Images of the origin of mass - MENU 2013

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16 Νοε 2013 (πριν από 3 χρόνια και 4 μήνες)

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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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Craig Roberts: Images of the Origin of Mass (44p)

2

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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Craig Roberts: Images of the Origin of Mass (44p)

3



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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4


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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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10

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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11

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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Craig Roberts: Images of the Origin of Mass (44p)

13

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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Craig Roberts: Images of the Origin of Mass (44p)

15

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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Craig Roberts: Images of the Origin of Mass (44p)

16

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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17

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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Craig Roberts: Images of the Origin of Mass (44p)

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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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19

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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Craig Roberts: Images of the Origin of Mass (44p)

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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56