, the
model’s only fundamental scalar, something like which has now been seen
• This sector is essentially perturbative, so the parameters are readily
determined
– SUc(3) represents the strong interaction component
• Just 2 of the parameters are intrinsic to SUc(3) – QCD
• However, this is the really interesting sector because it is Nature’s only
example of a truly and essentially nonperturbative fundamental theory
• Impact of the 2 parameters is not fully known. One might even be zero.
Craig Roberts: Calories for Quarks: The Origin of Mass
23.Sep.2014: ECT* (89p)
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 There are certainly phenomena
Beyond the Standard Model
– Neutrinos have mass, which
is not true within the
Standard Model
– Empirical evidence: νe ↔ νμ, ντ
Standard Model
- Complete?
… neutrino flavour is not a
constant of motion
• The first experiment to detect
the effects of neutrino
oscillations was Ray Davis'
Homestake Experiment in the
late 1960s, which observed a
deficit in the flux of solar
neutrinos νe
• Verified and quantified in
experiments at the Sudbury
Neutrino Observatory
Craig Roberts: Calories for Quarks: The Origin of Mass
 A number of experimental
hints and, almost literally,
innumerably many
theoretical speculations
about other phenomena
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Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
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Excerpt from the top-10
 Can we quantitatively understand quark and gluon confinement in
quantum chromodynamics and the existence of a mass gap?
Quantum chromodynamics is the theory describing the strong nuclear
force. Carried by gluons, it binds quarks into particles like protons and
neutrons. Apparently, the tiny subparticles are permanently confined:
one can't pull a quark or a gluon from a proton because the strong
force gets stronger with distance and snaps them right back inside.
Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
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 QCD: The piece of the
Standard Model that
describes strong interactions.
 The physics of neutrons,
protons, pions, etc. – i.e.,
Hadron Physics – is a
nonperturbative problem in
QCD
 Notwithstanding the 2013
Nobel Prize in Physics, the
origin of 98% of the visible
mass in the Universe is –
somehow – found within QCD
Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
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 China
– Beijing Electron-Positron Collider
 Germany
–
–
–
–
Facilities
QCD Machines
COSY (Jülich Cooler Synchrotron)
ELSA (Bonn Electron Stretcher and Accelerator)
MAMI (Mainz Microtron)
Facility for Antiproton and Ion Research,
under construction near Darmstadt.
New generation experiments in 2018 (perhaps)
 Japan
– J-PARC (Japan Proton Accelerator Research Complex),
under construction in Tokai-Mura, 150km NE of Tokyo.
New generation experiments to begin soon
− KEK: Tsukuba, Belle Collaboration
 Switzerland (CERN)
– Large Hadron Collider: ALICE Detector and COMPASS Detector
“Understanding deconfinement and chiral-symmetry restoration”
Craig Roberts: Calories for Quarks: The Origin of Mass
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Facilities
QCD Machines
 USA
– Thomas Jefferson National Accelerator Facility,
Newport News, Virginia
Nature of cold hadronic matter
Upgrade underway
Construction cost ≈ $370-million
New generation experiments in 2015
– Relativistic Heavy Ion Collider, Brookhaven National Laboratory,
Long Island, New York
Strong phase transition, 10μs after Big Bang
A three dimensional view of the
calculated particle paths resulting
from collisions occurring within
RHIC's STAR detector
Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
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Thomas Jefferson National Accelerator Facility (JLab)
 Driving distance:
Washington DC to JLab
≈ 270km
Craig Roberts: Calories for Quarks: The Origin of Mass
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Thomas Jefferson National Accelerator Facility (JLab)
 1984 … DoE provided initial funding for research,
development and design
 1987 … Construction began on Continuous Electron Beam
Accelerator Facility (CEBAF) - February 13
 1994 … Accelerator reached design energy of 4 GeV
 Construction cost in $FY14 ≈ $1-Billion
 Goal … Write the book about the strongest force in
nature – the force that holds nuclei together – and
determine how that force can be explained in terms of
the quarks and gluons of quantum chromodynamics
(QCD).
