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N & N* Structure in Continuum Strong QCD
Craig Roberts
Physics Division
StudentsEarly-career scientists
Published collaborations: 2010-present Rocio BERMUDEZ (U Michoácan);
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); 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)
2
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Craig Roberts: N & N* Structure in Continuum Strong QCD
Confinement
Craig Roberts: N & N* Structure in Continuum Strong QCD
3
Confinement Gluon and Quark Confinement
– Empirical Fact: No coloured states have yet been observed to reach a detectorX
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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.
4
Regge Trajectories? Martinus Veltmann, “Facts and Mysteries in Elementary Particle Physics” (World
Scientific, Singapore, 2003): In time the Regge trajectories thus became the cradle of string theory. Nowadays the Regge trajectories have largely disappeared, not in the least because these higher spin bound states are hard to find experimentally. At the peak of the Regge fashion (around 1970) theoretical physics produced many papers containing families of Regge trajectories, with the various (hypothetically straight) lines based on one or two points only!
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Craig Roberts: N & N* Structure in Continuum Strong QCD
Phys.Rev. D 62 (2000) 016006 [9 pages]
1993: "for elucidating the quantum structure of electroweak interactions in physics"
Craig Roberts: N & N* Structure in Continuum Strong QCD
5
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); …
complex-P2 complex-P2
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 & hence state cannot exist in observable spectrum
Normal particle Confined particle
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timelike axis: P2<0
6
Dynamical Chiral Symmetry Breaking
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Craig Roberts: N & N* Structure in Continuum Strong QCD
Craig Roberts: N & N* Structure in Continuum Strong QCD
7
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 light-
quarks.
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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.
8
DSE prediction of DCSB confirmed
Mass from nothing!
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C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227
Craig Roberts: N & N* Structure in Continuum Strong QCD
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.
9
Hint of lattice-QCD support for DSE prediction of violation of reflection positivity
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C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227
Craig Roberts: N & N* Structure in Continuum Strong QCD
12GeVThe Future of JLab
Jlab 12GeV: This region scanned by 2<Q2<9 GeV2 elastic & transition form factors.
1015.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
The Future of Drell-Yan
Valence-quark PDFs and PDAs probe this critical and complementary region
1115.08.12: USC Summer Academy - 56
π or K
N
Craig Roberts: N & N* Structure in Continuum Strong QCD
12
Science Challenges for the coming decade: 2013-2022
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
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
13
Overarching Science Challenges for the
coming decade: 2013-2022
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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
Discover meaning of confinement, and its relationship to DCSB – the origin of visible mass
Charting the interaction between light-quarks
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 ofo Hadron 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
14
This is a well-posed problem whose solution is an elemental goal of modern hadron physics.The answer provides QCD’s running coupling.
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Process-independent αS(Q2) → unified description of observables
15
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 system
Dichotomy of the pionGoldstone mode and bound-state
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Craig Roberts: N & N* Structure in Continuum Strong QCD
fπ Eπ(p2) = B(p2)
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Craig Roberts: N & N* Structure in Continuum Strong QCD
Looking deeply
17
Empirical status of the Pion’s valence-quark distributions
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!
ProblemConway 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
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
Pion
18
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=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
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
Pion
19
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=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
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
Pion
Completely unsatisfactory. Impossible to suggest that there’s even qualitative agreement!
20
DSE prediction of the Pion’s valence-quark distributions
Consider a theory in which quarks scatter via a vector-boson exchange interaction whose k2>>mG
2 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
Pion
21
Consider a theory in which quarks scatter via a vector-boson exchange interaction whose k2>mG
2 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
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
Pion
22
“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 - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
Pion
Modern DSE studies have exposed a natural value for the model scale; viz., the gluon mass
Q0 ≈ mG ≈ 0.6 GeV ≈ 1/0.33 fmwhich is the location of the inflexion point in the chiral-limit dressed-quark mass function
Esse
ntial
ly n
onpe
rtur
bativ
e do
mai
n
23
QCD-based DSE calculation = (1-
x)2+γ 15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
24
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.
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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. 2991-3044
25
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-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 - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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) 252003
26
Current status of qv
π(x) Data as reported byE615
DSE prediction (2001)
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Craig Roberts: N & N* Structure in Continuum Strong QCD
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]
27
Current status of qv
π(x) Data after inclusion of soft-gluon resummation
DSE prediction andmodern representation of the data are
indistinguishable on the valence-quark domain
Emphasises the value of using a single internally-consistent, well-constrained framework to correlate and unify the description of hadron observables
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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]
28
Pion’s Light-Front Distribution Amplitude15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
Craig Roberts: N & N* Structure in Continuum Strong QCD
29
Reconstruct φπ(x) from moments:
entails
Contact interaction(1/k2)ν , ν=0Straightforward exercise to show∫0
1 dx xm φπ(x) = fπ 1/(1+m) , hence φπ(x)= fπ Θ(x)Θ(1-x)
Pion’s valence-quark Distribution Amplitude
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Pion’s Bethe-Salpeter wave function
Work now underway with sophisticated rainbow-ladder interaction: Chang, Cloët, Roberts, Schmidt & Tandy
Expression exact in QCD – no corrections
Craig Roberts: N & N* Structure in Continuum Strong QCD
30
Pion’s valence-quark Distribution Amplitude
Using 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/k2)ν =1
Again, unambiguous and direct mapping between behaviour of interaction and behaviour of distribution amplitude
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Leading pQCD φπ(x)=6 x (1-x)
Craig Roberts: N & N* Structure in Continuum Strong QCD
31
Pion’s valence-quark Distribution Amplitude
Preliminary results: rainbow-ladder QCD analyses of renormalisation-group-improved (1/k2)ν =1 interaction – humped disfavoured but modest flattening
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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 φπ(x)=6 x (1-x)
Reconstructed from 100 moments
Eπ(k2) but constant mass quark
a2<0
a2>0
Craig Roberts: N & N* Structure in Continuum Strong QCD
32
Pion’s valence-quark Distribution Amplitude
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
15.08.12: USC Summer Academy - 56
Leading pQCD φπ(x)=6 x (1-x)
Preliminary results, rainbow-ladder QCD analyses of (1/k2)ν =1 interaction humped disfavoured but modest flattening
Craig Roberts: N & N* Structure in Continuum Strong QCD
33
Pion’s valence-quark Distribution Amplitude
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
15.08.12: USC Summer Academy - 56
Leading pQCD φπ(x)=6 x (1-x)
Preliminary results, rainbow-ladder QCD analyses of (1/k2)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.
