Download Strong coupling QCD

Craig Roberts, Physics Division
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: Strong-coupling QCD and the ins and outs of bound-states
19. Lei Chang (U. Adelaide) ;
20. Ian Cloet (ANL) ;
21. Bruno El-Bennich (São Paulo);
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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
U) STRONG INTERACTIONS IN
574.(Nanjing
WE-Heraeus-Seminar:
THE LHC ERA. 79pp
2
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
3
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
4
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
5
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG
INTERACTIONS IN THE LHC ERA. 79pp
6
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG
INTERACTIONS IN THE LHC ERA. 79pp
7
Key Questions for the Future
 What is confinement?
 Where is the mass of the nucleon?
 Where is the nucleon's magnetic moment?
What is the nucleon?
What is a hadron?
…
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
8
Key Questions for the Future
 What is confinement?
 Where is the mass of the nucleon?
 Where is the nucleon's magnetic moment?
What is the nucleon?
What is a hadron?
…
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
9
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
10
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
 Initially imagined that Λ = 1GeV!
 So, JLab was initially built to reach 4GeV.
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
11
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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Particle physics paradigm
Particle physics paradigm
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
12
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: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
13
Critical Theory Needs for JLab12
 Experiment – Goal: accurate measurement of pion form factor
to 6 GeV2; and it can produce a 10% measurement at 9 GeV2
 Experiment – Goal: Accurate measurement of nucleon elastic
and transition form factors to 15 GeV2
 Experiment – Goal: Hadron tomography in
momentum and configuration space
 Critical need for success of Laboratory’s programme
– Insightful computational framework
• Capable of computing hadron wave functions
• Capable of predicting and unifying meson & nucleon
elastic and transition form factors on 0<Q2<15 GeV2
• Possessing direct connection to QCD, so that connection
with established predictions of (perturbative) QCD can
be established
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
14
Contemporary Theory
 Dyson-Schwinger equations
– Insightful computational framework
– Established connection
with predictions of (perturbative) QCD
– Capable of predicting and unifying meson & nucleon
elastic and transition form factors on 0<Q2<20 GeV2
… and beyond
– Capable of predicting pointwise behaviour of hadronic
parton distribution functions/amplitudes
… valence-quark domain is understood
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
15
Significant Progress
on All Fronts
 Novel understanding of gluon and quark
confinement and its consequences
is emerging from quantum field theory
 Arriving at a clear picture of how hadron masses emerge
dynamically in a universe with light quarks
Dynamical Chiral Symmetry Breaking (DCSB)
 Realistic computations of ground-state hadron wave
functions with a direct connection to QCD are now available
 Quark-quark correlations are crucial in hadron structure
and accumulating empirical evidence in support of this
prediction
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
16
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
17
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: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
18
Light quarks & Confinement
Problem:
Pions …
They’re unnaturally light
16 tonnes of force
makes a lot of them.
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
19
Light quarks & Confinement
Problem:
16 tonnes of force
makes a lot of pions.
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
20
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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
21
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: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
22
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
23
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE
LHC ERA. 79pp
24
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: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE
LHC ERA. 79pp
25
 Not just quarks …
 Gluons also have a
gap equation …
 Gluons are cannibals
– a particle species
whose members
become massive by
eating each other!
In QCD: Gluons also
become massive!
mg2 (k 2 ) 
g4
 k
2
g
2
Gluon mass-squared function
Present level of uncertainty using
phenomenology and theory ∼ 30%
Power-law suppressed in
ultraviolet, so invisible in
perturbation theory
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
26
 Gauge boson cannibalism
… a new physics frontier … within the Standard Model
 Asymptotic freedom means
… ultraviolet behaviour of QCD is controllable
 Dynamically generated masses for gluons and quarks means
that QCD dynamically generates its own infrared cutoffs
– Gluons and quarks with
wavelength λ > 2/mass ≈ 1 fm
decouple from the dynamics … Confinement?!
 How does that affect observables?
– It will have an impact in
any continuum study
– Must play a role in gluon saturation ...
In fact, perhaps it’s a harbinger of gluon saturation?
