Continuum Strong QCD Craig Roberts Physics Division Students Earlycareer scientists Published collaborations 2010present Rocio BERMUDEZ U Micho á can Chen CHEN ID: 152848
Download Presentation The PPT/PDF document "N & N* Structure in" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
N & N* Structure in Continuum Strong QCD
Craig Roberts
Physics Division
StudentsEarly-career scientists
Published collaborations: 2010-present
Rocio
BERMUDEZ (
U
Micho
á
can
)
;
Chen
CHEN
(ANL, IIT, USTC);
Xiomara
GUTIERREZ-GUERRERO (U
Micho
á
can
)
;
Trang
NGUYEN (KSU)
;
Si-
xue
QIN (PKU)
;
Hannes
ROBERTS (ANL, FZJ,
UBerkeley
)
;
Lei CHANG (ANL, FZJ, PKU)
;
Huan
CHEN (BIHEP)
;
Ian CLOËT (
UAdelaide
)
;
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)Slide2
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD
Confinement
2Slide3
ConfinementGluon and Quark ConfinementEmpirical Fact: No coloured states have yet been observed to reach a detectorCraig Roberts: N & N* Structure in Continuum Strong QCD3
X
15.08.12: USC Summer Academy - 56
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.Slide4
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!
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
4
Phys.Rev. D
62 (2000) 016006 [9 pages]
1993:
"for elucidating the quantum structure of electroweak interactions in physics"Slide5
ConfinementQFT 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-propagatorGribov (1978); Munczek (1983); Stingl (1984); Cahill (1989); Roberts, Williams & Krein (1992); Tandy (1994); …Craig Roberts: N & N* Structure in Continuum Strong QCD5
complex-P
2
complex-P
2
Real-axis mass-pole splits, moving into pair(s) of complex conjugate poles or branch points,
or more complicated
nonanalyticities
…
Spectral density no longer positive
semidefinite
& hence state cannot exist in observable spectrum
Normal particle
Confined particle
15.08.12: USC Summer Academy - 56
timelike
axis: P
2
<0Slide6
Dynamical Chiral
Symmetry Breaking
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
6Slide7
Dynamical Chiral Symmetry BreakingWhilst confinement is contentious …DCSB is a fact in QCDIt 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 light-quarks.
Craig Roberts: N & N* Structure in Continuum Strong QCD
715.08.12: USC Summer Academy - 56Slide8
Frontiers of Nuclear Science:Theoretical Advances 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.Craig Roberts: N & N* Structure in Continuum Strong QCD
8
DSE prediction of DCSB confirmed
Mass from nothing!
15.08.12: USC Summer Academy - 56
C.D. Roberts,
Prog
. Part.
Nucl
. Phys. 61 (2008) 50
M.
Bhagwat
& P.C. Tandy,
AIP Conf.Proc. 842 (2006) 225-227Slide9
Frontiers of Nuclear Science:Theoretical Advances 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.Craig Roberts: N & N* Structure in Continuum Strong QCD
9
Hint of lattice-QCD support for DSE prediction of violation of reflection positivity
15.08.12: USC Summer Academy - 56
C.D. Roberts,
Prog
. Part.
Nucl
. Phys. 61 (2008) 50
M.
Bhagwat
& P.C. Tandy,
AIP Conf.Proc. 842 (2006) 225-227Slide10
12GeVThe 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 QCD10
15.08.12: USC Summer Academy - 56Slide11
The Future of Drell-Yan Valence-quark PDFs and PDAs probe this critical and complementary regionCraig Roberts: N & N* Structure in Continuum Strong QCD
11
15.08.12: USC Summer Academy - 56
π
or K
N Slide12
Science Challenges for the coming decade: 2013-2022
Search for exotic hadronsExploit 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 amplitudesDevelop QCD as a probe for physics beyond the Standard Model15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD12Slide13
Overarching Science Challenges for the coming decade: 2013-2022
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD13
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
Discover meaning of confinement, and its relationship to DCSB – the origin of visible massSlide14
Charting the interaction between light-quarksConfinement 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-functionThrough 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 ofHadron spectrum, Elastic & transition form factors, Parton distribution fnscan be used to chart β-function’s long-range behaviour
.Craig Roberts: N & N* Structure in Continuum Strong QCD
14This is a well-posed problem whose solution is an elemental goal of modern
hadron physics.
The answer provides QC
D’s running coupling.
15.08.12: USC Summer Academy - 56
Process-independent
α
S
(Q
2
)
→ unified description of observablesSlide15
Goldstone’s theorem has a pointwise expression in QCD; Namely, in the chiral limit the wave-function for the two-body 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 systemDichotomy of the pion
Goldstone mode and bound-state
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD15
f
π
E
π
(p
2
) = B(p
2
)Slide16
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD16
Looking deeplySlide17
Empirical status of the Pion’s valence-quark distributionsOwing 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 pQC
D; viz
,
expt. (1-x)
1+
ε
cf.