Craig Roberts: Calories for Quarks: The Origin of Mass
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Thomas Jefferson National Accelerator Facility (JLab)
e.g. S. J. Brodsky and G. R. Farrar,
Phys. Rev. Lett. 31, 1153 (1973)
 One of the primary reasons for building CEBAF/JLab
Prediction: at energy-scales greater than some a priori unknown
minimum value, Λ, cross-sections and form factors will behave as
Parton
model
scaling
QCD scaling
violations
power = ( number valence-quarks – 1 + Δλ )
Δλ=0,1, depending on whether helicity is conserved
or flipped
… prediction of 1/k2 vector-boson exchange
logarithm = distinctive feature & concrete prediction of QCD
 Claims were made that Λ = 1GeV!
 So, JLab was initially built to reach 4GeV.
Craig Roberts: Calories for Quarks: The Origin of Mass
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Thomas Jefferson National Accelerator Facility (JLab)
 1994 – 2004
o An enormous number of
fascinating experimental results
o Including an empirical
demonstration that the
distribution of charge and
magnetisation within the proton
are completely different,
o Suggesting that quark-quark
correlations play a crucial role in
nucleon structure
But no sign of parton model scaling
and certainly not of scaling
violations
Particle physics paradigm
Particle physics paradigm
Craig Roberts: Calories for Quarks: The Origin of Mass
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Thomas Jefferson National Accelerator Facility (JLab)
 2004 … Mission Need Agreed on upgrade of CEBAF (JLab's
accelerator) to 12GeV
 2014 … 12GeV commissioning beams
now being delivered to
the experimental halls
 Final cost of upgrade is
approximately $370-Million
 Physics of JLab at 12GeV
arXiv:1208.1244 [hep-ex]
Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
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 Very likely a self-contained, nonperturbatively renormalisable
and hence well defined Quantum Field Theory
This is not true of QED – cannot be defined nonperturbatively
 No confirmed breakdown over an enormous energy domain:
0 GeV < E < 8 TeV
 Increasingly probable that any extension of the Standard
Model will be based on the paradigm established by QCD
– Extended Technicolour: electroweak symmetry breaks via a
fermion bilinear operator in a strongly-interacting non-Abelian
theory. (Andersen et al. “Discovering Technicolor” Eur.Phys.J.Plus 126 (2011) 81)
– Higgs sector of the SM becomes an effective description of a
more fundamental fermionic theory, similar to the GinzburgLandau theory of superconductivity
Craig Roberts: Calories for Quarks: The Origin of Mass
wikipedia.org/wiki/Technicolor_(physics)
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What is QCD?
 Lagrangian of QCD
– G = gluon fields
– Ψ = quark fields
 The key to complexity in QCD … gluon field strength tensor
 Generates gluon self-interactions, whose consequences are
extraordinary
Craig Roberts: Calories for Quarks: The Origin of Mass
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cf.Quantum Electrodynamics
 QED is the archetypal gauge field theory
 Perturbatively simple
but nonperturbatively undefined
 Chracteristic feature:
Light-by-light scattering; i.e.,
photon-photon interaction – leading-order contribution takes
place at order α4. Extremely small probability because α4 ≈10-9 !
Craig Roberts: Calories for Quarks: The Origin of Mass
23.Sep.2014: ECT* (89p)
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What is QCD?
Relativistic Quantum Gauge Field Theory:
 Interactions mediated by vector boson exchange
 Vector bosons are perturbatively-massless
3-gluon vertex
 Similar interaction in QED
 Special feature of QCD – gluon self-interactions
4-gluon vertex
Craig Roberts: Calories for Quarks: The Origin of Mass
23.Sep.2014: ECT* (89p)
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Running couplings
 Quantum gauge-field theories are all typified by the feature that
Nothing is Constant
 Distribution of charge and mass, the number of particles, etc.,
indeed, all the things that quantum mechanics holds fixed, depend
upon the wavelength of the tool used to measure them
– particle number is generally not conserved in quantum field theory
 Couplings and masses are renormalised via processes involving
virtual-particles. Such effects make these quantities depend on the
energy scale at which one observes them
Craig Roberts: Calories for Quarks: The Origin of Mass
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QED cf. QCD?
