Transcript Slide 1

Craig Roberts
Physics Division
Students
Postdocs
Asst. Profs.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Rocio BERMUDEZ (U Michoácan);
Xiomara GUTIERREZ-GUERRERO (U Michoácan);
S. HERNÁNDEZ (U Michoácan);
Trang NGUYEN (KSU);
Khépani RAYA (U Michoácan);
Hannes ROBERTS (ANL, FZJ, UBerkeley);
Chien-Yeah SENG (UW-Mad)
Kun-lun WANG (PKU);
Chen CHEN (USTC);
J. Javier COBOS-MARTINEZ (U.Sonora);
Mario PITSCHMANN (ANL & UW-Mad);
Si-xue QIN (U. Frankfurt am Main);
Jorge SEGOVIA (ANL);
David WILSON (ODU);
Lei CHANG (U.Adelaide);
Ian CLOËT (ANL);
Bruno EL-BENNICH (São Paulo);
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Adnan BASHIR (U Michoácan);
Stan BRODSKY (SLAC);
Gastão KREIN (São Paulo)
Roy HOLT (ANL);
Mikhail IVANOV (Dubna);
Yu-xin LIU (PKU);
Michael RAMSEY-MUSOLF (UW-Mad)
Alfredo RAYA (U Michoácan);
Sebastian SCHMIDT (IAS-FZJ & JARA);
Robert SHROCK (Stony Brook);
Peter TANDY (KSU);
Tony THOMAS (U.Adelaide)
Shaolong WAN (USTC)
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
2
 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.
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
3
 Exploit opportunities provided by new data on
hadron elastic and transition form factors
– Chart infrared evolution of QCD’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
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
4
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
5
 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 QCD
– Extended Technicolour: electroweak symmetry breaks via a
fermion bilinear operator in a strongly-interacting non-Abelian
theory. (Andersen et al. “Discovering Technicolor” Eur.Phys.J.Plus 126 (2011) 81)
Higgs sector of the SM becomes an effective description of a
more fundamental fermionic theory, similar to the GinzburgLandau theory of superconductivity
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
6
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
7
Light quarks & Confinement
 Folklore … 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: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
8
Light quarks & Confinement
Problem:
16 tonnes of force
makes a lot of pions.
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
9
Light quarks & Confinement
Problem:
16 tonnes of force
makes a lot of pions.
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
10
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: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
11
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 dressedpropagator for a coloured state
Confined particle
Normal particle
complex-P2
complex-P2
timelike axis: P2<0
s ≈ 1/Im(m) ≈ 1/2ΛQCD ≈ ½fm
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
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
12
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
13
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 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.
Craig Roberts: Images of the Origin of Mass (44p)
Confinement contains condensates, S.J. Brodsky, C.D. Roberts, R. Shrock and P.C.
Tandy, arXiv:1202.2376 [nucl-th], Phys. Rev. C85 (2012) 065202
MENU 2013: 30/09-04/10
14
DCSB
C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50
M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227
 In QCD, all “constants” of
quantum mechanics are
actually strongly momentum
dependent: couplings,
Mass from nothing!
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-QCD
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.
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
15
Valence
quarks
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
16
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 QCD
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
17
Valence quark distributions in the pion, M.B.
Hecht, Craig D. Roberts, S.M. Schmidt, nuclth/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: uvπ ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with
QCD;
o 2001: DSE- QCD predicts
uvπ ~ (1-x)2
argues that distribution
inferred from data
can’t be correct;
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
18
Valence quark distributions in the pion, M.B.
Hecht, Craig D. Roberts, S.M. Schmidt, nuclth/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: uvπ ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with
Soft-gluon resummation
QCD;
and the valence parton
distribution function of the
o 2001: DSE- QCD predicts
pion, M. Aicher, A. Schafer,
W. Vogelsang,
uvπ ~ (1-x)2
Phys.Rev.Lett. 105 (2010)
argues that distribution
252003, arXiv:1009.2481
[hep-ph]
inferred from data
can’t be correct;
o 2010: NLO reanalysis including
soft-gluon resummation,
inferred distribution agrees
with DSE and QCD
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
19
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
 Same methods can be used to compute φπ(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.
xα (1-x)α, with α=0.3
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
20
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 φπ(x), which owes to DCSB
 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(p2) is more
slowly varying with DB kernel
and hence a more balanced
result
Asymptotic
DB
RL
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
21
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 φπ(x), which owes to DCSB
 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(p2) is more
slowly varying with DB kernel
and hence a more balanced
result
Asymptotic
DB
RL
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
22
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].