Q
C
D
(1-x)
2+
γ
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
17
PionSlide18
Models of the Pion’s valence-quark distributions(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
=1Nambu–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<2Instanton
-based models, all of which have incorrect large-k2 behaviour15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
18
PionSlide19
Models of the Pion’s valence-quark distributions(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
=1Nambu–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<2Instanton
-based models15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD
19
Pion
Completely unsatisfactory.
Impossible to suggest that there’s even qualitative agreement!Slide20
DSE prediction of the Pion’s valence-quark distributionsConsider 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
uπ
(x;Q0
) ~ (1-x)
2
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
20
PionSlide21
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 u
π(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
π(x;Q
0) ~ (1-x)2
Completely
unambigous
!
Direct connection between experiment and theory, empowering both as tools of discovery.
DSE
prediciton
of the
Pion’s
valence-quark distributions
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
21
PionSlide22
“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 low-moments of the PDF that are determined empirically. 15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD22
Pion
Modern DSE studies have exposed a natural value for the model scale; viz.,
the gluon
mass
Q
0
≈
m
G
≈
0.6
GeV
≈ 1/0.33 fm
which is the location of the inflexion point in the
chiral
-limit dressed-quark mass function
Essentially
nonperturbative
domainSlide23
QCD-based DSE calculation = (1-x)2+
γ
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
23Slide24
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 predictionNB. Within pQCD
, one can readily understand why adding a higher-order correction leads to a suppression of qvπ(x) at large-x.
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD
24
Hecht, Roberts, Schmidt Phys.Rev. C
63 (2001) 025213
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. 2991-3044Slide25
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 QCDIt 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-leading-logarithmic 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 Dyson-Schwinger equations.15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD
25
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
Aicher, Schäfer, Vogelsang,
“Soft-Gluon
Resummation
and the Valence Parton Distribution Function of the
Pion
,”
Phys. Rev. Lett.
105
(2010) 252003Slide26
Current status of qvπ(x)Data as reported byE615 DSE prediction (2001)15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
26Trang, Bashir, Roberts & Tandy,
“Pion and kaon
valence-quark parton distribution functions,” arXiv:1102.2448 [nucl-th
], Phys.
Rev. C 83
, 062201(R) (2011) [5 pages]Slide27
Current status of qvπ(x)Data after inclusion of soft-gluon resummationDSE prediction and modern representation of the data are
indistinguishable on the valence-quark domainEmphasises
the value of using a single internally-consistent, well-constrained framework to correlate and unify the description of hadron observables15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD
27
Trang, Bashir, Roberts & Tandy,
“
Pion
and
kaon
valence-quark
parton
distribution functions,”
arXiv:1102.2448 [
nucl-th
],
Phys.
Rev
. C
83
, 062201(R) (2011) [5 pages]Slide28
Pion’s
Light-Front Distribution
Amplitude
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
28Slide29
Reconstruct φπ(x) from moments: entailsContact 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)Pion’s valence-quark Distribution Amplitude
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
29
Pion’s
Bethe-
Salpeter
wave function
Work now underway with
sophisticated rainbow-ladder interaction:
Chang, Cloët, Roberts, Schmidt & Tandy
Expression
exact in
Q
C
D
– no correctionsSlide30
Pion’s valence-quark Distribution AmplitudeUsing simple parametrisations of solutions to the gap and Bethe-Salpeter equations, rapid and semiquantitatively reliable estimates can be made for φπ(x)(1/k2)ν=0(1/k2
)ν =½(1/k
2)ν =1Again, unambiguous and direct mapping between behaviour of interaction and behaviour of distribution amplitude
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD
30Leading
pQCD
φπ(x)=6 x (1-x)Slide31
Pion’s valence-quark Distribution AmplitudePreliminary results: rainbow-ladder QCD analyses of renormalisation-group-improved (1/k2)ν =1 interaction – humped
disfavoured but modest flattening
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD31
Such
behaviour
is only
obtained with
(1)
Running mass in dressed-quark propagators
(2)
Pointwise
expression of Goldstone’s theorem
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)
Leading
pQCD
φ
π
(x)=6 x (1-x)
Reconstructed from 100 moments
E
π
(k
2
) but constant mass quark
a
2
<0
a
2
>0Slide32
Pion’s valence-quark Distribution Amplitudex ≈ 0 & x ≈ 1 correspond to maximum relative momentum within bound-stateexpose pQCD physicsx ≈ ½ corresponds to minimum possible relative momentumbehaviour of distribution around midpoint is strongly influence by DCSB15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
32Leading
pQCD φπ(x)=6 x (1-x)
Preliminary
results,
rainbow-ladder Q
C
D
analyses of
(1/k
2