 2004 Nobel Prize in Physics : Gross, Politzer and Wilczek
500%
5 x10-5=0.7%
QED (Q ) 

2 Q
1
ln
3 me
Craig Roberts: Calories for Quarks: The Origin of Mass
Add 3-gluon self-interaction
gluon
antiscreening
fermion
screening
QCD (Q ) 
6
Q
(33  2 N f ) ln

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Strong-interaction: QCD
 Asymptotically free
– Perturbation theory is valid and
accurate tool at large-Q2
– Hence chiral limit is defined
 Essentially nonperturbative
for Q2 < 2 GeV2
 Nature’s only (now known) example of a truly
nonperturbative, fundamental theory
 A-priori, no idea as to what such a theory
can produce
Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
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Wilson Loop &
the Area Law
τ
z
 C is a closed curve in space,
P is the path order operator
 Now, place static (infinitely heavy) fermionic
sources of any charge at positions
z0=0 & z=½L
 Then, evaluate <WC(z, τ)> as a functional
integral over gauge-field configurations
 In the strong-coupling limit, the result can be
Linear potential
obtained algebraically; viz.,
<WC(z, τ)> = exp(-V(z) τ )
Craig Roberts: Calories for Quarks: The Origin of Mass
σ = String tension
where V(z) is the potential between the static
sources, which behaves as V(z) = σ z
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Light quarks & Confinement
 Folklore … JLab Hall-D Conceptual Design Report(5)
“The color field lines between a quark and an anti-quark form flux tubes.
A unit area placed midway
between the quarks and
perpendicular to the line
connecting them intercepts
a constant number of field
lines, independent of the
distance between the
quarks.
This leads to a constant
force between the quarks –
and a large force at that,
equal to about 16 metric
tons.”
Craig Roberts: Calories for Quarks: The Origin of Mass
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Light quarks & Confinement
Problem:
Pions
They’re extremely light
16 tonnes of force
makes a lot of them.
Craig Roberts: Calories for Quarks: The Origin of Mass
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Light quarks & Confinement
Problem:
16 tonnes of force
makes a lot of pions.
Craig Roberts: Calories for Quarks: The Origin of Mass
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G. Bali et al., PoS LAT2005 (2006) 308
Light quarks & Confinement
 In the presence of
light quarks, pair
creation seems to
occur non-localized
and instantaneously
 No flux tube in a
theory with lightquarks.
 Flux-tube is not the
correct paradigm for
confinement in
hadron physics
Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
23.Sep.2014: ECT* (89p)
 QFT Paradigm:
Confinement
– Confinement is expressed through a dramatic
change in the analytic structure of propagators
for coloured states
– It can almost be read from a plot of the dressedpropagator for a coloured state
Confined particle
Normal particle
State described by rapidly damped
wave & hence state cannot exist in
observable spectrum
σ ≈ 1/Im(m)
≈ 1/2ΛQCD ≈ ½fm
Real-axis mass-pole splits,
moving into pair(s) of complex conjugate singularities, (or qualitatively
analogous structures chracterised by a dynamically generated mass-scale)
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 Feynman propagator for
a fermion describes a
Plane Wave
 A fermion begins to
propagate
 It can proceed a long
way before undergoing
any qualitative changes
meson
meson
meson
Baryon
meson
Craig Roberts: Calories for Quarks: The Origin of Mass
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 A quark begins to
propagate
 But after each “step” of
length σ, on average, an
interaction occurs, so
that the quark loses its
identity, sharing it with
other partons
 Finally, a cloud of
partons is produced,
which coalesces into
colour-singlet final states
σ
meson
meson
meson
Baryon
meson
Confinement is a
dynamical phenomenon!