34
Grand Unification15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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
3515.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
Faddeev Equation
Linear, Homogeneous Matrix equationYields 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 correlations36
diquark
quark
quark exchangeensures Pauli statistics
composed of strongly-dressed quarks bound by dressed-gluons
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R.T. Cahill et al.,Austral. J. Phys. 42 (1989) 129-145
37
ContactInteraction
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Craig Roberts: N & N* Structure in Continuum Strong QCD
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
38
Contact Interaction arXiv:1204.2553 [nucl-th]
Spectrum of hadrons with strangenessChen 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. 1-25Masses of ground and excited-state hadronsH.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 productionHannes 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
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Symmetry-preserving treatment of vector-vector contact-interaction: series of papers establishes strengths & limitations.
39
Spectrum of Hadronswith 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
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
40
Spectrum of Mesonswith Strangeness
Solve Bethe-Salpeter equations for mesons and diquarks
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
41
Spectrum of Mesonswith Strangeness
Solve Bethe-Salpeter equations for mesons and diquarks
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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 mayphenomenologically 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. Wilson
42
Spectrum of Diquarkswith Strangeness
Solve Bethe-Salpeter equations for mesons and diquarks
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
43
Spectrum of Diquarkswith Strangeness
Solve Bethe-Salpeter equations for mesons and diquarks
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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: o Meson mass bounds the diquark’s mass from below;o Splitting always less than 0.13GeV and decreases with
increasing meson massScalar channel “special” owing to DCSB
44
Bethe-Salpeter amplitudes
Bethe-Salpeter amplitudes are couplings in Faddeev Equation
Magnitudes for diquarks follow precisely the meson pattern
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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+ !
45
Spectrum of Baryonswith Strangeness
Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons.
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
46
Spectrum of Baryonswith Strangeness
Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons.
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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.
JülichEBAC
47
Structure of Baryonswith Strangeness Baryon structure is flavour-blind
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
arXiv:1204.2553 [nucl-th], Spectrum of hadrons with strangeness, Chen Chen, L. Chang, C.D. Roberts, Shaolong Wan and D.J. Wilson
Diquark content
48
Structure of Baryonswith Strangeness Baryon structure is flavour-blind
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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
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!
80%
50%
50%
0%
49
Spectrum of Hadronswith Strangeness
Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons.
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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)-
50
Spectrum of Hadronswith Strangeness
Solved all Faddeev equations, obtained masses and eigenvectors of the octet and decuplet baryons.
15.08.12: USC Summer Academy - 56
Craig Roberts: N & N* Structure in Continuum Strong QCD
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 ordering
Craig Roberts: N & N* Structure in Continuum Strong QCD
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Neutron 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. RobertsarXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
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DSE: “contact”
Melnitchouk et al. Phys.Rev. D84 (2011) 117501
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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
Theory challenge is toexplain the measurements
Notable result is zero in F2p→N*,
explanation of which is a realchallenge to theory.
First observation of a zero in a form factor
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I. Aznauryan et al., Results of the N* Program at JLabarXiv:1102.0597 [nucl-ex]
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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
Theory challenge is toexplain the measurements
Notable result is zero in F2p→N*,
explanation of which is a realchallenge to theory.
DSE study connects appearanceof zero in F2
p→N* with axial-vector-diquark dominance in Roper resonance and structure of form factors of J=1 state
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I. Aznauryan et al., Results of the N* Program at JLabarXiv:1102.0597 [nucl-ex]
Γμ,αβNucleon 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]
Solid – DSEDashed – EBAC Quark CoreNear match supports picture of Roper as quark core plus meson cloud
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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 bedelocalised from the always-positive core than the positive u-quark
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{uu}
d
2 {ud}
u
1+
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Epilogue
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Epilogue 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 two-body 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.
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QCD is the most interesting part of the standard model - Nature’s only example of an essentially nonperturbative fundamental theory,
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This is not the end
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Craig Roberts: N & N* Structure in Continuum Strong QCD
Universal Misapprehensions
Since 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.
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4620
4
103
8
HG QCDNscondensateQCD
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New Paradigm“in-hadron condensates”
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“Orthodox Vacuum”
Vacuum = “frothing sea” Hadrons = bubbles in that “sea”,
containing nothing but quarks & gluonsinteracting perturbatively, unless they’re near the bubble’s boundary, whereat they feel they’re trapped!
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u
u
ud
u ud
du
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New Paradigm
Vacuum = hadronic fluctuations but no condensates
Hadrons = complex, interacting systemswithin which perturbative behaviour is restricted to just 2% of the interior
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u
u
ud
u ud
du
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Some Relevant References arXiv:1202.2376, Phys. Rev. C85, 065202 (2012) [9 pages]
Confinement contains condensatesStanley 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 condensatesLei 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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