C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50
Pion’s valence-quark
Distribution Amplitude
Dilation of pion’s wave
function is measurable in
pion’s electromagnetic form
factor at JLab12
A-rated: E12-06-10
 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
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
23
Explanation and Prediction of Observables using
Continuum Strong QCD, I.C. Cloët & C.D. Roberts
 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?
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: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
24
Explanation and Prediction of Observables using
Continuum Strong QCD, I.C. Cloët & C.D. Roberts
 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?
Craig Roberts: Images of the Origin of Mass (44p)
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 = 25%
<x>glue = 54%, <x>sea-quarks = 21%
MENU 2013: 30/09-04/10
25
Explanation and Prediction of Observables using
Continuum Strong QCD, I.C. Cloët & C.D. Roberts
 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?
Craig Roberts: Images of the Origin of Mass (44p)
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 = 25%
<x>glue = 54%, <x>sea-quarks = 21%
MENU 2013: 30/09-04/10
26
Pion electromagnetic form factor at spacelike momenta,
Lei Chang et al. arXiv:1307.0026 [nucl-th],
Phys. Rev. Lett. in press
 Single interaction kernel,
determined by just 1 parameter
and preserving the one-loop RGbehaviour of QCD, had unified
Fπ(Q2) and φπ(x) (and many other
quantities)
 New Algorithm
DSE 2000
15%
DSE 2013
pQCD obtained with φπ(x;2GeV),
i.e., the PDA appropriate to the
scale of the experiment
pQCD obtained with φπasy(x)
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
27
Pion electromagnetic form factor at spacelike momenta,
Lei Chang et al. arXiv:1307.0026 [nucl-th],
Phys. Rev. Lett. in press
 Single interaction kernel,
determined by just 1 parameter
and preserving the one-loop RGbehaviour of QCD, has unified
DSE 2013
Fπ(Q2) and φπ(x) (and many other
15%
quantities)
pQCD obtained with φπ(x;2GeV),
 Prediction of pQCD obtained when
i.e., the PDA appropriate to the
the pion valence-quark PDA has
scale of the experiment
the form appropriate to the scale
accessible in modern experiments
pQCD obtained with φπasy(x)
is markedly different from the
result obtained using the
asymptotic PDA
 Near agreement between the pertinent perturbative QCD prediction and DSE-2013
prediction is striking.
 Dominance of hard contributions to the pion form factor for Q2>8GeV2.
 Normalisation is fixed by a pion wave-function whose dilation with respect to φπasy(x) is
a definitive signature of DCSB
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
28
R.T. Cahill et al.,
Austral. J. Phys. 42 (1989) 129-145
 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
Craig Roberts: Images of the Origin of Mass (44p)
SUc(3):
3 3  3 6
MENU 2013: 30/09-04/10
29
Faddeev Equation
Remarks
SU(2) isospin symmetry of hadrons might
emerge from mixing half-integer spin
particles with their antiparticles.
 Diquark correlations are not inserted by hand
Such correlations are a dynamical consequence of strongcoupling in QCD
 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, r0+ ~ rπ & r1+ ~ rρ (actually 10% larger)
– They have soft form factors
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
30
Structure of Hadrons
 Elastic form factors
– Provide vital information about the structure and composition
of the most basic elements of nuclear physics.
– They are a measurable and physical manifestation of the nature
of the hadrons' constituents and the dynamics that binds them
together.
 Accurate form factor data are driving paradigmatic shifts
in our pictures of hadrons and their structure; e.g.,
– role of orbital angular momentum and nonpointlike diquark
correlations
– scale at which p-QCD effects become evident
– strangeness content
– meson-cloud effects
– etc.
