Published collaborations:
2010-present
Rocio BERMUDEZ (U Michoácan);
Craig Roberts
Physics Division
Chen CHEN (ANL, IIT, USTC);
Xiomara GUTIERREZ-GUERRERO (U Michoácan);
Trang NGUYEN (KSU);
Si-xue QIN (PKU);
Hannes ROBERTS (ANL, FZJ, UBerkeley);
Lei CHANG (ANL, FZJ, PKU);
Students
Huan CHEN (BIHEP);
Early-career
Ian CLOËT (UAdelaide);
scientists
Bruno EL-BENNICH (São Paulo);
David WILSON (ANL);
Adnan BASHIR (U Michoácan);
Stan BRODSKY (SLAC);
Gastão KREIN (São Paulo)
Roy HOLT (ANL);
Mikhail IVANOV (Dubna);
Yu-xin LIU (PKU);
Robert SHROCK (Stony Brook);
Peter TANDY (KSU)
Shaolong WAN (USTC)
Craig Roberts: N & N* Structure in Continuum Strong QCD
15.08.12: USC Summer Academy - 56
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X
Confinement
 Gluon and Quark Confinement
– Empirical Fact: No coloured states have yet been
observed to reach a detector
 However
– There is no agreed, theoretical definition of light-quark
confinement
– Static-quark confinement is irrelevant to real-world QCD
• There are no long-lived, very-massive quarks
• But light-quarks are ubiquitous
 Flux tubes, linear potentials and string tensions play no role in
relativistic quantum field theory with light degrees of freedom.
Craig Roberts: N & N* Structure in Continuum Strong QCD
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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]
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Confinement
 QFT Paradigm: Confinement is expressed through a
dramatic change in the analytic structure of
propagators for coloured particles & can almost be
read from a plot of a states’ dressed-propagator
– Gribov (1978); Munczek (1983); Stingl (1984); Cahill (1989);
Roberts, Williams & Krein (1992); Tandy (1994); …
Confined particle
Normal particle
complex-P2
complex-P2
timelike axis: P2<0
o Real-axis mass-pole splits, moving into pair(s) of complex conjugate poles or branch points,
or more complicated nonanalyticities …
o Spectral density no longer positive semidefinite
Craig Roberts: N & N* Structure in Continuum Strong QCD
& hence state cannot exist in observable spectrum
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Craig Roberts: N & N* Structure in Continuum Strong QCD
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Dynamical Chiral
Symmetry Breaking
Whilst confinement is contentious …
DCSB is a fact in QCD
– It is the most important mass generating
mechanism for visible matter in the Universe.
• Responsible for approximately 98% of the
proton’s mass.
• Higgs mechanism is (almost) irrelevant to lightquarks.
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Frontiers of Nuclear Science:
Theoretical Advances
C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50
M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227
In QCD a quark's effective mass
depends on its momentum. The
function describing this can be
calculated and is depicted here.
Numerical simulations of lattice
QCD (data, at two different bare
masses) have confirmed model
predictions (solid curves) that the
vast bulk of the constituent mass
of a light quark comes from a
cloud of gluons that are dragged
along by the quark as it
propagates. In this way, a quark
that appears to be absolutely
massless at high energies (m =0,
red curve) acquires a large
constituent mass at low energies.
Mass from nothing!
DSE prediction of DCSB confirmed
Craig Roberts: N & N* Structure in Continuum Strong QCD
15.08.12: USC Summer Academy - 56
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Frontiers of Nuclear Science:
Theoretical Advances
C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50
M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227
In QCD a quark's effective mass
depends on its momentum. The
function describing this can be
calculated and is depicted here.
Numerical simulations of lattice
QCD (data, at two different bare
masses) have confirmed model
predictions (solid curves) that the
vast bulk of the constituent mass
of a light quark comes from a
cloud of gluons that are dragged
along by the quark as it
propagates. In this way, a quark
that appears to be absolutely
massless at high energies (m =0,
red curve) acquires a large
constituent mass at low energies.
Hint of lattice-QCD support for DSE prediction of violation of reflection positivity
Craig Roberts: N & N* Structure in Continuum Strong QCD
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12GeV
The Future of JLab
 Jlab 12GeV: This region
scanned by 2<Q2<9 GeV2
elastic & transition form
factors.
