Craig Roberts Physics Division Origin of Mass The 2013 Nobel Prize in Physics was awarded to Higgs and Englert following discovery of the Higgs boson at the Large Hadron Collider ID: 318653
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Slide1
Calories for Quarks
Craig Roberts
Physics DivisionSlide2
Origin of Mass
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.
23.Sep.2014: ECT* (89p)
Craig Roberts: Calories for Quarks: The Origin of Mass
2
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 ModelSlide3
Collaborators: 2012-Present
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);
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Craig Roberts: Calories for Quarks: The Origin of Mass
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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)
Students, Postdocs, Asst. Profs.
Lei Chang (U. Adelaide
)
Ian
Cloet
(ANL)
Bruno
El-
Bennich
(São Paulo);Slide4
Collaborators: 2012-Present
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);
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Craig Roberts: Calories for Quarks: The Origin of Mass
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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 (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)
Students, Postdocs, Asst. Profs.
Lei Chang (U. Adelaide
)
Ian
Cloet
(ANL)
Bruno
El-
Bennich
(São Paulo);Slide5
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Standard ModelSlide6
Standard Model- Formulation23.Sep.2014: ECT* (89p)
Craig Roberts: Calories for Quarks: The Origin of Mass6
The Standard Model of Particle Physics
is a local gauge field theory, which can
be completely expressed in a very compact form
Lagrangian
possesses
U
Y
(1)xSUL(2)
xSUc(3) gauge symmetry19 parameters, which must be determined through comparison with experiment
Physics is an empirical science
U
Y(1)xSUL(2) represents the electroweak theory17 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 seenThis sector is essentially perturbative, so the parameters are readily determinedSUc(3) represents the strong interaction component Just 2 of the parameters are intrinsic to SUc(3) – QCDHowever, 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.Slide7
Standard Model- Complete?
There are certainly phenomena Beyond the Standard ModelNeutrinos have mass, which is not true within the Standard ModelEmpirical evidence: νe ↔ νμ, ντ
… 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 νeVerified and quantified in experiments at the Sudbury Neutrino Observatory23.Sep.2014: ECT* (89p)
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A number of experimental hints and,
almost literally,
innumerably many theoretical speculations about other phenomenaSlide8
Death of Super-
String Theory?
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Top Open Questions in Physics
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Excerpt from the top-10Can 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.
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23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
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Quantum
ChromodynamicsSlide12
Quantum
Chromodynamics
Q
C
D: 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
Q
CDNotwithstanding the 2013 Nobel Prize in Physics, the origin of 98% of the visible mass in the Universe is –
somehow
– found within
QCD23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass12Slide13
Facilities
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13Slide14
FacilitiesQCD
MachinesChinaBeijing Electron-Positron ColliderGermanyCOSY (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)JapanJ-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”23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass14Slide15
Facilities
QCD MachinesUSAThomas 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 Bang23.Sep.2014: ECT* (89p)
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A three dimensional view of the calculated particle paths resulting from collisions occurring within RHIC's
STAR detectorSlide16
Jefferson Lab
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16Slide17
Thomas Jefferson National Accelerator Facility (
JLab)Driving distance: Washington DC to JLab ≈ 270km
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Thomas Jefferson National Accelerator Facility (JLab)
1984 … DoE provided initial funding for research, development and design1987 … Construction began on Continuous Electron Beam Accelerator Facility (CEBAF) - February 131994 … Accelerator reached design energy of 4 GeVConstruction cost in $FY14 ≈ $1-BillionGoal … 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).
23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass18Slide19
Thomas Jefferson National Accelerator Facility (JLab)
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
power
= ( number valence-quarks
– 1 + Δλ ) Δλ=0,1, depending on whether helicity
is conserved or flipped
… prediction of 1/k
2
vector-boson exchange
logarithm = distinctive feature & concrete prediction of QCD
Claims were made that Λ = 1GeV!
So,
JLab
was initially built to reach 4GeV.23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass19Parton model scalingQCD scaling violations
e.g. S. J. Brodsky and G. R. Farrar, Phys. Rev.
