Craig Roberts
Physics Division
1.
Rocio
BERMUDEZ (U
Michoácan
)
;
2.
Xiomara
GUTIERREZ

GUERRERO (
U
Michoácan
)
;
3.
S. HERNÁNDEZ
(
U
Michoácan
)
;
4.
Trang
NGUYEN (KSU)
;
5.
Khépani
RAYA (U
Michoácan
)
;
6.
Hannes
ROBERTS (ANL, FZJ,
UBerkeley
)
;
7.
Chien

Yeah SENG (UW

Mad)
8.
Kun

lun
WANG (
PKU
);
9.
Chen
CHEN
(USTC);
10.
J. Javier
COBOS

MARTINEZ (
U.Sonora
)
;
11.
Mario PITSCHMANN (ANL & UW

Mad)
;
12.
Si

xue
QIN
(U. Frankfurt am Main)
;
13.
Jorge SEGOVIA (ANL)
;
14.
David WILSON (ODU)
;
15.
Lei CHANG (
U.Adelaide
);
16.
Ian CLOËT (ANL)
;
17.
Bruno EL

BENNICH (São Paulo)
;
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18.
Adnan
BASHIR (
U
Michoácan
);
19.
Stan BRODSKY (SLAC);
20.
Gastão
KREIN (São Paulo)
21.
Roy HOLT (ANL);
22.
Mikhail IVANOV (
Dubna
);
23.
Yu

xin
LIU (
PKU
);
24.
Michael RAMSEY

MUSOLF (UW

Mad)
25.
Alfredo RAYA
(
U
Michoácan
);
26.
Sebastian SCHMIDT (IAS

FZJ & JARA);
27.
Robert SHROCK (Stony Brook);
28.
Peter TANDY (KSU);
29.
Tony THOMAS (
U.Adelaide
)
30.
Shaolong
WAN (
USTC
)
Students
Postdocs
Asst. Profs.
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
In my view, it is unlikely that two phenomena,
so critical in the Standard Model and tied to the
dynamical generation of a single mass

scale, can
have different origins and fates.
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Exploit opportunities provided by new data on
hadron
elastic and transition form factors
–
Chart infrared evolution of
Q
C
D
’s coupling and dressed

masses
–
Reveal correlations that are key to baryon structure
–
Expose facts & fallacies in modern descriptions of
hadron
structure
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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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 likely that any extension of the Standard Model
will be based on the paradigm established by
Q
C
D
–
Extended
T
e
c
h
n
i
c
o
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 superconductivity
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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.
”
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8
Folklore
…
Hall

D
Conceptual Design Report(5
)
“
The color field lines between a quark and an anti

quark form flux tubes.
Light quarks & Confinement
Problem:
16
tonnes
of force
makes a lot of
pions
.
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Light quarks & Confinement
Problem:
16
tonnes
of force
makes a lot of
pions
.
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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 light

quarks.
Flux

tube is not the
correct paradigm for
confinement in
hadron
physics
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G. Bali
et al
.,
PoS
LAT2005 (2006) 308
Confinement
QFT Paradigm:
–
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 dressed

propagator for a
coloured
state
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complex

P
2
complex

P
2
o
Real

axis mass

pole splits, moving into pair(s) of complex conjugate singularities,
(or other qualitatively analogous structures
chracterised
by a dynamically generated mass

scale)
o
State described by rapidly damped wave & hence state cannot exist in observable spectrum
Normal particle
Confined particle
timelike axis: P
2
<0
s
≈ 1/
Im
(m)
≈ 1/2
Λ
QCD
≈ ½
fm
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Dynamical
Chiral
Symmetry Breaking
DCSB is a fact in
Q
C
D
–
Dynamical
, not spontaneous
•
Add nothing to
Q
C
D , no Higgs field, nothing!
•
Effect achieved purely through the
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.
–
Just like gluons and quarks, and for the same reasons,
condensates are confined within hadrons.
•
There are
no
vacuum condensates.
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Confinement contains condensates,
S.J. Brodsky, C.D. Roberts, R.
Shrock
and P.C.
Tandy,
arXiv:1202.2376 [
nucl

th
]
,
Phys. Rev. C
85
(2012) 065202
DCSB
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Mass from nothing!
C.D. Roberts,
Prog
. Part.
Nucl
. Phys. 61 (2008) 50
M.
Bhagwat
& P.C. Tandy,
AIP Conf.Proc. 842 (2006) 225