Craig Roberts: N & N* Structure in Continuum Strong QCD
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The Future of
Drell-Yan
 Valence-quark PDFs and
PDAs probe this critical and
complementary region
Craig Roberts: N & N* Structure in Continuum Strong QCD
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 Search for exotic hadrons
 Exploit opportunities provided by new data on
nucleon elastic and transition form factors
 Precision experimental study of valence region, and
theoretical computation of distribution functions
and distribution amplitudes
 Develop QCD as a probe for physics beyond the
Standard Model
Craig Roberts: N & N* Structure in Continuum Strong QCD
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 Search for exotic hadrons
 Exploit opportunities provided by new data on
nucleon elastic and transition form factors
 Precision experimental study of valence region, and
theoretical computation of distribution functions
and distribution amplitudes
 Develop QCD as a probe for physics beyond the
Standard Model
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Charting the interaction
between light-quarks
Process-independent αS(Q2)
This is a well-posed problem whose solution is
→ unified description of
observables
an elemental goal of modern hadron physics.
The answer provides QCD’s running coupling.
 Confinement can be related to the analytic properties of QCD's
Schwinger functions.
 Question of light-quark confinement is thereby translated into the
challenge of charting the infrared behavior
of QCD's universal β-function
 Through QCD's DSEs, the pointwise behaviour of the β-function
determines the pattern of chiral symmetry breaking.
 DSEs connect β-function to experimental observables. Hence,
comparison between computations and observations of
o Hadron spectrum, Elastic & transition form factors, Parton distribution fns
can be used to chart β-function’s long-range behaviour.
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Dichotomy of the pion
Goldstone mode
and bound-state
 Goldstone’s theorem
has a pointwise expression in QCD;
Namely, in the chiral limit the wave-function for the twobody bound-state Goldstone mode is intimately connected
with, and almost completely specified by, the fully-dressed
one-body propagator of its characteristic constituent
• The one-body momentum is equated with the relative momentum
of the two-body system
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Craig Roberts: N & N* Structure in Continuum Strong QCD
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Empirical status of the Pion’s
valence-quark distributions
Pion
 Owing to absence of pion targets, the pion’s valence-quark
distribution functions are measured via the Drell-Yan process:
π p → μ+ μ− X
 Three experiments: CERN (1983 & 1985)
and FNAL (1989). No more recent
experiments because theory couldn’t
even explain these!
 Problem
Conway et al. Phys. Rev. D 39, 92 (1989)
Wijesooriya et al. Phys.Rev. C 72 (2005) 065203
PDF behaviour at large-x inconsistent
with pQCD; viz,
expt. (1-x)1+ε
cf. QCD (1-x)2+γ
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Models of the Pion’s
valence-quark distributions
Pion
 (1−x)β with β=0 (i.e., a constant – any fraction is equally probable! )
– AdS/QCD models using light-front holography
– Nambu–Jona-Lasinio models, when a translationally invariant
regularization is used
 (1−x)β with β=1
– Nambu–Jona-Lasinio NJL models with a hard cutoff
– Duality arguments produced by some theorists
 (1−x)β with 0<β<2
– Relativistic constituent-quark models, with power-law depending on
the form of model wave function
 (1−x)β with 1<β<2
– Instanton-based models, all of which have incorrect large-k2 behaviour
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Models of the Pion’s
valence-quark distributions
Pion
 (1−x)β with β=0 (i.e., a constant – any fraction is equally probable! )
– AdS/QCD models using light-front holography
– Nambu–Jona-Lasinio models, when a translationally invariant
regularization is used
 (1−x)β with β=1
– Nambu–Jona-Lasinio NJL models with a hard cutoff
– Duality arguments produced by some theorists
 (1−x)β with 0<β<2
– Relativistic constituent-quark models, depending on the form of
model wave function
 (1−x)β with 1<β<2
– Instanton-based models
Craig Roberts: N & N* Structure in Continuum Strong QCD
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DSE prediction of the Pion’s
valence-quark distributions
Pion
 Consider a theory in which quarks scatter via a vector-boson
exchange interaction whose k2>>mG2 behaviour is (1/k2)β,
 Then at a resolving scale Q0
uπ(x;Q0) ~ (1-x)2β
namely, the large-x behaviour of the quark distribution
function is a direct measure of the momentum-dependence
of the underlying interaction.