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
27
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
28
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG
INTERACTIONS IN THE LHC ERA. 79pp
 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
Propagation 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)
29
 A quark begins to
propagate in spacetime
 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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
An EIC will enable “3D” measurements relating
to fragmentation and insight into real-world
meson
confinement
meson
meson
Baryon
meson
Real-world confinement is
a dynamical phenomenon,
surrounded by mystery!
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
30
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
31
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
 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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
32
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
33
 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.
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
34
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
35
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: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
36
“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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
37
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 in-vacuum condensates.
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
38
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
39
“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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
40
 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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
41
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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
42
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
43
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
 Last two years, methods have been developed that enable direct
computation of meson light-front wave functions
 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≈0.5
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
44
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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
45
arXiv:1301.0324 [nucl-th], arXiv:1306.2645 [nucl-th],
arXiv:1311.1390 [nucl-th], arXiv:1405.0289 [nucl-th],
arXiv:1406:3353 [nucl-th]
Features of
Ground-state PDAs
 A diverse array of studies since Caraguatatuba (2012) have shown
that ground-state meson PDAs are broad, concave functions
Concave function: no
line segment lies above
any point on the graph
 Camel-humped distributions – popular with some for many years –
are physically unreasonable because they correspond to boundstate amplitudes that disfavour equal momentum partitioning
between valence-quark degrees of freedom
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
46
Pion electromagnetic
form factor
 2013: existing data and
theory – no hint of a
trend toward the socalled asymptotic pQCD
prediction?
 Jlab 12 will allow an
extension of the
Fπ measurement up to a
value of Q2 of about 6
(GeV/c)2
& 10% measurement at 9
GeV2
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
E12-06-101 and E12-07-105
Projected JLab reach
Result imagined by many
to be QCD prediction
Evaluated with φπ = 6x(1-x)
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
47
Pion electromagnetic form factor
 Understanding – 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
 Understanding – 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)
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
48
Explanation and Prediction of Observables using Continuum
Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv:1310.2651
[nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line]
 PDA is a wave function
 not directly observable
but PDF is.
 φπasy(x) can only be a good
approximation to the
pion's PDA when it is
accurate to write
When is
asymptotic PDA valid?
Basic features of the pion valence-quark distribution
function, L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29
Q2=27 GeV2
This is not δ(x)!
uvπ (x) ≈ δ(x)
for the pion's valencequark distribution
function.
 This is far from valid at
currently accessible scales
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
49
Explanation and Prediction of Observables using Continuum
Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv:1310.2651
[nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line]
 When is asymptopia reached?
 If uvπ(x) ≈ δ(x), then
JLab 2GeV
<x> = ∫01 dx x uvπ(x) = 0;
i.e., the light-front
momentum fraction carried
by valence-quarks is ZERO
 Asymptopia is reached
when <x> is “small”
 As usual, the computed
valence-quark distribution
produces (π = u+dbar)
2<x>2GeV = 44%
 When is <x> small?
When is
asymptotic PDA valid?
LHC: 16TeV
Evolution in QCD is LOGARITHMIC
 NLO evolution of PDF, computation of <x>.
 Even at LHC energies, light-front fraction of
the π momentum:
<x>dressed valence-quarks = 21%
<x>glue = 54%, <x>sea-quarks = 25%
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE
LHC ERA. 79pp
50
Explanation and Prediction of Observables using Continuum
Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv:1310.2651
[nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line]
At the
“Planck scale”
Evolution in QCD is LOGARITHMIC
 In the truly
asymptotic
domain, way,
way beyond LHC
energy scales,
gluons and seaquarks share the
momentum of a
hadron, each
with roughly
50% of the
momentum
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
EIC Reach
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE
LHC ERA. 79pp
51
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG
INTERACTIONS IN THE LHC ERA. 79pp
52
GPDs & TMDs
 PDFs … only describe hadron light-front structure
incompletely because inclusive deep inelastic scattering (DIS)
measurements do not yield information about the
distribution of partons in the plane perpendicular to the
bound-state's total momentum; i.e., within the light front.
 Generalised Parton Distributions (GPDs)
– Spatial tomography of hadrons
– Measured in DVCS
 Transverse Momentum-dependent Distributions (TMDs)
– Momentum tomography of hadrons
– Measured in SIDIS
 A new generation of experiments – more than ½ beam time
at JLab – aims to provide the empirical information necessary
to develop a phenomenology of nucleon Wigner distributions.