227
In
Q
C
D
, all “constants” of
quantum mechanics are
actually
strongly
momentum
dependent: couplings,
number density, mass, etc.
So, a quark’s mass depends
on its momentum.
Mass function can be
calculated and is depicted
here.
Continuum

and Lattice

Q
C
D
are in agreement: the vast bulk of the light

quark mass comes from a
cloud of gluons, dragged along by the quark as it propagates.
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Valence
quarks
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
Poincaré

invariant macroscopic quantum numbers
–
Via evolution, determines background at LHC
Sea

quark distributions
–
Flavour
content, asymmetry, intrinsic: yes or no?
Answers are essentially
nonperturbative
features of
Q
C
D
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Parton Structure of Hadrons
Need for calculation is
emphasised
by Saga of
pion’s
valence

quark distribution:
o
1989:
u
v
π
~ (1

x)
1
–
inferred from LO

Drell

Yan & disagrees with
Q
C
D
;
o
2001: DSE

Q
C
D
predicts
u
v
π
~ (1

x)
2
argues that distribution
inferred from data
can’t be correct;
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Valence quark distributions in the
pion
, M.B.
Hecht, Craig D. Roberts, S.M. Schmidt
,
nucl

th
/0008049
,
Phys.Rev
. C63 (2001) 025213
.
Parton Structure of Hadrons
Need for calculation is
emphasised
by Saga of
pion’s
valence

quark distribution:
o
1989:
u
v
π
~ (1

x)
1
–
inferred from LO

Drell

Yan & disagrees with
Q
C
D
;
o
2001: DSE

Q
C
D
predicts
u
v
π
~ (1

x)
2
argues that distribution
inferred from data
can’t be correct;
o
2010: NLO reanalysis including
soft

gluon
resummation
,
inferred distribution agrees
with DSE and
Q
C
D
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Soft

gluon
resummation
and the valence
parton
distribution function of the
pion
,
M.
Aicher
, A. Schafer,
W.
Vogelsang
,
Phys.Rev.Lett
. 105 (2010)
252003
,
arXiv:1009.2481
[
hep

ph]
Valence quark distributions in the
pion
, M.B.
Hecht, Craig D. Roberts, S.M. Schmidt
,
nucl

th
/0008049
,
Phys.Rev
. C63 (2001) 025213
.
Pion’s
valence

quark
Distribution Amplitude
Same methods can be used to compute
φ
π
(x)
= 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.
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]
.
Pion’s
valence

quark
Distribution Amplitude
Both kernels agree: marked broadening of
φ
π
(x), which owes to DCSB
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Asymptotic
RL
DB
This may be claimed because
PDA is computed at a low
renormalisation
scale in the
chiral
limit, whereat the
quark mass function owes
entirely to DCSB.
Difference between RL and
DB results is readily
understood:
B(p
2
)
is more
slowly varying with DB kernel
and hence a more
balanced
result
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
Both kernels agree: marked broadening of
φ
π
(x), which owes to DCSB
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Asymptotic
RL
DB
This may be claimed because
PDA is computed at a low
renormalisation
scale in the
chiral
limit, whereat the
quark mass function owes
entirely to DCSB.
Difference between RL and
DB results is readily
understood:
B(p
2
)
is more
slowly varying with DB kernel
and hence a more
balanced
result
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
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Established a one

to

one connection
between DCSB and the
pointwise
form of the
pion’s
wave function.
Dilation measures the rate at which dressed

quark
approaches the asymptotic
bare

parton
limit
Experiments at JLab12 can empirically verify the
behaviour
of
M(p),
and hence
chart the IR limit of QCD
C.D. Roberts,
Prog
. Part.
Nucl
. Phys. 61 (2008) 50
Dilation of
pion’s
wave
function is measurable in
pion’s
electromagnetic
form
factor at JLab12
A