Lett
. 31, 1153 (1973)Slide20
Thomas Jefferson National Accelerator Facility (
JLab)1994 – 2004 An enormous number of fascinating experimental resultsIncluding an empirical demonstration that the distribution of charge and magnetisation within the proton are completely different,
Suggesting that quark-quark correlations play a crucial role in nucleon structure
But no sign of parton
model scaling and certainly not of scaling violations23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
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Particle physics
paradigm
Particle physics
paradigmSlide21
Thomas Jefferson National Accelerator Facility (JLab)
2004 … Mission Need Agreed on upgrade of CEBAF (JLab's accelerator) to 12GeV2014 … 12GeV commissioning beams now being delivered to the experimental hallsFinal cost of upgrade is approximately $370-MillionPhysics of
JLab at 12GeV
arXiv:1208.1244 [
hep-ex]23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
21Slide22
What is
Q
C
D
?
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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 nonperturbativelyNo confirmed breakdown over an enormous energy domain: 0 GeV < E < 8 TeVIncreasingly probable that any extension of the Standard Model will be based on the paradigm established by
QCD
Extended T
echnico
l
o
u
r
: 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 Ginzburg-Landau theory of superconductivity23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass23(not an effective theory)QCD is a Theory
wikipedia.org/wiki/Technicolor_(physics)Slide24
What is QCD?
Lagrangian of QCDG =
gluon fieldsΨ = quark fields
The key to complexity in
QCD … gluon field strength tensor
Generates gluon self-interactions, whose consequences are extraordinary
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24Slide25
QED is the archetypal gauge field theory
Perturbatively simple but nonperturbatively undefinedChracteristic 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 !cf.Quantum Electrodynamics23.Sep.2014: ECT* (89p)
Craig Roberts: Calories for Quarks: The Origin of Mass
25Slide26
Relativistic Quantum
Gauge Field Theory:
Interactions mediated by vector
boson exchange
Vector bosons are perturbatively
-massless
Similar interaction in QED
Special feature of QCD – gluon self-interactions
What is
Q
C
D
?
Craig Roberts: Calories for Quarks: The Origin of Mass
263-gluon vertex4-gluon vertex
23.Sep.2014: ECT* (89p)Slide27
Running couplings
Quantum gauge-field theories are all typified by the feature that Nothing is ConstantDistribution 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 themparticle number is generally not conserved in quantum field theoryCouplings and masses are renormalised via processes involving virtual-particles. Such effects make these quantities depend on the energy scale at which one observes them
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QED cf.
QCD? Craig Roberts: Calories for Quarks: The Origin of Mass
28
2004 Nobel Prize in Physics : Gross,
Politzer and Wilczek
fermion
screening
gluon
antiscreening
23.Sep.2014: ECT* (89p)
Add 3-gluon self-interaction
5 x10
-5
=0.7%
500%Slide29
Strong-interaction:
QCDAsymptotically freePerturbation theory is valid and accurate tool at large-
Q2
Hence chiral
limit is definedEssentially nonperturbative for
Q
2
< 2
GeV
2
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Nature’s only (now known) example of a truly nonperturbative, fundamental theory A-priori, no idea as to what such a theory can produceSlide30
Confinement?
Millennium prize of $1,000,000 for proving that
SU
c
(3) gauge theory is mathematically well-defined, which will necessarily prove or disprove the confinement conjecture
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30Slide31
What is Confinement?
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Wilson Loop & the Area Law
23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass32
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=½LThen, evaluate <WC(z, τ)> as a functional integral over gauge-field configurationsIn the strong-coupling limit, the result can be obtained algebraically; viz., <WC(z, τ)> = exp(-V(z) τ ) where V(z) is the potential between the static sources, which behaves as V(z) = σ zLinear potentialσ = String tensionSlide33
Light quarks & Confinement 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.”23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
33
Folklore
…
JLab
Hall-D
Conceptual Design Report(5
)
“
The color field lines between a quark and an anti-quark form flux tubes.