Craig Roberts: Calories for Quarks: The Origin of Mass
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QCD
 Remarkably simple Lagrangian density
Craig Roberts: Calories for Quarks: The Origin of Mass
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QCD
0
 Remarkably simple Lagrangian density
 Classically, the massless theory does not possess a mass-scale
The theory is “conformally invariant”
Everything is massless: gluons and quarks.
There are no bound states (no length-scale to define a size)
This is not our Universe
Craig Roberts: Calories for Quarks: The Origin of Mass
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QCD
0
 Remarkably simple Lagrangian density
 Define the quantum field theory via a Functional Integral,
which generalises the Feynman path integral for quantum
mechanics.
How does that help?
Craig Roberts: Calories for Quarks: The Origin of Mass
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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: Calories for Quarks: The Origin of Mass
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Nambu – Jona-Lasinio
Dynamical Model of Elementary Particles
Based on an Analogy with Superconductivity. I
Model
Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961) 345–358
Dynamical Model Of Elementary Particles
Based On An Analogy With Superconductivity. II
Y. Nambu, G. Jona-Lasinio, Phys.Rev. 124 (1961) 246-254
 Treats a massless (chirally-invariant) four-fermion Lagrangian &
solves the gap equation in Hartree-Fock approximation (analogous
to rainbow truncation)
Craig Roberts: Calories for Quarks: The Origin of Mass
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Chiral Symmetry
 Interacting gauge theories, in which it makes sense to speak
of massless fermions, have a nonperturbative chiral symmetry
 A related concept is Helicity, which is the projection of a
particle’s spin, J, onto it’s direction of motion:
Jp
 For a massless particle, helicity is a Lorentz-invariant spinobservable λ = ± ; i.e., it’s parallel or antiparallel to the
direction of motion
– Obvious:
• massless particles travel at speed of light
• hence no observer can overtake the particle and thereby view its
momentum as having changed sign
Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
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Nambu—Jona-Lasinio Model
 Gap equation
Free fermion piece
Interactions
 NJL gap equation
Craig Roberts: Calories for Quarks: The Origin of Mass
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Critical coupling for
dynamical mass generation?
NJL model
& a mass gap?
 Some algebra ⇒ NJL gap equation is an equation for fermion mass
 Chiral limit, m=0
– Clearly, one solution is M=0.
– That is the solution in perturbation theory … Start with no mass, endup with no mass.
 Suppose, on the other hand, that M ≠ 0 so that it can be cancelled
– This nontrivial solution can exist if-and-only-if one can satisfy
3π2 mG2 = C(M2,1)
Craig Roberts: Calories for Quarks: The Origin of Mass
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Critical coupling for
dynamical mass generation!
NJL model
& a mass gap?
 Can one satisfy 3π2 mG2 = C(M2,1) ?
mG=0.17GeV
– C(M2, 1) = 1 − M2 ln [ 1 + 1/M2 ]
mG=0.21GeV
• Monotonically decreasing function of M
• Maximum value at M = 0; viz., C(M2=0, 1) = 1
 Consequently, there is a solution iff 3π2 mG2 < 1
– Typical scale for hadron physics: Λ = 1 GeV
• There is a M≠0 solution iff mG2 < (Λ/(3 π2)) = (0.2 GeV)2
 Interaction strength is proportional to 1/mG2
– Hence, if interaction is strong enough, then one can start with no
mass but end up with a massive, perhaps very massive fermion
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 Appears fairly simple, perhaps, but
these two papers have had an
enormous impact
 Together, cited more than 5950 times
 Google Scholar returns ≈ 9820 items for
the term “Nambu – Jona-Lasinio”
 Defined the paradigm for dynamical
chiral symmetry breaking
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Craig Roberts: Calories for Quarks: The Origin of Mass
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Dynamical Chiral Symmetry Breaking
DCSB is a fact in QCD
– Dynamical, not spontaneous
• Add nothing to QCD ,
No Higgs field, nothing!