rated:
E12

06

10
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]
.
When is
asymptotic PDA valid?
PDA is a wave function
not directly observable
but PDF is
.
φ
π
asy
(x) can only be a good
approximation to the
pion's
PDA when it is
accurate to write
u
v
π
(x) ≈
δ
(x)
for the
pion's
valence

quark distribution
function.
This is far from valid at
currently accessible scales
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Q
2
=27
GeV
2
This is not
δ
(x)!
Explanation and Prediction of Observables using
Continuum Strong QCD,
I.C
.
Cloët
& C.D. Roberts
When is
asymptotic PDA valid?
When is
asymptopia
reached?
If
u
v
π
(x) ≈
δ
(x),
then
<x> = ∫
0
1
dx
x
u
v
π
(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+d
bar
)
2<x>
2GeV
= 44%
When is
<x>
small?
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25
Explanation and Prediction of Observables using
Continuum Strong QCD,
I.C
.
Cloët
& C.D. Roberts
NLO evolution of PDF, computation of <x>.
Even at LHC energies, light

front fraction of
the
π
momentum:
<x>
dressed valence

quarks
=
25%
<x>
glue
= 54%, <x>
sea

quarks
= 21%
LHC:
16TeV
Evolution in QCD is
LOGARITHMIC
JLab
2GeV
When is
asymptotic PDA valid?
When is
asymptopia
reached?
If
u
v
π
(x) ≈
δ
(x),
then
<x> = ∫
0
1
dx
x
u
v
π
(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+d
bar
)
2<x>
2GeV
= 44%
When is
<x>
small?
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Explanation and Prediction of Observables using
Continuum Strong QCD,
I.C
.
Cloët
& C.D. Roberts
NLO evolution of PDF, computation of <x>.
Even at LHC energies, light

front fraction of
the
π
momentum:
<x>
dressed valence

quarks
=
25%
<x>
glue
= 54%, <x>
sea

quarks
= 21%
LHC:
16TeV
Evolution in QCD is
LOGARITHMIC
JLab
2GeV
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Single interaction kernel,
determined by just 1 parameter
and preserving the one

loop RG

behaviour
of QCD, had unified
F
π
(Q
2
)
and
φ
π
(x)
(and many other
quantities)
New Algorithm
Pion
electromagnetic form factor at
spacelike
momenta
,
Lei Chang
et
al
.
arXiv:1307.0026 [
nucl

th
]
,
Phys. Rev.
Lett
.
in press
DSE 2013
pQCD
obtained with
φ
π
asy
(x)
pQCD
obtained with
φ
π
(x;2GeV),
i.e.,
the PDA appropriate to the
scale of the experiment
15%
DSE 2000
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Single interaction kernel,
determined by just 1 parameter
and preserving the one

loop RG

behaviour
of QCD, has unified
F
π
(Q
2
)
and
φ
π
(x)
(and many other
quantities)
Prediction of
pQCD
obtained when
the
pion
valence

quark PDA has
the form appropriate to the scale
accessible in modern experiments
is markedly different from the
result obtained using the
asymptotic PDA
Pion
electromagnetic form factor at
spacelike
momenta
,
Lei Chang
et
al
.
arXiv:1307.0026 [
nucl

th
]
,
Phys. Rev.
Lett
.
in press
DSE 2013
pQCD
obtained with
φ
π
asy
(x)
pQCD
obtained with
φ
π
(x;2GeV),
i.e.,
the PDA appropriate to the
scale of the experiment
15%
Near agreement between the pertinent
perturbative
QCD prediction and DSE