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
53
GPDs & TMDs
 Principal problem with phenomenology
– If one wishes to use measured GPDs as a means by which to
validate our basic perception of strong interactions in the
Standard Model, then data fitting is inadequate.
 Instead, it is necessary to compute GPDs using a framework
that possesses a direct connection with QCD.
 This observation is highlighted by experience drawn from the
simpler case of the pion's valence-quark PDF (L. Chang et al.,
Phys. Lett. B 737 (2014) pp. 23–29)
–
–
–
–
Phenomenology contradicted QCD predictions
Many claimed QCD was challenged
Until nonperturbative continuum-QCD predictions appeared …
Data reanalysed … now the PDF is seen as a success for QCD
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
54
GPDs – unify & extend
 GPDs unify PDFs and elastic form factors, and extend both
into a new domain
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
55
Pion valence
-quark GPD
 Rainbow-ladder (RL) truncation
– δnxP(ℓ):= δ(n⋅ℓ - x n⋅P), ℓ+R =ηbar ℓ++η ℓP, ℓ-R= η ℓ- + ηbarℓP,
ℓ± = ℓ ± Δ/2, ℓP = ℓ - P.
 Triangle corresponds to the textbook handbag diagram
– Certainly guarantees connection between H(x,ξ,t) and Fπ(t), at same
order of truncation
 However, handbag diagram is not complete set of diagrams in RL
truncation of valence-quark PDF and hence it’s not adequate for
H(x,ξ,t) Basic features of the pion valence-quark distribution
function, L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29
 Correction for PDF is known … Extension of Hπ(x,ξ,t) to all ξ ≠ 0 is
not yet known but ξ =0 can be handled
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
56
Sketching the pion's valence-quark generalised parton distribution,
C. Mezrag, L. Chang, H. Moutarde, C.D. Roberts, J. Rodriguez-Quintero,
F. Sabatié, S.M. Schmidt in progress
 Completely general
expression:
uvπ(x)
Pion valence
-quark GPD
computed directly
from triangle diagram
 Use fact that H(x,ξ,t) can be written as a Radon transform, owing to
its general properties:
ξ =0
 Then … compute handbag diagram plus first-guess correction …
inspect the result … read off the surviving Radon amplitude, F(α,β,t)
… obtain
 Hπ(x,ξ,t) is then completely determined … not just a limited number
of moments but the entire function
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
57
Sketching the pion's valence-quark generalised parton distribution,
C. Mezrag, L. Chang, H. Moutarde, C.D. Roberts, J. Rodriguez-Quintero,
F. Sabatié, S.M. Schmidt in progress
 GPD in impact parameter
space:
Pion valence
-quark GPD
qπ(x
 A true quantum mechanics
density …
… describes the probability
of finding a parton within
the light-front at a
transverse position |bperp|
from the hadron's centre of
transverse momentum
(CoTM)
 Computed result …
… not a guess
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
58
Sketching the pion's valence-quark generalised parton distribution,
C. Mezrag, L. Chang, H. Moutarde, C.D. Roberts, J. Rodriguez-Quintero,
F. Sabatié, S.M. Schmidt in progress
 GPD in impact parameter space:
Pion valence
-quark GPD
qπ(x
 Peaked at (xVm, |bperp|=0) …
peak becomes sharper as
resolving scale, ζ, increases
 Broad at |bperp| =0, becomes
even broader as ζ increases
 Narrowing as x → 1 …
increasing ζ: xVm → 0; GPD
becomes even narrower …
there can’t be many partons
carrying x≃1; i.e., all the
hadron’s light-front momentum
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
59
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
60
 Poincaré covariant Faddeev equation sums all possible
exchanges and interactions that can take place between three
dressed-quarks
 Confinement and DCSB are readily expressed
 Prediction: strong diquark correlations exist within baryons as
a dynamical consequence of DCSB in QCD
– The same mechanism that produces an almost massless pion from
two dynamically-massive quarks forces a strong correlation
between two quarks in colour-antitriplet channels within a baryon
 Diquark correlations are not pointlike
– Typically, r0+ ~ rπ & r1+ ~ rρ (actually 10% larger)
– They have soft form factors
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
61
 Poincaré covariant Faddeev equation sums all possible
exchanges and interactions that can take place between three
dressed-quarks
 Confinement and DCSB are readily expressed
 Prediction: strong diquark correlations exist within baryons as
a dynamical consequence of DCSB in QCD