 In QCD, β=1 and hence
QCD u
2
(x;Q
)
~
(1-x)
π
0
Craig Roberts: N & N* Structure in Continuum Strong QCD
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DSE prediciton of the Pion’s
valence-quark distributions
Pion
 Consider a theory in which quarks scatter via a vector-boson
exchange interaction whose k2>mG2 behaviour is (1/k2)β,
 Then at a resolving scale Q0
uπ(x;Q0) ~ (1-x)2β
namely, the large-x behaviour of the quark distribution
function is a direct measure of the momentum-dependence
of the underlying interaction.
 In QCD, β=1 and hence
QCD u
2
(x;Q
)
~
(1-x)
π
0
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Essentially nonperturbative domain
Pion
“Model Scale”
 At what scale Q0 should the
prediction be valid?
 Hitherto, PDF analyses within
models have used the resolving
scale Q0 as a parameter, to be
chosen by requiring agreement
between the model and lowmoments of the PDF that are
determined empirically.
 Modern DSE studies have exposed a natural value for the
model scale; viz., the gluon mass
Q0 ≈ mG ≈ 0.6 GeV ≈ 1/0.33 fm
which is the location of the inflexion point in the chiral-limit
dressed-quark mass function
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Craig Roberts: N & N* Structure in Continuum Strong QCD
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Hecht, Roberts, Schmidt
Phys.Rev. C 63 (2001) 025213
Reanalysis of qvπ(x)
 After first DSE computation, the “Conway et al.” data were reanalysed, this time at
next-to-leading-order (Wijesooriya et al. Phys.Rev. C 72 (2005) 065203)
 The new analysis produced a much larger exponent than initially obtained; viz.,
β=1.87, but now it disagreed equally with model results and the DSE prediction
 NB. Within pQCD, one can readily understand why adding a higher-order
correction leads to a suppression of qvπ(x) at large-x.
 New experiments were
proposed … for accelerators
that do not yet exist but the
situation remained
otherwise unchanged
 Until the publication of
Distribution Functions of the Nucleon
and Pion in the Valence Region, Roy J.
Holt and Craig D. Roberts,
arXiv:1002.4666 [nucl-th], Rev. Mod.
Phys. 82 (2010) pp. 2991-3044
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Distribution Functions of the Nucleon and Pion in the
Valence Region, Roy J. Holt and Craig D. Roberts,
arXiv:1002.4666 [nucl-th], Rev. Mod. Phys. 82 (2010)
pp. 2991-3044
Reanalysis of qvπ(x)
 This article emphasised and explained the importance of the
persistent discrepancy between the DSE result and experiment as a
challenge to QCD
 It prompted another reanalysis of the data, which accounted for a
long-overlooked effect: viz., “soft-gluon resummation,”
– Compared to previous analyses, we include next-to-leadinglogarithmic threshold resummation effects in the calculation of the
Drell-Yan cross section. As a result of these, we find a considerably
softer valence distribution at high momentum fractions x than
obtained in previous next-to-leading-order analyses, in line with
expectations based on perturbative-QCD counting rules or DysonAicher, Schäfer, Vogelsang, “Soft-Gluon Resummation and
Schwinger equations.