2013
prediction is striking.
Dominance of hard contributions to the
pion
form factor for
Q
2
>8
GeV
2
.
Normalisation
is fixed by a
pion
wave

function whose dilation with respect to
φ
π
asy
(x)
is
a definitive signature of DCSB
Dynamical
chiral
symmetry breaking
(DCSB)
–
has enormous impact on meson properties.
Must be included in description
and prediction of baryon properties
.
DCSB
is essentially a quantum field theoretical effect.
In quantum field theory
Meson appears as pole in four

point quark

antiquark
Green function
→ Bethe

Salpeter
Equation
Nucleon appears as a pole in a six

point quark Green function
→
Faddeev
Equation
.
Poincaré
covariant
Faddeev
equation
sums all possible exchanges
and interactions that can take place between three dressed

quarks
Tractable equation
is based on the observation that an interaction
which describes
colour

singlet mesons also generates
nonpointlike
quark

quark (
diquark
) correlations in the
colour

antitriplet
channel
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29
R.T. Cahill
et al
.,
Austral. J. Phys. 42 (1989) 129

145
6
3
3
3
SU
c
(3):
Remarks
Diquark
correlations are
not
inserted by hand
Such correlations are a dynamical consequence of strong

coupling in
Q
C
D
The same mechanism that produces an almost
massless
pion
from two dynamically

massive quarks;
i.e., DCSB, forces a strong correlation between two quarks in
colour

antitriplet
channels within a baryon
–
an indirect consequence of Pauli

Gürsey
symmetry
Diquark
correlations are not
pointlike
–
Typically,
r
0+
~ r
π
&
r
1+
~ r
ρ
(actually 10% larger)
–
They have soft form factors
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30
SU(2)
isospin
symmetry of hadrons might
emerge from mixing half

integer spin
particles with their antiparticles.
Faddeev
Equation
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

Q
C
D
effects become evident
–
strangeness content
–
meson

cloud effects
–
etc.
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31
Flavor separation of proton form factors
Very different behavior for
u
&
d
quarks
Means apparent scaling in proton F2/F1 is
purely accidental
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32
Cates, de
Jager
,
Riordan,
Wojtsekhowski
,
PRL 106 (2011) 252003
Q
4
F
2
q
/
k
Q
4
F
1
q
Diquark
correlations!
Poincaré
covariant
Faddeev
equation
–
Predicts scalar and axial

vector
diquarks
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
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33
Cloët
, Eichmann, El

Bennich
,
Klähn
, Roberts,
Few Body Syst. 46 (2009) pp.1

36
Wilson,
Cloët
, Chang, Roberts,
PRC 85 (2012) 045205
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
d
u
=Q
2
/M
2
Visible Impacts
of DCSB
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34
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
Q
2
F
2
p
(Q
2
)
Like the
pion’s
PDA,
Q
2
F
2
p
(Q
2
)
measures the rate at which dressed

quarks become
parton

like:
F
2
p
=0
for bare quark

partons
Therefore,
G
E
p
can’t be zero on
the bare

parton
domain
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
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Craig Roberts: Images of the Origin of Mass (44p)
35
Leads to
Prediction
neutron:proton
G
En
(Q
2
) >
G
Ep
(Q
2
) at Q
2
> 4GeV
2
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
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Craig Roberts: Images of the Origin of Mass (44p)
36
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.,
–
lim
x→1
d
v
(x)/
u
v
(x)
is unambiguous, scale invariant,
nonperturbative
feature of QCD.
步敮楳捲c浩湡瑯爠扥瑷敥渠晲慭敷潲歳
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.
St
ructure functions inferred experimentally on
x
≃
1
are determined theoretically by target's elastic form factors.
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Craig Roberts: Images of the Origin of Mass (44p)
37
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
in press
Neutron Structure
Function at high

x
Valence

quark distributions at
x=1
–
Fixed point under DGLAP evolution
–
Strong discriminator between theories
Algebraic formula
–
P
1
p,s
= contribution to the proton's charge arising from diagrams
with a scalar
diquark
component in both the initial and final
state
–
P
1
p,a
= kindred axial

vector
diquark
contribution
–
P
1
p,m
= contribution to the proton's charge arising from diagrams
with a different
diquark
component in the initial and final state.
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Craig Roberts: Images of the Origin of Mass (44p)
38
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. C
85
(2012) 025205 [21 pages]
Measures relative strength
of
axial

vector/scalar
diquarks
in proton
Neutron Structure
Function at high

x
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Craig Roberts: Images of the Origin of Mass (44p)
39
d/u=1/2
SU(6
) symmetry
pQCD
, uncorrelated
Ψ
0
+
qq
only,
d/u=0
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
)
d/u=0.28
DSE: “realistic”
Distribution of neutron’s
momentum amongst quarks
on the valence