– The same mechanism that produces an almost massless pion from
two dynamically-massive quarks forces a strong correlation
between two quarks in colour-antitriplet channels within a baryon
 Diquark correlations are not pointlike
– Typically, r0+ ~ rπ & r1+ ~ rρ (actually 10% larger)
– They have soft form factors
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
62
I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via
the proton's charge distribution,
arXiv:1304.0855 [nucl-th], Phys. Rev. Lett. 111 (2013) 101803
Visible Impacts
of DCSB
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
 Apparently small changes in M(p)
within the domain 1<p(GeV)<3
have striking effect on the proton’s
electric form factor
 The possible existence and location of
the zero is determined by behaviour
of Q2F2p(Q2), proton’s Pauli form factor
 Like the pion’s PDA, Q2F2p(Q2)
measures the rate at which dressedquarks become parton-like:
 F2p=0 for bare quark-partons
 Therefore, GEp can’t be zero on
the bare-parton domain
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE63
LHC ERA. 79pp
I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via
the proton's charge distribution,
arXiv:1304.0855 [nucl-th], Phys. Rev. Lett. 111 (2013) 101803
Visible Impacts
of DCSB
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
64
J. Segovia, I.C. Cloët, C.D. Roberts, S.M. Schmidt:
Nucleon and Δ Elastic and Transition Form Factors,
arXiv:1408.2919 [nucl-th], Few Body Systems (in press)
 Proton: if one accelerates the
rate at which the dressed-quark
sheds its cloud of gluons to
become a parton, then zero in
Gep is pushed to larger Q2
 Opposite for neutron!
 Explained by presence of
diquark correlations
Electric Charge
 These features entail that at
x≈ 5 the electric form factor
of the neutral neutron will
become larger than that of
the unit-charge proton!
 JLab12 will probe this
prediction
Leads to Prediction neutron:proton
GEn(Q2) > GEp(Q2) at Q2 > 4GeV2
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
65
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
66
Nucleon spin structure at very high-x
Craig D. Roberts, Roy J. Holt and Sebastian M. Schmidt
arXiv:1308.1236 [nucl-th], Phys. Lett. B 727 (2013) pp. 249–254
Far valence domain
x≃1
 Endpoint of the far valence domain: x ≃ 1, is especially significant
– All familiar PDFs vanish at x=1; but ratios of any two need not
– Under DGLAP evolution, the value of such a ratio is invariant.
 Thus, e.g.,
– limx→1 dv(x)/uv(x)
is unambiguous, scale invariant, nonperturbative feature of QCD.
 keen discriminator between frameworks
that claim to explain nucleon structure.
 Furthermore, Bjorken-x=1 corresponds strictly to the situation in
which the invariant mass of the hadronic final state is precisely that
of the target; viz., elastic scattering.
 Structure functions inferred experimentally on x≃1
are determined theoretically by target's elastic form factors.
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
67
I.C. Cloët, C.D. Roberts, et al.
arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36
D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts
arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
Neutron Structure
Function at high-x
 Valence-quark distributions at x=1
– Fixed point under DGLAP evolution
– Strong discriminator between theories
 Algebraic formula
Measures relative strength
of axial-vector/scalar
diquarks in proton
– P1p,s = contribution to the proton's charge arising from diagrams
with a scalar diquark component in both the initial and final
state
– P1p,a = kindred axial-vector diquark contribution
– P1p,m = contribution to the proton's charge arising from diagrams
with a different diquark component in the initial and final state.
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
68
I.C. Cloët, C.D. Roberts, et al.
arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36
D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts
arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
Neutron Structure
Function at high-x
x>0.9
d/u=1/2
SU(6) symmetry
Deep inelastic scattering
– the Nobel-prize winning
quark-discovery experiments
Reviews:
 S. Brodsky et al.
NP B441 (1995)
 W. Melnitchouk & A.W.Thomas
PL B377 (1996) 11
 N. Isgur, PRD 59 (1999)
 R.J. Holt & C.D. Roberts
RMP (2010)
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
d/u=0.28
DSE: “realistic”
pQCD, uncorrelated Ψ
DSE: “contact”
d/u=0.18
0+ qq only, d/u=0
Melnitchouk, Accardi et al.