Craig Roberts: N & N* Structure in Continuum Strong QCD
the Valence Parton Distribution Function of the Pion,”
Phys. Rev. Lett. 105 (2010) 252003
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Trang, Bashir, Roberts & Tandy, “Pion and kaon valencequark parton distribution functions,” arXiv:1102.2448
[nucl-th], Phys. Rev. C 83, 062201(R) (2011) [5 pages]
 Data
as reported byE615
 DSE prediction (2001)
Current status
of qvπ(x)
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Trang, Bashir, Roberts & Tandy, “Pion and kaon valencequark parton distribution functions,” arXiv:1102.2448
[nucl-th], Phys. Rev. C 83, 062201(R) (2011) [5 pages]
 Data after inclusion of
soft-gluon resummation
 DSE prediction and
modern representation
of the data are
indistinguishable
on the valence-quark
domain
 Emphasises the value of
using a single internallyconsistent, wellconstrained framework
to correlate and unify the
description of hadron
observables
Current status
of qvπ(x)
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Craig Roberts: N & N* Structure in Continuum Strong QCD
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Expression exact in QCD
– no corrections
Pion’s valence-quark
Distribution Amplitude
 Reconstruct φπ(x) from moments:
entails
Pion’s Bethe-Salpeter wave function
 Contact interaction
(1/k2)ν , ν=0
Straightforward exercise to show
∫01 dx xm φπ(x) = fπ 1/(1+m) , hence φπ(x)= fπ Θ(x)Θ(1-x)
Craig Roberts: N & N* Structure in Continuum Strong QCD
Work now underway with sophisticated rainbow-ladder
interaction: Chang, Cloët, Roberts, Schmidt & Tandy
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 Using simple
parametrisations of
solutions to the gap and
Bethe-Salpeter equations,
rapid and semiquantitatively
reliable estimates can be
made for φπ(x)
Pion’s valence-quark
Distribution Amplitude
Leading pQCD φπ(x)=6 x (1-x)
– (1/k2)ν=0
– (1/k2)ν =½
– (1/k2)ν =1
 Again, unambiguous and
direct mapping between
behaviour of interaction and
behaviour of distribution
amplitude
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Chang, Cloët, Roberts, Schmidt & Tandy, in progress;
Si-xue Qin, Lei Chang, Yu-xin Liu, Craig Roberts and David Wilson,
arXiv:1108.0603 [nucl-th], Phys. Rev. C 84 042202(R) (2011)
Pion’s valence-quark
Distribution Amplitude
 Preliminary results: rainbow-ladder QCD analyses of
renormalisation-group-improved (1/k2)ν =1 interaction
Leading pQCD
– humped disfavoured but modest flattening
φ (x)=6 x (1-x)
π
 Such behaviour is
only obtained with
(1) Running mass in
dressed-quark
propagators
(2) Pointwise
expression of
Goldstone’s theorem
Eπ(k2) but constant
mass quark
a2>0
a2<0
Reconstructed from
100 moments
Craig Roberts: N & N* Structure in Continuum Strong QCD
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 x ≈ 0 & x ≈ 1 correspond
to maximum relative
momentum within
bound-state
– expose pQCD physics
 x ≈ ½ corresponds to
minimum possible
relative momentum
– behaviour of
distribution around
midpoint is strongly
influence by DCSB
Pion’s valence-quark
Distribution Amplitude
Leading pQCD φπ(x)=6 x (1-x)
 Preliminary results, rainbow-ladder QCD analyses of (1/k2)ν =1 interaction
Craig Roberts: N & N* Structure in Continuum Strong QCD
humped disfavoured but modest flattening
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 x ≈ 0 & x ≈ 1 correspond
to maximum relative
momentum within
bound-state
– expose pQCD physics
 x ≈ ½ corresponds to
minimum possible
relative momentum
– behaviour of
distribution around
midpoint is strongly
influence by DCSB
Pion’s valence-quark
Distribution Amplitude
Leading pQCD φπ(x)=6 x (1-x)
 Preliminary results, rainbow-ladder QCD analyses of (1/k2)ν =1 interaction
Craig Roberts: N & N* Structure in Continuum Strong QCD
humped disfavoured but modest flattening
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Craig Roberts: N & N* Structure in Continuum Strong QCD
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Unification of
Meson & Baryon Properties
 Correlate the properties of meson and baryon ground- and
excited-states within a
single, symmetry-preserving framework
 Symmetry-preserving means:
 Poincaré-covariant
 Guarantee Ward-Takahashi identities
 Express accurately the pattern by which symmetries are
broken
Craig Roberts: N & N* Structure in Continuum Strong QCD
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R.T. Cahill et al.,
Austral. J. Phys. 42 (1989) 129-145
Faddeev Equation
quark exchange
ensures Pauli statistics
quark
 Linear, Homogeneous Matrix equation
diquark composed of stronglydressed quarks bound
by dressed-gluons
 Yields wave function (Poincaré Covariant Faddeev Amplitude)
that describes quark-diquark relative motion within the nucleon
 Scalar and Axial-Vector Diquarks . . .