quark domain
DSE: “contact”
d/u=0.18
Melnitchouk
,
Accardi
et al
.
Phys.Rev
. D84 (2011) 117501
x>0.9
Melnitchouk
, Arrington
et al
.
Phys.Rev.Lett
. 108 (2012) 252001
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. C
85
(2012) 025205 [21 pages]
Neutron Structure
Function at high

x
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Craig Roberts: Images of the Origin of Mass (44p)
40
d/u=1/2
SU(6
) symmetry
pQCD
, uncorrelated
Ψ
0
+
qq
only,
d/u=0
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
)
d/u=0.28
DSE: “realistic”
Distribution of neutron’s
momentum amongst quarks
on the valence

quark domain
DSE: “contact”
d/u=0.18
Melnitchouk
,
Accardi
et al
.
Phys.Rev
. D84 (2011) 117501
x>0.9
Melnitchouk
, Arrington
et al
.
Phys.Rev.Lett
. 108 (2012) 252001
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. C
85
(2012) 025205 [21 pages]
Neutron Structure
Function at high

x
“
While it is quite hazardous to
extrapolate from our limited
x
B
range all the way to
x
B
= 1,
these results appear to disfavor
models of the proton with
d/u=0 at
x
B
= 1
”
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41
Short Range Correlations and the EMC Effect,
L.B. Weinstein
et al
.,
Phys.Rev.Lett
. 106 (2011) 052301
,
arXiv:1009.5666 [
hep

ph]
Figure courtesy
of
D.W.
Higinbotham
Observation:
EMC effect measured in electron DIS at
0.35 <
x
B
< 0.7
, is linearly related to the Short Range
Correlation (SRC) scale factor obtained from electron
inclusive scattering at
x
B
> 1
.
Nucleon spin structure
at very high
x
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Craig Roberts: Images of the Origin of Mass (44p)
42
Similar formulae for nucleon longitudinal
structure functions.
Plainly, 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.
NB.
pQCD
is actually model

dependent: assumes
SU(6)
spin

flavour
wave function for the proton's
valence

quarks and the corollary that a hard
photon may interact only with a quark that
possesses the same
helicity
as the target.
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
in press
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43
The Physics of Hadrons is Unique:
–
Confronting a fundamental theory in which the
elementary degrees

of

freedom are intangible and only
composites reach detectors
Confinement in real

world is NOT understood
But DCSB is understood, and is crucial to any
understanding of
hadron
phenomena
Experimental and theoretical study of the Bound

state problem in continuum QCD promises to
provide many more
predictions
,
insights
and
answers
.
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Craig Roberts: Images of the Origin of Mass (44p)
44
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45
Lattice comparison
Pion’s
valence

quark PDA
Employ the
generalised

Gegenbauer
method described previously
(and in
Phys.
Rev
.
Lett
.
110
(2013) 132001 (2013) [5 pages]
)
.
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Craig Roberts: Images of the Origin of Mass (44p)
46
Lattice

QCD
=> one nontrivial
moment:
<(2x

1)
2
> = 0.27
±
0.04
Legend
•
Solid = DB (Best) DSE
•
Dashed = RL DSE
•
Dotted (black) = 6 x (1

x)
•
Dot

dashed = midpoint
lattice; and the yellow
shading exhibits band
allowed by lattice errors
φ
π
~ x
α
(1

x)
α
α
=0.35
+0.32 = 0.67

0.24 = 0.11
DB
α
=0.31 but 10% a
2
<0
RL
α
=0.29 and 0% a
2
V. Braun
et al
., PRD 74 (2006) 074501
Pion
distribution amplitude from lattice