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
31
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: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
32
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: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
33
I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks
via the proton's charge distribution, arXiv:1304.0855 [nuclth], Phys. Rev. Lett. 111 (2013) 101803
Visible Impacts
of DCSB
Craig Roberts: Images of the Origin of Mass (44p)
 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)
 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
MENU 2013: 30/09-04/10
34
I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks
via the proton's charge distribution, arXiv:1304.0855 [nuclth], Phys. Rev. Lett. 111 (2013) 101803
Visible Impacts
of DCSB
Leads to Prediction neutron:proton
GEn(Q2) > GEp(Q2) at Q2 > 4GeV2
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
35
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
36
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
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: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
37
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: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
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. 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: Images of the Origin of Mass (44p)
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
MENU 2013: 30/09-04/10
39
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: Images of the Origin of Mass (44p)
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
MENU 2013: 30/09-04/10
40
Short Range Correlations and the EMC Effect,
L.B. Weinstein et al., Phys.Rev.Lett. 106 (2011) 052301,
arXiv:1009.5666 [hep-ph]
Observation: EMC effect measured in electron DIS at
0.35 < xB < 0.7, is linearly related to the Short Range
Correlation (SRC) scale factor obtained from electron
inclusive scattering at xB > 1.
Neutron Structure
Function at high-x
 “While it is quite hazardous to
extrapolate from our limited xB
range all the way to xB = 1,
these results appear to disfavor
models of the proton with
d/u=0 at xB = 1”
Figure courtesy of
D.W. Higinbotham
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
41
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
Nucleon spin structure
at very high x
 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.
Craig Roberts: Images of the Origin of Mass (44p)
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.
MENU 2013: 30/09-04/10
42
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
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 Boundstate problem in continuum QCD promises to
provide many more
predictions, insights and answers.
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
44
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
45
Pion distribution amplitude from lattice-QCD,
I.C. Cloët et al. arXiv:1306.2645 [nucl-th]
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]).
 Lattice-QCD V. Braun et al., PRD 74 (2006) 074501
=> 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
DB α=0.31 but 10% a2<0
RL α=0.29 and 0% a2
φπ~ xα (1-x)α
= 0.67
α=0.35 +0.32
- 0.24 = 0.11
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
46
Pion distribution amplitude from lattice-QCD,
I.C. Cloët et al. arXiv:1306.2645 [nucl-th],
Phys. Rev. Lett. 111 (2013) 092001 [5 pages]
 Under leading-order
evolution, the PDA remains
broad to Q2>100 GeV2
 Feature signals persistence
of the influence of
dynamical chiral symmetry
breaking.
When is
asymptotic PDA valid?
asymptotic
4 GeV2
100 GeV2
 Consequently, the asymptotic distribution,
φπasy(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 φπasy(x) should be revised.
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
47
I.C. Cloët & C.D. Roberts … continuing
Flavor separation of proton form factors
Visible Impacts of DCSB
u-quark
 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 … GEpu
≈ GEp
d-quark
 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
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
48
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
49
“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: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
50
New Paradigm
 Vacuum = hadronic fluctuations
but no 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: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
51
1993: "for elucidating the quantum structure
of electroweak interactions in physics"
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!
Phys.Rev. D 62 (2000) 016006 [9 pages]
Systematics of radial and angular-momentum Regge trajectories of light non-strange qqbarstates“ P. Masjuan, E. Ruiz Arriola, W. Broniowski. arXiv:1305.3493 [hep-ph]
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
52
Hybrid Hadrons & Lattice QCD
– Robert Edwards, Baryons13
arXiv:1104.5152, 1201.2349
 Heavy pions … so, naturally, constituent-quark like spectra
 To which potential does it correspond?
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
53
Hybrid meson models – Robert Edwards, Baryons13
arXiv:1104.5152, 1201.2349
With minimal quark content,
, gluonic field can in a color singlet or octet
`constituent’ gluon
in S-wave
bag model
`constituent’ gluon
in P-wave
flux-tube model
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-
54
Hybrid baryon models – Robert Edwards, Baryons13
arXiv:1104.5152, 1201.2349
Minimal quark content,
, gluonic field can be in color singlet, octet or decuplet
Now must take into account permutation symmetry of quarks and gluonic field
bag model
flux-tube model
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
55
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.
B.
C.
D.
DSE cf. Lattice PDA & PDA evolution
GE/GM flavour separation
Confinement contains condensates
Regge Trajectories?
Craig Roberts: Images of the Origin of Mass (44p)
MENU 2013: 30/09-04/10
56