 Both have “correct” parity and “right” masses
 In Nucleon’s Rest Frame Amplitude has
s−, p− & d−wave correlations
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Contact
Interaction
 Symmetry-preserving treatment of vector×vector contact
interaction is useful tool for the study of phenomena characterised
by probe momenta less-than the dressed-quark mass, M.
Because: For experimental observables determined by probe
momenta Q2<M2, contact interaction results are not realistically
distinguishable from those produced by the most sophisticated
renormalisation-group-improved kernels.
 Symmetry-preserving regularisation of the contact interaction
serves as a useful surrogate, opening domains which analyses using
interactions that more closely resemble those of QCD are as yet
unable to enter.
 They’re critical in attempts to use data as tool for charting nature of
the quark-quark interaction at long-range; i.e., identifying signals of
the running of couplings and masses in QCD.
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Symmetry-preserving treatment of vectorvector contact-interaction: series of papers
establishes strengths & limitations.
Contact
Interaction
 arXiv:1204.2553 [nucl-th]
Spectrum of hadrons with strangeness
Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
 arXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
Nucleon and Roper electromagnetic elastic and transition form factors,
D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts
 arXiv:1102.4376 [nucl-th], Phys. Rev. C 83, 065206 (2011) [12 pages] ,
π- and ρ-mesons, and their diquark partners, from a contact interaction,
H.L.L. Roberts, A. Bashir, L.X. Gutierrez-Guerrero, C.D. Roberts and David J. Wilson
 arXiv:1101.4244 [nucl-th], Few Body Syst. 51 (2011) pp. 1-25
Masses of ground and excited-state hadrons
H.L.L. Roberts, Lei Chang, Ian C. Cloët and Craig D. Roberts
 arXiv:1009.0067 [nucl-th], Phys. Rev. C82 (2010) 065202 [10 pages]
Abelian anomaly and neutral pion production
Hannes L.L. Roberts, C.D. Roberts, A. Bashir, L. X. Gutiérrez-Guerrero & P. C. Tandy
 arXiv:1002.1968 [nucl-th], Phys. Rev. C 81 (2010) 065202 (5 pages)
Pion form factor from a contact interaction
L. Xiomara Gutiérrez-Guerrero, Adnan Bashir, Ian C. Cloët and C. D. Roberts
Craig Roberts: N & N* Structure in Continuum Strong QCD
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Spectrum of Hadrons
with Strangeness
 Solve gap equation for u & s-quarks
 Input ratio ms /mu = 24 is consistent with modern estimates
 Output ratio Ms /Mu = 1.43 shows dramatic impact of DCSB, even
on the s-quark: Ms-ms = 0.36 GeV = M0
… This is typical of all DSE and lattice studies
 κ = in-hadron condensate rises slowly with mass of hadron
Craig Roberts: N & N* Structure in Continuum Strong QCD
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Spectrum of Mesons
with Strangeness
 Solve Bethe-Salpeter equations for mesons and diquarks
Craig Roberts: N & N* Structure in Continuum Strong QCD
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Spectrum of Mesons
with Strangeness
 Solve Bethe-Salpeter equations for mesons and diquarks
Perhaps underestimate radialground splitting by 0.2GeV
 Computed values for ground-states are greater than the
empirical masses, where they are known.
 Typical of DCSB-corrected kernels that omit resonant
contributions; i.e., do not contain effects that may
phenomenologically be associated with a meson cloud.
Craig Roberts: N & N* Structure in Continuum Strong QCD
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Spectrum of Diquarks
with Strangeness
 Solve Bethe-Salpeter equations for mesons and diquarks
Craig Roberts: N & N* Structure in Continuum Strong QCD
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Spectrum of Diquarks
with Strangeness
 Solve Bethe-Salpeter equations for mesons and diquarks
 Level ordering of diquark correlations is same as that for mesons.