Effect achieved purely through
quark+gluon dynamics.
– It’s the most important mass generating mechanism for
visible matter in the Universe.
• Responsible for ≈98% of the proton’s mass.
• Higgs mechanism is (almost) irrelevant to light-quarks.
Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
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 Deceptively simply picture
Where does the
mass come from?
 Corresponds to the sum of a countable infinity of diagrams.
NB. QED has 12,672 α5 diagrams
 Impossible to compute this in perturbation theory.
The standard algebraic manipulation
αS23
tools are just inadequate
Craig Roberts: Calories for Quarks: The Origin of Mass
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Craig Roberts: Calories for Quarks: The Origin of Mass
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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 nonperturbative vacuum state, characterized by many nonvanishing 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: Calories for Quarks: The Origin of Mass
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“Orthodox Vacuum”
 Vacuum = “frothing sea”
u
 Hadrons = bubbles in that “sea”,
d
u
containing nothing but quarks & gluons
interacting perturbatively, unless they’re
near the bubble’s boundary, whereat they feel they’re
trapped!
ud
u
u
u
d
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Historically, DCSB has
come to be associated
with the presumed
existence of spacetimeindependent condensates
that permeate the
Universe.
However, just like gluons and quarks, and
for the same reasons:
Condensates are confined within hadrons.
There are no vacuum condensates.
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Expanding the concept of in-hadron condensates
Lei Chang, Craig D. Roberts and Peter C. Tandy
arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)
GMOR Relation
 Valuable to highlight the precise form of the Gell-Mann–
Oakes–Renner (GMOR) relation: Eq. (3.4) in Phys.Rev. 175
(1968) 2195
o mπ is the pion’s mass
o Hχsb is that part of the hadronic Hamiltonian density which
explicitly breaks chiral symmetry.
 The operator expectation value in this equation is evaluated
between pion states.
 Un-approximated form of the GMOR relation doesn’t make
any reference to a vacuum condensate
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Expanding the concept of in-hadron condensates
Lei Chang, Craig D. Roberts and Peter C. Tandy
arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)
GMOR Relation
 Demonstrated algebraically that the so-called Gell-Mann –
Oakes – Renner relation is the following statement
Namely, the mass of the pion is completely determined by the
pion’s scalar form factor at zero momentum transfer Q2 = 0.
viz., by the pion’s scalar charge
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Hadron
Charges
 Matrix elements associated with hadron form factors
 Scalar charge of a hadron is an intrinsic property of
that hadron … no more a property of the vacuum
than the hadron’s electric charge, axial charge,
tensor charge, etc. …
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“Orthodox Vacuum”
 Vacuum = “frothing sea”
u
 Hadrons = bubbles in that “sea”,
d
u
containing nothing but quarks & gluons
interacting perturbatively, unless they’re
near the bubble’s boundary, whereat they feel they’re
trapped!
ud
u
u
u
d
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 Vacuum = perturbative hadronic fluctuations
but no nonperturbative condensates
 Hadrons = complex, interacting systems
within which perturbative behaviour is
restricted to just 2% of the interior
u
d
u
ud
u
u
u
d
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Paradigm shift:
In-Hadron Condensates
“Void that is truly empty
solves dark energy puzzle”
“The biggest
embarrassment in
Rachel Courtland, New Scientist 4th Sept. 2010
theoretical physics.”
“EMPTY space may really be empty. Though quantum theory suggests that a
vacuum should be fizzing with particle
it turns out that this paradoxical
activity,
QCD
46
picture
of
nothingness
may
not
be
needed.
A
calmer
of the vacuum would
QCD condensates  8 GN
 10 view
* experiment
2
also help resolve a nagging inconsistency
dark energy, the elusive force
3Hwith
0
thought to be speeding up the expansion of the universe.”