)
ν
=1
interaction
humped
disfavoured
but modest flatteningSlide33
Pion’s valence-quark Distribution Amplitudex ≈ 0 & x ≈ 1 correspond to maximum relative momentum within bound-stateexpose pQCD physicsx ≈ ½ corresponds to minimum possible relative momentumbehaviour of distribution around midpoint is strongly influence by DCSB15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
33Leading
pQCD φπ(x)=6 x (1-x)
Preliminary
results,
rainbow-ladder Q
C
D
analyses of
(1/k
2
)
ν
=1
interaction
humped
disfavoured
but modest flattening
These computations are the first to offer the possibility of directly exposing DCSB –
pointwise
– in the light-front frame.Slide34
Grand Unification15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD34Slide35
Unification of Meson & Baryon PropertiesCorrelate the properties of meson and baryon ground- and excited-states within a single, symmetry-preserving frameworkSymmetry-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
35
15.08.12: USC Summer Academy - 56Slide36
Faddeev EquationLinear, Homogeneous Matrix equationYields wave function (Poincaré Covariant Faddeev Amplitude)
that describes quark-diquark
relative motion within the nucleonScalar and Axial-Vector Diquarks . . . Both have “correct” parity and “
right” massesIn Nucleon’s Rest Frame Amplitude has s−, p− & d−wave correlations
Craig Roberts: N & N* Structure in Continuum Strong QCD36
diquark
quark
quark exchange
ensures Pauli statistics
composed of strongly-dressed quarks bound by dressed-gluons
15.08.12: USC Summer Academy - 56
R.T. Cahill
et al
.,
Austral. J. Phys. 42 (1989) 129-145Slide37
ContactInteraction 15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD37Symmetry-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
.Slide38
Contact InteractionarXiv:1204.2553 [nucl-th] Spectrum of hadrons with strangenessChen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. WilsonarXiv:1112.2212 [nucl-th], Phys. Rev. C
85 (2012) 025205 [21 pages]
Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C. Cloët, L. Chang and C. D. RobertsarXiv: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. C
82
(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
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD38Symmetry-preserving treatment of vector-vector contact-interaction: s
eries of papers establishes strengths & limitations.Slide39
Spectrum of Hadronswith StrangenessSolve gap equation for u & s-quarksInput ratio ms /mu = 24 is consistent with modern estimatesOutput ratio Ms /Mu = 1.43 shows dramatic impact of DCSB, even on the s-quark: Ms
-ms = 0.36 GeV = M
0 … This is typical of all DSE and lattice studiesκ = in-hadron condensate rises slowly with mass of hadron
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD
39
arXiv:1204.2553 [nucl-th],
Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong
Wan and D.J. WilsonSlide40
Spectrum of Mesonswith StrangenessSolve Bethe-Salpeter equations for mesons and diquarks15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD40
arXiv:1204.2553 [
nucl-th], Spectrum of hadrons with strangeness, Chen
Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. WilsonSlide41
Spectrum of Mesonswith StrangenessSolve Bethe-Salpeter equations for mesons and diquarks15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD41
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.
Perhaps underestimate
radial-ground splitting by 0.2GeV
arXiv:1204.2553 [
nucl-th
],
Spectrum of hadrons with strangeness,
Chen
Chen
, L. Chang, C.D. Roberts,
Shaolong
Wan and D.J. WilsonSlide42
Spectrum of Diquarkswith StrangenessSolve Bethe-Salpeter equations for mesons and diquarks15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD42
arXiv:1204.2553 [
nucl-th], Spectrum of hadrons with strangeness,
Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. WilsonSlide43
Spectrum of Diquarkswith StrangenessSolve Bethe-Salpeter equations for mesons and diquarks15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD43
arXiv:1204.2553 [
nucl-th], Spectrum of hadrons with strangeness,
Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
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:
Meson mass bounds the
diquark’s
mass from below;
Splitting always less than 0.13GeV and decreases with
increasing meson mass
Scalar channel “special” owing to DCSBSlide44
Bethe-Salpeter amplitudesBethe-Salpeter amplitudes are couplings in Faddeev EquationMagnitudes for diquarks follow precisely the meson pattern15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
44
arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong
Wan and D.J. Wilson
Owing to DCSB, FE couplings in
½
-
channels are 25-times weaker than
in
½
+
!Slide45
Spectrum of Baryonswith StrangenessSolved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. 15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD45
arXiv:1204.2553 [nucl-th
], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. WilsonSlide46
Spectrum of Baryonswith StrangenessSolved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. 15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD46
arXiv:1204.2553 [nucl-th
], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
As with mesons, computed baryon masses lie uniformly above the empirical values.
Success because our results are those for the baryons’ dressed-quark
cores, whereas empirical values include effects associated with meson-cloud, which typically produce sizable reductions.