 In all diquark channels, except scalar, mass of diquark’s partner meson
is a fair guide to the diquark’s mass:
o Meson mass bounds the diquark’s mass from below;
o Splitting always less than 0.13GeV and decreases with
increasing meson mass
Craig
Roberts: N & N*channel
Structure in Continuum
Strong QCD owing to DCSB
Scalar
“special”
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Bethe-Salpeter
amplitudes
 Bethe-Salpeter amplitudes are couplings in Faddeev Equation
 Magnitudes for diquarks follow precisely the meson pattern
Craig Roberts: N & N* Structure in Continuum Strong QCD
Owing to DCSB, FE couplings in ½- channels
are 25-times weaker than in ½+ !
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Spectrum of Baryons
with Strangeness
 Solved all Faddeev equations, obtained masses and eigenvectors of
the octet and decuplet baryons.
Craig Roberts: N & N* Structure in Continuum Strong QCD
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Spectrum of Baryons
with Strangeness
 Solved all Faddeev equations, obtained masses and eigenvectors of
the octet and decuplet baryons.
Jülich
EBAC
 As with mesons, computed baryon masses lie uniformly above the
empirical values.
 Success because our results are those for the baryons’ dressedquark cores, whereas empirical values include effects associated
with meson-cloud, which typically produce sizable reductions.
Craig Roberts: N & N* Structure in Continuum Strong QCD
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Structure of Baryons
with Strangeness
 Baryon structure is flavour-blind
Diquark content
Craig Roberts: N & N* Structure in Continuum Strong QCD
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness,
Chen, Chang, Roberts, Wan and Wilson & Nucleon and Roper em
elastic and transition form factors, D. J. Wilson, I. C. Cloët, L.
Chang and C. D. Roberts, arXiv:1112.2212 [nucl-th], Phys. Rev.
C85 (2012) 025205 [21 pages]
Structure of Baryons
with Strangeness
 Baryon structure is flavour-blind
Diquark content
80%
0%
50%
50%
 Jqq=0 content of J=½ baryons is almost
independent of their flavour structure
 Radial excitation of ground-state octet
possess zero scalar diquark content!
 This is a consequence of DCSB
 Ground-state (1/2)+ possess unnaturally
large scalar diquark content
 Orthogonality forces radial excitations to
possess (almost) none at all!
Craig Roberts: N & N* Structure in Continuum Strong QCD
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Spectrum of Hadrons
with Strangeness
 Solved all Faddeev equations, obtained masses and eigenvectors of
the octet and decuplet baryons.
(1/2)(1/2)+
(1/2)+
Craig Roberts: N & N* Structure in Continuum Strong QCD
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arXiv:1204.2553 [nucl-th], Spectrum of hadrons with
strangeness, Chen Chen, L. Chang, C.D. Roberts,
Shaolong Wan and D.J. Wilson
Spectrum of Hadrons
with Strangeness
 Solved all Faddeev equations, obtained masses and eigenvectors of
the octet and decuplet baryons.
 This level ordering has long been a
problem in CQMs with linear or HO
(1/2)confinement potentials
(1/2)+
 Correct ordering owes to DCSB
(1/2)+
Craig Roberts: N & N* Structure in Continuum Strong QCD
 Positive parity diquarks have
Faddeev equation couplings 25times greater than negative parity
diquarks
 Explains why approaches within
which DCSB cannot be realised
(CQMs) or simulations whose
parameters suppress DCSB will both
have difficulty reproducing
experimental ordering
50
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I.C. Cloët, C.D. Roberts, et al.
arXiv:0812.0416 [nucl-th]
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
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: N & N* Structure in Continuum Strong QCD
DSE: “realistic”
pQCD, uncorrelated Ψ
DSE: “contact”
0+ qq only
Melnitchouk et al.
Phys.Rev. D84 (2011) 117501
Distribution of neutron’s
momentum amongst quarks
on the valence-quark domain
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Nucleon to Roper Transition Form Factors
 Extensive CLAS @ JLab Programme has produced the first
measurements of nucleon-to-resonance transition form factors
I. Aznauryan et al.,
Results of the N* Program at JLab
arXiv:1102.0597 [nucl-ex]
 Theory challenge is to
explain the measurements
 Notable result is zero in F2p→N*,
explanation of which is a real
challenge to theory.