4
Cosmological Constant:
Putting QCD condensates back into hadrons reduces the
mismatch between experiment and theory by a factor of 1046
Possibly by far more, if technicolour-like theories are the correct
paradigm for extending the Standard Model
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 Discover the meaning of confinement
 Determine its connection with DCSB
(dynamical chiral symmetry breaking)
 Elucidate their signals in observables
… so experiment and theory together can map the
nonperturbative behaviour of the strong interaction
It is unlikely that two phenomena, so critical in the
Standard Model, tied to the dynamical generation of a
single mass-scale and masses of all the normal
particles, can have different origins and fates.
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Maris, Roberts and Tandy
nucl-th/9707003, Phys.Lett. B420 (1998) 267-273
Pion’s Goldberger
-Treiman relation
 Pion’s Bethe-Salpeter amplitude
Solution of the Bethe-Salpeter equation
Pseudovector components
necessarily nonzero.
Cannot be ignored!
 Dressed-quark propagator
 Axial-vector Ward-Takahashi identity entails
B(k2)
Owing to DCSB
& Exact in
Chiral QCD
Miracle: two body problem solved,
almost completely, once solution of
one body problem is known
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 The quark level Goldberger-Treiman relation shows that DCSB has a
very deep and far reaching impact on physics within the strong
interaction sector of the Standard Model; viz.,
Goldstone's theorem is fundamentally an expression of equivalence
between the one-body problem
and the two-body problem in
the pseudoscalar channel.
 This emphasises that Goldstone's theorem has a pointwise
expression in QCD
 Hence, pion properties are an almost direct measure of
the dressed-quark mass function.
 Thus, enigmatically, the properties of the massless pion
are the cleanest expression of the mechanism that is
responsible for almost all the visible mass in the universe.
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Valence
quarks
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Parton Structure of Hadrons
 Valence-quark structure of hadrons
– Definitive of a hadron.
After all, it’s how we distinguish a proton from a neutron
– Expresses charge; flavour; baryon number; and other Poincaréinvariant macroscopic quantum numbers
– Via evolution, determines background at LHC
 Foreseeable future will bring precision experimental study of (far)
valence region, and theoretical computation of distribution
functions and distribution amplitudes
– Computation is critical
– Without it, no amount of data will reveal anything about the theory
underlying the phenomena of strong interaction physics
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Imaging dynamical chiral symmetry breaking: pion wave function
on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th],
Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].
Pion’s valence-quark
Distribution Amplitude
 Following a workshop in Brazil (2012), methods were developed
that enable direct computation of the pion’s light-front wave
function
 φπ(x) = twist-two parton distribution amplitude = projection of the
pion’s Poincaré-covariant wave-function onto the light-front
 Results have been obtained with rainbow-ladder DSE kernel,
simplest symmetry preserving form; and the best DCSB-improved
kernel that is currently available.
xα (1-x)α, with α≈0.3
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Imaging dynamical chiral symmetry breaking: pion wave function
on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th],
Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].
Pion’s valence-quark
Distribution Amplitude
 Continuum-QCD prediction:
marked broadening of φπ(x), which owes to DCSB
Asymptotic
DB
RL
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Elastic Form Factors
Structure of Hadrons
 Elastic form factors
– Provide vital information about the structure and composition of the
most basic elements of nuclear physics.
– They are a measurable and physical manifestation of the nature of
the hadrons' constituents and the dynamics that binds them
together.
 Accurate form factor data are driving paradigmatic shifts in our
pictures of hadrons and their structure; e.g.,
– role of orbital angular momentum and nonpointlike diquark
correlations
– scale at which p-QCD effects become evident
– strangeness content
– meson-cloud effects
– etc.
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Hard Exclusive Processes
& PDAs
 In the theory of strong interactions, the cross-sections for many
hard exclusive hadronic reactions can be expressed in terms of the
PDAs of the hadrons involved
 Example: pseudoscalar-meson elastic electromagnetic form factor
o αS(Q2) is the strong running coupling,
o φπ(u) is the meson’s twist-two valence-quark PDA
o fP is the meson's leptonic decay constant
It was promised that
JLab would verify this
fundamental
prediction
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Pion electromagnetic
form factor
 In 2001 – seven years after
beginning operations,
Jefferson Lab provided the
first high precision pion
electroproduction data for
Fπ between Q2 values of 0.6
and 1.6 (GeV/c)2.