QCD,
I.C
.
Cloët
et
al
.
arXiv:1306.2645 [
nucl

th
]
When is
asymptotic PDA valid?
Under leading

order
evolution, the PDA remains
broad to
Q
2
>100
GeV
2
Feature signals persistence
of the influence of
dynamical
chiral
symmetry
breaking.
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Craig Roberts: Images of the Origin of Mass (44p)
47
Consequently, the asymptotic distribution,
φ
π
asy
(x)
, is a poor approximation to the
pion's
PDA
at all such scales that are either currently accessible or
foreseeable in experiments on
pion
elastic and transition form factors.
Thus, related expectations based on
φ
π
asy
(x)
should be revised.
asymptotic
4 GeV
2
100 GeV
2
Pion
distribution amplitude from lattice

QCD,
I.C
.
Cloët
et
al
.
arXiv:1306.2645 [
nucl

th
]
,
Phys. Rev.
Lett
.
111
(2013) 092001 [5 pages]
Flavor separation of proton form factors
Visible Impacts of DCSB
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48
Effect driven primarily by electric
form factor of doubly

represented
u

quark
u

quark is 4

times more likely than
d

quark to be involved in hard
interaction
So …
G
Ep
u
≈
G
Ep
Singly

represented
d

quark is
usually sequestered inside a soft
diquark
correlation
So, although it also becomes
parton

like more quickly as
α
increases, that is hidden from view
d

quark
u

quark
I.C.
Cloët
& C.D. Roberts … continuing
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Craig Roberts: Images of the Origin of Mass (44p)
49
“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!
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Craig Roberts: Images of the Origin of Mass (44p)
50
u
u
u
d
u
u
d
d
u
New Paradigm
Vacuum =
hadronic
fluctuations
but no condensates
Hadrons = complex, interacting systems
within which
perturbative
behaviour
is
restricted to just 2% of the interior
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51
u
u
u
d
u
u
d
d
u
Regge
Trajectories?
Martinus
Veltmann
, “Facts and Mysteries in Elementary Particle Physics” (World Scientific,
Singapore, 2003):
In time the
Regge
trajectories thus became the cradle of string theory. Nowadays the
Regge
trajectories have largely disappeared, not in the least because these higher spin
bound states are hard to find experimentally. At the peak of the
Regge
fashion (around
1970) theoretical physics produced many papers containing families of
Regge
trajectories,
with the various (hypothetically straight) lines based on one or two points only!
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52
Phys.Rev
. D
62
(2000) 016006
[9 pages]
1993:
"for elucidating the quantum structure
of electroweak interactions in physics"
Systematics
of radial and angular

momentum
Regge
trajectories of light non

strange
qqbar

states“ P.
Masjuan
, E. Ruiz
Arriola
, W.
Broniowski
.
arXiv:1305.3493 [
hep

ph]
Hybrid Hadrons & Lattice QCD
–
Robert Edwards, Baryons13
Heavy
pions
… so, naturally, constituent

quark like spectra
To which potential does it correspond?
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Craig Roberts: Images of the Origin of Mass (44p)
53
arXiv:1104.5152, 1201.2349
Hybrid meson models
–
Robert Edwards, Baryons13
With minimal quark content, , gluonic field can in a color singlet or octet
`constituent’ gluon
in S

wave
`constituent’ gluon
in P

wave
bag model
flux

tube model
arXiv:1104.5152, 1201.2349
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54
Craig Roberts: Images of the Origin of Mass (44p)
Hybrid baryon models
–
Robert Edwards, Baryons13
Minimal quark content, , gluonic field can be in color singlet, octet or
decuplet
bag model
flux

tube model
Now must take into account
permutation
symmetry of quarks and gluonic field
arXiv:1104.5152, 1201.2349
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55
Craig Roberts: Images of the Origin of Mass (44p)
I.
Introduction
II.
Pion
valence

quark distribution
III.
Pion
valence

quark
parton
distribution amplitude
IV.
When is the asymptotic PDA a good approximation?
V.
Charged
pion
elastic form factor
VI.
Nucleon form factors
VII.
Nucleon structure functions at large

x
VIII.
Epilogue
A.
DSE cf. Lattice PDA
&
PDA evolution
B.
GE/GM
flavour
separation
C.
Confinement contains condensates
D.
Regge
Trajectories?
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Craig Roberts: Images of the Origin of Mass (44p)
56
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