 First observation of a zero in
a form factor
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Nucleon to Roper Transition Form Factors
 Extensive CLAS @ JLab Programme has produced the first
measurements of nucleon-to-resonance transition form factors
I. Aznauryan et al.,
Results of the N* Program at JLab
arXiv:1102.0597 [nucl-ex]
 Theory challenge is to
explain the measurements
 Notable result is zero in F2p→N*,
explanation of which is a real
challenge to theory.
 DSE study connects appearance
of zero in F2p→N* with
Solid – DSE
Dashed – EBAC Quark Core
Near match supports
picture of Roper as quark
core plus meson cloud
 axial-vector-diquark dominance in Roper resonance
 and structure of form factors of J=1 state
Nucleon and Roper electromagnetic elastic and transition form
factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts, Phys. Rev.
C85 (2012) 025205 [21 pages]
Γμ,αβ
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Nucleon to Roper Transition Form Factors
 Tiator and Vanderhaeghen – in progress
– Empirically-inferred light-front-transverse
charge density
– Positive core plus negative annulus
 Readily explained by dominance of
axial-vector diquark configuration in Roper
– Considering isospin and charge
Negative d-quark twice as likely to be
delocalised from the always-positive core
than the positive u-quark
d
2
{uu}
u
+
1
{ud}
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Craig Roberts: N & N* Structure in Continuum Strong QCD
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QCD is the most interesting part of the standard
model - Nature’s only example of an essentially
nonperturbative fundamental theory,
 Confinement with light-quarks is not connected in any known
way with a linear potential; not with a potential of any kind.
 Confinement with light-quarks is associated with a dramatic
change in the infrared structure of the parton propagators.
 Dynamical chiral symmetry breaking, the origin of 98% of
visible matter in universe, is manifested unambiguously and
fundamentally in an equivalence between the one- and twobody problem in QCD
 Working together to chart the behaviour of the running
masses in QCD, experiment and theory can potentially answer
the questions of confinement and dynamical chiral symmetry
breaking; a task that currently each alone find hopeless.
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Craig Roberts: N & N* Structure in Continuum Strong QCD
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Universal
Misapprehensions
 Since 1979, DCSB has commonly been associated literally with a spacetimeindependent mass-dimension-three “vacuum condensate.”
 Under this assumption, “condensates” couple directly to gravity in general
relativity and make an enormous contribution to the cosmological constant
QCD condensates  8 GN
 Experimentally, the answer is

4
QCD
2
0
3H
 10
46
Ωcosm. const. = 0.76
 This mismatch is a bit of a problem.
Craig Roberts: N & N* Structure in Continuum Strong QCD
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New Paradigm
“in-hadron condensates”
Craig Roberts: N & N* Structure in Continuum Strong QCD
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“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: N & N* Structure in Continuum Strong QCD
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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
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Some Relevant References
 arXiv:1202.2376, Phys. Rev. C85, 065202 (2012) [9 pages]
Confinement contains condensates
Stanley J. Brodsky, Craig D. Roberts, Robert Shrock, Peter C. Tandy
 arXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(RapCom),
Expanding the concept of in-hadron condensates
Lei Chang, Craig D. Roberts and Peter C. Tandy
 arXiv:1005.4610 [nucl-th], Phys. Rev. C82 (2010) 022201(RapCom.)
New perspectives on the quark condensate,
Brodsky, Roberts, Shrock, Tandy
 arXiv:0905.1151 [hep-th], PNAS 108, 45 (2011)
Condensates in Quantum Chromodynamics and the Cosmological
Constant , Brodsky and Shrock,
 hep-th/0012253
The Quantum vacuum and the cosmological constant problem,
Svend Erik Rugh and Henrik Zinkernagel.
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Contents










Confinement
Dynamical chiral symmetry breaking
Dichotomy of the pion
Pion valence-quark distribution
Pion’s Distribution Amplitude
Grand Unification - Mesons and Baryons
Neutron Structure Function at high x
Nucleon to Roper Transition Form Factors
Epilogue
New Paradigm “in-hadron condensates”
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