40 years of lQCD only
provides access to this small
domain, which is already
well-mapped by experiments
JLab Data
Result imagined by many
to be QCD prediction
Evaluated with φπ = 6x(1-x)
 2006 & 2007 – new result, at Q2=2.45 (GeV/c)2
 Authors of the publications stated: “still far from the transition
to the Q2 region where the pion looks like a simple quarkantiquark pair”
 disappointment and surprise
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Pion electromagnetic
form factor
 Year 2000 prediction for
Fπ(Q2)
– P.Maris & P.C. Tandy,
Phys.Rev. C62 (2000)
055204
Factor of three
discrepancy
JLab Data
Result imagined by many
to be QCD prediction
Evaluated with φπ = 6x(1-x)
 Problem … used brute-force
computational method …
unable to compute for
Q2>4GeV2
 Shape of prediction suggested to many that one might never see
parton model scaling and QCD scaling violations
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Pion electromagnetic
form factor
 Plans were made and an
experiment approved that
use the higher-energy
electron beam at the 12
GeV Upgrade at Jefferson
Lab.
 The Upgrade will allow an
extension of the
Fπ measurement up to a
value of Q2 of about 6
(GeV/c)2, which will probe
the pion at double the
resolution.
Projected JLab reach
Result imagined by many
to be QCD prediction
Evaluated with φπ = 6x(1-x)
 Will there be any hint of a trend
toward the asymptotic pQCD
prediction?
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Pion electromagnetic form factor
 Solution – Part 1
– Compare data with the
real QCD prediction; i.e.
the result calculated using
the broad pion PDA
predicted by modern
analyses of continuum
QCD
Real QCD prediction – obtained
withResult
realistic,
computed
PDA
imagined
by many
to be QCD prediction
Evaluated with φπ = 6x(1-x)
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Pion electromagnetic form factor
 Solution – Part 1
– Compare data with the
real QCD prediction; i.e.
the result calculated using
the broad pion PDA
predicted by modern
analyses of continuum
QCD
Agreement within 15%
maximum
Real QCD prediction – obtained
with realistic, computed PDA
 Solution – Part 2
– Algorithm used to
compute the PDA can also
be employed to compute
Fπ(Q2) directly, to
arbitrarily large Q2
 Predictions:
 JLab will see maximum
 Experiments to 8GeV2 will see
parton model scaling and QCD
Pion electromagnetic form factor at spacelike momenta
scaling violations for the first
L. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy,
time in a hadron form factor
arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013)
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Implications
 Verify the theory of factorisation in hard exclusive processes,
with dominance of hard contributions to the pion form factor
for Q2>8GeV2.
 Notwithstanding that, normalisation of Fπ(Q2) is fixed by a
pion wave-function whose dilation with respect to
φπasy(x)=6x(1-x) is a definitive signature of DCSB
– Empirical measurement of the strength of DCSB in the
Standard Model – the origin of visible mass
 Close the book on a story that began thirty-five years ago
 Paves the way for a dramatic reassessment of pictures of
proton & neutron structure, which is already well underway
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Tμν
 QCD, an apparently simple element of the Standard Model
 Classically, in the massless theory, the stress-energy tensor,
Tμν, is associated with a conserved Noether current

The Noether current becomes anomalous
 At the most fundamental level, this is the origin of (almost) all
visible nonleptonic mass in the Universe

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I.
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
Abstract
XIII. Enigma of Mass
Standard Model
XIV. Pion Elastic FF
Death of Super- String Theory? XV. Epilogue
Quantum Chromodynamics
Facilities
QCD is a Theory
What is Confinement?
Confinement
Dynamical Chiral Symmetry
Breaking
X. Gap Equation
XI. Calories for quarks
XII. Overarching Science Challenges
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