Jülich
EBACSlide47
Structure of Baryonswith StrangenessBaryon structure is flavour-blind15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD47
arXiv:1204.2553 [
nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
Diquark contentSlide48
Structure of Baryonswith StrangenessBaryon structure is flavour-blind15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD48
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]
Diquark content
J
qq
=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!
80%
5
0%
5
0%
0%Slide49
Spectrum of Hadronswith StrangenessSolved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. 15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD49
arXiv:1204.2553 [nucl-th
], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
(1/2)+
(1/2)+
(1/2)-Slide50
Spectrum of Hadronswith StrangenessSolved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons. 15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD50
arXiv:1204.2553 [nucl-th
], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
(1/2)+
(1/2)+
(1/2)-
This level ordering has long
been a problem in CQMs with linear or HO confinement potentials
Correct ordering owes to DCSB
Positive parity
diquarks
have
Faddeev
equation couplings 25-times 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 orderingSlide51
Craig Roberts: N & N* Structure in Continuum Strong QCD51Neutron Structure Function at high x
SU(6) symmetry
pQCD
, uncorrelated
Ψ
0
+
qq
only
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
)
DSE: “realistic”
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. C
85
(2012) 025205 [21 pages]
Distribution of neutron’s
momentum amongst quarks
on the valence-quark domain
15.08.12: USC Summer Academy - 56
DSE: “contact”
Melnitchouk
et al
.
Phys.Rev
. D84 (2011) 117501 Slide52
Nucleon to Roper Transition Form FactorsExtensive CLAS @ JLab Programme has produced the first measurements of nucleon-to-resonance transition form factorsTheory challenge is to explain the measurementsNotable result is zero in F2p→N*, explanation of which is a real challenge to theory.First observation of a zero in a form factor15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
52I.
Aznauryan et al., Results of the N* Program at JLab
arXiv:1102.0597 [nucl-ex]Slide53
Nucleon to Roper Transition Form FactorsExtensive CLAS @ JLab Programme has produced the first measurements of nucleon-to-resonance transition form factorsTheory challenge is to explain the measurementsNotable 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 axial-vector-diquark dominance in Roper resonance and structure of form factors of J=1 state
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD
53I. Aznauryan
et al., Results of the N* Program at
JLabarXiv:1102.0597 [
nucl
-ex]
Γ
μ
,
αβ
Nucleon and Roper electromagnetic elastic and transition form factors, D. J. Wilson, I. C.
Cloët
, L. Chang and C. D. Roberts,
Phys.
Rev
. C
85
(2012) 025205 [21 pages]
Solid –
DSE
Dashed – EBAC Quark Core
Near match supports picture of Roper as quark core plus meson cloudSlide54
Nucleon to Roper Transition Form FactorsTiator and Vanderhaeghen – in progressEmpirically-inferred light-front-transverse charge densityPositive core plus negative annulusReadily explained by dominance of axial-vector diquark configuration in RoperConsidering isospin and charge
Negative d-quark twice as likely to be
delocalised from the always-positive core than the positive u-quark
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD
54
{
uu
}
d
2
{
u
d
}
u
1
+Slide55
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD55
EpilogueSlide56
EpilogueConfinement 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 two-body problem in QCDWorking together to chart the
behaviour of the running masses in Q
CD, experiment and theory can potentially answer the questions of confinement and dynamical chiral symmetry breaking
; a task that currently each alone find hopeless.15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD
56
Q
CD is the most interesting part of the standard model - Nature’s only example of an essentially
nonperturbative
fundamental theory, Slide57
This is not the end15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD57Slide58
Universal MisapprehensionsSince 1979, DCSB has commonly been associated literally with a spacetime-independent 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
Experimentally, the answer is
Ωcosm. const. = 0.76
This mismatch is a bit of a problem.15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD58Slide59
New Paradigm“in-hadron condensates”15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD59Slide60
“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!15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD60
u
u
u
d
u
u
d
d
uSlide61
New ParadigmVacuum = hadronic fluctuations but no condensates Hadrons = complex, interacting systems within which perturbative behaviour is restricted to just 2% of the interior15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD61
u
u
u
d
u
u
d
d
uSlide62
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. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(RapCom)
, Expanding the concept of in-hadron
condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1005.4610 [nucl-th], Phys. Rev. C
82 (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
.
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
62Slide63
Contents ConfinementDynamical chiral symmetry breakingDichotomy of the pion Pion valence-quark distribution Pion’s Distribution AmplitudeGrand Unification - Mesons and BaryonsNeutron Structure Function at high x
Nucleon to Roper Transition Form Factors
EpilogueNew Paradigm “in-hadron condensates”
15.08.12: USC Summer Academy - 56Craig Roberts: N & N* Structure in Continuum Strong QCD63