Slide34
Light quarks & ConfinementProblem:
Pions They’re extremely light 16 tonnes of force makes a lot of them.23.Sep.2014: ECT* (89p)
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34Slide35
Light quarks & ConfinementProblem: 16
tonnes of force makes a lot of pions.23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
35Slide36
Light quarks & ConfinementIn the presence of light quarks,
pair creation seems to occur non-localized and instantaneouslyNo flux tube in a theory with light-quarks. Flux-tube is not the correct paradigm for confinement in hadron physics23.Sep.2014: ECT* (89p)
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36
G. Bali et al., PoS
LAT2005 (2006) 308Slide37
Confinement
QFT Paradigm: Confinement is expressed through a dramatic change in the analytic structure of propagators for coloured
statesIt can almost be read from a plot of the dressed-propagator for a coloured
state
23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
37
Normal particle
Confined particle
σ
≈ 1/
Im
(m)
≈ 1/2
Λ
QCD ≈ ½fmReal-axis mass-pole splits, moving into pair(s) of complex conjugate singularities, (or qualitatively analogous structures chracterised by a dynamically generated mass-scale)
State described by rapidly damped wave & hence state cannot exist in observable spectrumSlide38
Plane wave propagation
Feynman propagator for a
fermion describes a Plane Wave
A fermion begins to propagate
It can proceed a long way before undergoing any qualitative changes23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
38
meson
meson
meson
meson
BaryonSlide39
Quark Fragmentation
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
23.Sep.2014: ECT* (89p)
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meson
meson
meson
meson
Baryon
σ
Confinement is a dynamical phenomenon!Slide40
QCDRemarkably simple Lagrangian
density23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
40Slide41
Massless
QCDRemarkably simple Lagrangian densityClassically, 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 Universe23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
41
0Slide42
Massless
QCDRemarkably simple Lagrangian densityDefine the quantum field theory via a Functional Integral, which generalises the Feynman path integral for quantum mechanics.
How does that help?
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0Slide43
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 Mass43
23.Sep.2014: ECT* (89p)Slide44
Nambu –
Jona-LasinioModelCraig Roberts: Calories for Quarks: The Origin of Mass44
Treats a
massless
(chirally-invariant) four-fermion Lagrangian & solves the gap equation in Hartree-Fock approximation (analogous to rainbow truncation)
23.Sep.2014: ECT* (89p)
Dynamical Model of Elementary Particles
Based on an Analogy with Superconductivity. I
Y.
Nambu
and G.
Jona-Lasinio
, Phys. Rev. 122 (1961) 345–358
Dynamical Model Of Elementary Particles
Based On An Analogy With Superconductivity. IIY. Nambu, G. Jona-Lasinio, Phys.Rev. 124 (1961) 246-254Slide45
Chiral SymmetryInteracting gauge theories, in which it makes sense to speak of
massless fermions, have a nonperturbative chiral symmetryA related concept is Helicity, which is the projection of a particle’s spin, J, onto it’s direction of motion:
For a massless
particle, helicity is a Lorentz-invariant spin-observable
λ = ± ; i.e., it’s parallel or antiparallel to the direction of motionObvious:
massless
particles travel at speed of light
hence no observer can overtake the particle and thereby view its momentum as having changed sign
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Gap Equation
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Nambu—Jona-Lasinio Model
Gap equationNJL gap equation
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Free
fermion
piece
InteractionsSlide48
Some algebra ⇒ NJL gap equation is an equation for fermion mass
Chiral limit, m=0Clearly, one solution is M=0. That is the solution in perturbation theory … Start with no mass, end-up 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 3
π2
mG2 = C(M2,1)
NJL model
& a mass gap?
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48
Critical coupling for dynamical mass generation?Slide49
NJL model& a mass gap?
Can one satisfy 3π2 mG
2 = C(M
2,1) ?
C(M2, 1) = 1 − M2 ln [ 1 + 1/M2 ]Monotonically decreasing function of M
Maximum value at
M = 0
; viz.,
C(M
2
=0, 1) = 1Consequently, there is a solution iff
3π2
m
G
2 < 1Typical scale for hadron physics: Λ = 1 GeVThere is a M≠0 solution iff mG2 < (Λ/(3 π2)) = (0.2 GeV)2Interaction strength is proportional to 1/mG2Hence, if interaction is strong enough, then one can start with no mass but end up with a massive, perhaps very massive fermion23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass49Critical coupling for dynamical mass generation!Dynamical Chiral Symmetry Breaking
m
G
=0.17GeV
mG=0.21GeVSlide50
Impact
Appears fairly simple, perhaps, but these two papers have had an enormous impactTogether, cited more than 5950 times
Google Scholar returns ≈ 9820 items for the term “Nambu –
Jona-Lasinio”Defined the paradigm for dynamical chiral
symmetry breaking 23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
50Slide51
DCSB:
Mass from Nothing
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Dynamical
Chiral Symmetry BreakingDCSB is a fact in QCDDynamical, not spontaneous
Add nothing to Q
CD , 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.
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Calories for quarks
One of the most important figures in the Standard Model of Particle Physics
98% of the mass in this room owes to the phenomenon that produces this
behaviour
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53Slide54
Just one of the terms that are summed
in a solution of the simplest, sensible
gap equation
Where does the
mass come from?