Phys.Rev. D84 (2011) 117501
Melnitchouk, Arrington et al.
Phys.Rev.Lett. 108 (2012) 252001
Distribution of neutron’s
momentum amongst quarks
on the valence-quark domain
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC 69
ERA. 79pp
I.C. Cloët, C.D. Roberts, et al.
arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36
D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts
arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
Neutron Structure
Function at high-x
x>0.9
d/u=1/2
SU(6) symmetry
Deep inelastic scattering
– the Nobel-prize winning
quark-discovery experiments
d/u=0.28
DSE: “realistic”
pQCD, uncorrelated Ψ
Reviews:
 S. Brodsky et al.
NP B441 (1995)
 W. Melnitchouk & A.W.Thomas
PL B377 (1996) 11
 N. Isgur, PRD 59 (1999)
 R.J. Holt & C.D. Roberts
RMP (2010)
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
DSE: “contact”
d/u=0.18
0+ qq only, d/u=0
Melnitchouk, Accardi et al.
Phys.Rev. D84 (2011) 117501
Melnitchouk, Arrington et al.
Phys.Rev.Lett. 108 (2012) 252001
Distribution of neutron’s
momentum amongst quarks
onWE-Heraeus-Seminar:
the valence-quark
domain
574.
STRONG INTERACTIONS
IN THE70
LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
71
ERA. 79pp
Nucleon spin structure at very high-x
Craig D. Roberts, Roy J. Holt and Sebastian M. Schmidt
arXiv:1308.1236 [nucl-th], Phys. Lett. B 727 (2013) pp. 249–254
Quark helicity
at large Bjorken-x
 Correlations
between dressed-quarks within the proton
have an enormous impact on nucleon spin structure
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
72
Nucleon spin structure at very high-x
Craig D. Roberts, Roy J. Holt and Sebastian M. Schmidt
arXiv:1308.1236 [nucl-th], Phys. Lett. B 727 (2013) pp. 249–254
Quark helicity
at large Bjorken-x
 Existing data cannot distinguish
between modern pictures of
nucleon structure
 Empirical results for nucleon
longitudinal spin asymmetries on
x ≃ 1 promise to add greatly to
our capacity for discriminating
between contemporary pictures
of nucleon structure.
Craig Roberts: Strong-coupling QCD
and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
73
TMDs
 Eight leading-twist TMDs
 Three of these are nonzero in the collinear limit
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
74
Direction of motion
TMDs …
Transversity … Tensor Charge
 Intrinsic, defining property of the nucleon
… just as significant as axial-charge
 No gluon transversity distribution
 Value of tensor charge places constraints on some extensions of
the Standard Model <PRD85 (2012) 054512>
 Current knowledge of transversity:
SIDIS @HERMES, COMPASS, JLab
 Future SIDIS at JLab (SoLId), EIC, …
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
75
Direction of motion
Pitschmann et al., arXiv:1411.xxxx –
Nucleon tensor charges and electric
dipole moments
TMDs …
Transversity … Tensor Charge
 Presence of diquark
correlations in the
proton wave function
suppresses δu by 50%
cf. SU(6) quark model
prediction
 Axial-vector correlation
is crucial, e.g.: δd is only
nonzero because the
proton wave function
contains axial-vector
correlations; and axialvector suppresses δu
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Data fits
DSE
lattice
models
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
76
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
77
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
78
Future
 Strong self-interactions amongst gluons are a unique feature of QCD
– Plausibly, they make QCD the only known nonperturbatively welldefined theory in Nature
 Gluon cannibalism produces nonperturbatively massive gauge bosons
and dressed-quarks
– It is responsible for 98% of the mass of visible matter in the
Universe
 In this Universe, all readily accessible matter is defined by light quarks
– Confinement is therefore a complex, dynamical phenomenon
unrelated to static potentials in quantum mechanical models
 This is the Standard Model Frontier:
– Predict
– Measure
– Explain
All the phenomena driven by the
gluons that bind us all
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
79
Index
















Key Questions for the Future
Critical Theory Needs for JLab12
QCD is a Theory
Light quarks & Confinement
Quark Gap Equation
In QCD: Gluons also become massive!