Deceptively simply picture
Corresponds to the sum of a countable infinity of diagrams.
NB. QED has 12,672
α
5
diagrams
Impossible to compute this in perturbation theory.
The standard algebraic manipulation
tools are just inadequate
23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass54αS23Slide55
Dynamical
Chiral
Symmetry Breaking
Vacuum Condensates?
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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 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.”
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“Orthodox Vacuum”
Vacuum = “frothing sea” Hadrons = bubbles in that “sea”, containing nothing but quarks & gluons interacting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!23.Sep.2014: ECT* (89p)
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u
u
u
d
u
u
d
d
uSlide58
However, just like gluons and quarks, and for the same reasons:
Condensates are confined within hadrons. There are no vacuum condensates.
Historically, DCSB has come to be associated with the presumed existence of spacetime
-independent condensates that
permeate the Universe.23.Sep.2014: ECT* (89p)
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Confinement contains condensates
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GMOR Relation
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GMOR RelationValuable to highlight the precise form of
the Gell-Mann–Oakes–Renner (GMOR) relation: Eq. (3.4) in Phys.Rev. 175 (1968) 2195 mπ is the
pion’s mass H
χsb 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)Slide62
GMOR is synonymous with “Vacuum Quark Condensate”
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GMOR RelationDemonstrated 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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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)Slide64
Hadron
ChargesMatrix elements associated with hadron form factorsScalar 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. …23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
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“Orthodox Vacuum”
Vacuum = “frothing sea” Hadrons = bubbles in that “sea”, containing nothing but quarks & gluons interacting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!23.Sep.2014: ECT* (89p)
Craig Roberts: Calories for Quarks: The Origin of Mass
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u
u
u
d
u
u
d
d
uSlide66
New Paradigm
Vacuum =
perturbative
hadronic fluctuations but no nonperturbative condensates Hadrons = complex, interacting systems within which perturbative
behaviour
is
restricted to just 2% of the interior
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u
u
u
d
u
u
d
duSlide67
“EMPTY space may really be empty. Though quantum theory suggests that a vacuum should be fizzing with particle activity, it turns out that this paradoxical picture of nothingness may not be needed. A calmer view of the vacuum would also help resolve a nagging inconsistency with
dark energy, the elusive force thought to be speeding up the expansion of the universe
.”
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“Void that is truly empty
solves dark energy puzzle”
Rachel Courtland, New Scientist 4
th
Sept. 2010
Cosmological Constant:
Putting QCD condensates back into hadrons reduces the
mismatch between experiment and theory by a factor of 10
46Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard ModelParadigm shift:In-Hadron Condensates“The biggest embarrassment in theoretical physics.”Slide68
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Grand ChallengeSlide69
Overarching Science Challenges for the coming decade: 2014-2023
Discover the meaning of confinementDetermine 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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Enigma of Mass
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Pion’s Goldberger
-Treiman relationCraig Roberts: Calories for Quarks: The Origin of Mass71
Pion’s
Bethe-
Salpeter amplitude Solution of the Bethe-Salpeter equationDressed-quark propagator
Axial-vector
Ward-Takahashi identity entails
Pseudovector
components
necessarily nonzero.
Cannot be ignored!
Owing to DCSB
& Exact in
Chiral
QCD
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Miracle
:
two body problem solved, almost completely, once solution of one body problem is knownMaris, Roberts and Tandynucl-th/9707003, Phys.Lett. B420 (1998) 267-273 B(k2)Slide72
Enigma of mass
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 QCDHence, 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.
23.Sep.2014: ECT* (89p)
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Parton structure of hadrons
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Valence quarksSlide74
Parton Structure of HadronsValence-quark structure of hadrons
Definitive of a hadron. After all, it’s how we distinguish a proton from a neutronExpresses charge; flavour; baryon number; and other Poincaré-invariant macroscopic quantum numbersVia evolution, determines background at LHCForeseeable 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
23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
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Pion’s
Wave Function
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Craig Roberts: Calories for Quarks: The Origin of Mass
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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 functionφπ(x) = twist-two parton distribution amplitude = projection of the pion’s Poincaré
-covariant wave-function onto the light-frontResults have been obtained with rainbow-ladder DSE kernel, simplest symmetry preserving form; and the best DCSB-improved kernel that is currently available.