Confinement
What is an hadron?
Enigma of mass
Confinement contains condensates
Pion’s valence-quark Distribution
Amplitude
Pion electromagnetic form factor
When is asymptotic PDA valid?
Pion valence -quark GPD
Baryon Structure
Visible Impacts of DCSB
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
 Electric Charge
 Flavor separation of proton form
factors
 Far valence domain x≃1
 TMDs … Transversity … Tensor Charge
 Future
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
80
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
81
 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 wikipedia.org/wiki/Technicolor_(physics)
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
82
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
83
 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: Strong-coupling QCD and the ins and outs of bound-states
84
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
85
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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
86
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
87
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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
88
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. …
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
89
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
90
What is an hadron?
 Answer depends on your frame of reference,
even though truly observable quantities do not!
 Light-front (infinite momentum frame)
– Hadron is viewed as collection of infinitely many weakly interacting
partons
– Bound-state complexity is “factorised off” and parametrised in
nonperturbative distribution amplitudes
– Wave functions are complex but operators are simple
 “Human” frames
– Hadron structure is expressed in Schwinger functions
• propagators and bound-state wave functions
– Computable using known methods in quantum field theory and
expressed in terms of dressed-gluons and quarks, each of which is a
complex, coherent collections of partons.
– Wave functions are simple but operators are complex
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
91
What is an hadron?
 Answer depends on your frame of reference,
even though truly observable quantities do not!
 Light-front (infinite momentum frame)
Descriptions
areascompletely
andweakly
henceinteracting
one
– Hadron
is viewed
collection ofequivalent
infinitely many
partons
can choose whichever is most practical/useful/insightful,
so long as frame-dependence
of numerous
– Bound-state
complexity is “factorised
off” and parametrised in
nonperturbative
amplitudes
interpretationsdistribution
is not forgotten.
– Wave functions are complex but operators are simple
 “Human” frames
– Hadron structure is expressed in Schwinger functions
• propagators and bound-state wave functions
– Computable using known methods in quantum field theory and
expressed in terms of dressed-gluons and quarks, each of which is a
complex, coherent collections of partons.
– Wave functions are simple but operators are complex
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
92
Pion valence
-quark GPD
 Kinematics:
–
–
–
–
–
–
k, n are light-like four-vectors, satisfying k2=0=n2, k⋅n=1;
zperp represents that two-component part of z annihilated by both k, n;
P± = P ± Δ/2
ξ = -n⋅Δ/2n⋅P = skewness: -1 ≤ ξ ≤ 1
t=-Δ2 is the momentum transfer
P2 = t/4-mπ2, P ⋅ Δ=0
 Poincaré invariance:
– Support -1 ≤ x ≤ 1
 GPD also depends on renormalisation scale ζ. Evolution equations
are known: ERBL for |x|<ξ ; DGLAP for |x|>ξ (ξ >0)
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
93
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE 94
LHC ERA. 79pp
Flavor separation of proton form factors
Q4F2q/k
Cates, de Jager,
Riordan, Wojtsekhowski,
PRL 106 (2011) 252003
Q4 F1q
 Very different behavior for u & d quarks
Means apparent scaling in proton F2/F1 is purely accidental
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
THE LHC ERA. 79pp
95
Cloët, Eichmann, El-Bennich, Klähn, Roberts,
Few Body Syst. 46 (2009) pp.1-36
Wilson, Cloët, Chang, Roberts, PRC 85 (2012)
045205
Diquark correlations!
 Poincaré covariant Faddeev equation
– Predicts scalar and axial-vector
diquarks
u
d
=Q2/M2
 Proton's singly-represented d-quark
more likely to be struck in association
with 1+ diquark than with 0+
– form factor contributions involving
1+ diquark are softer
 Doubly-represented u-quark is predominantly linked with harder
0+ diquark contributions
 Interference produces zero in Dirac form factor of d-quark in proton
– Location of the zero depends on the relative probability of finding
1+ & 0+ diquarks in proton
– Correlated, e.g., with valence d/u ratio at x=1
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN
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96