x
α (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].Slide77
Pion’s
valence-quark Distribution AmplitudeContinuum-QCD prediction: marked broadening of φπ(x), which owes to DCSB
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Asymptotic
RL
DB
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].Real-world PDAs are squat and fatSlide78
Elastic Scattering
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e(p) + H(q)
→ e(p’) +
H(q
’
)Slide79
Elastic Form Factors
Structure of HadronsElastic form factorsProvide 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 evidentstrangeness contentmeson-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 involvedExample: pseudoscalar-meson elastic electromagnetic form factorα
S(Q2) is the strong running coupling,
φπ
(u) is the meson’s twist-two valence-quark PDAfP is the meson's leptonic decay constant
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It was promised that
JLab
would verify this fundamental predictionSlide81
Pion electromagnetic
form factorIn 2001 – seven years after beginning operations, Jefferson Lab provided the first high precision pion electroproduction data for Fπ between Q
2 values of 0.6 and 1.6 (GeV/c)2
.
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2006 & 2007 – new result, at
Q
2
=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 quark-antiquark pair”disappointment and surprise
Result imagined by many to be
QCD prediction
JLab
DataEvaluated with φπ = 6x(1-x)40 years of lQCD only provides access to this small domain, which is already well-mapped by experimentsSlide82
Pion electromagnetic
form factorYear 2000 prediction for Fπ(Q2) P.Maris
& P.C. Tandy, Phys.Rev. C62 (2000) 055204
Problem … used brute-force computational method … unable to compute for Q2
>4GeV223.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass
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Result imagined by many to be
QCD prediction
JLab
Data
Shape of prediction suggested to many that one might
never
see
parton
model scaling and QCD scaling violations
Factor of three
discrepancy
Evaluated with
φπ = 6x(1-x)Slide83
Pion electromagnetic
form factorPlans 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.
23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass83
Projected
JLab
reach
Will there be any hint of a trend toward the asymptotic
pQCD
prediction?
Result imagined by many to be
QCD prediction
Evaluated with
φπ = 6x(1-x)Slide84
New Algorithm
New Insights
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Result imagined by many to be
QCD prediction
Evaluated with
φ
π
= 6x(1-x)
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
23.Sep.2014: ECT* (89p)
Craig Roberts: Calories for Quarks: The Origin of Mass85Real QCD prediction – obtained with realistic, computed PDA Slide86
Pion electromagnetic form factor
Solution – Part 1Compare data with the real QCD prediction; i.e. the result calculated using the broad pion PDA predicted by modern analyses of continuum QCD Solution – Part 2Algorithm used to compute the PDA can also be employed to compute Fπ(Q
2) directly, to arbitrarily large Q
2
23.Sep.2014: ECT* (89p)Craig Roberts: Calories for Quarks: The Origin of Mass86
Real QCD prediction
– obtained with realistic, computed PDA
Predictions:
JLab
will see maximum
Experiments to 8GeV
2
will see
parton
model scaling and QCD scaling violations for the first time in a hadron form factorPion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013)maximum
Agreement within 15%
Slide87
ImplicationsVerify 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 F
π(Q2) is fixed by a
pion wave-function whose dilation with respect to φ
πasy(x)=6x(1-x) is a definitive signature of DCSBEmpirical measurement of the strength of DCSB in the Standard Model – the origin of visible massClose the book on a story that began thirty-five years agoPaves the way for a dramatic reassessment of pictures of proton & neutron structure, which is already well underway
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Epilogue
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Craig Roberts: Calories for Quarks: The Origin of Mass
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Calories for quarks
QCD, an apparently simple element of the Standard ModelClassically, in the massless theory, the stress-energy tensor, Tμν, is associated with a conserved Noether current
Quantisation
destroys that conservation law
The Noether current becomes anomalousAt the most fundamental level, this is the origin of (almost) all visible
nonleptonic
mass in the Universe
Running masses for the gluons and quarks are the inevitable consequence … and their effects are measurable
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T
μνSlide90
Table of Contents
AbstractStandard Model
Death of Super- String Theory?
Quantum
ChromodynamicsFacilitiesQCD is a Theory
What is Confinement?
Confinement
Dynamical
Chiral
Symmetry Breaking
Gap Equation
Calories for quarks
Overarching Science Challenges
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Craig Roberts: Calories for Quarks: The Origin of Mass90Enigma of MassPion Elastic FFEpilogue