Craig Roberts, Physics Division. 1.Rocio BERMUDEZ (U Michoácan); 2.Shi CHAO (Nanjing U) ;...
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Transcript of Craig Roberts, Physics Division. 1.Rocio BERMUDEZ (U Michoácan); 2.Shi CHAO (Nanjing U) ;...
Strong coupling QCD – the ins and outs of
bound-statesCraig Roberts, Physics Division
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
2
Collaborators: 2012-Present1. Rocio BERMUDEZ (U Michoácan);2. Shi CHAO (Nanjing U) ;3. Ming-hui DING (PKU);4. Fei GAO (PKU) ;5. S. HERNÁNDEZ (U Michoácan);6. Cédric MEZRAG (CEA, Saclay) ;7. Trang NGUYEN (KSU);8. Khépani RAYA (U Michoácan);9. Hannes ROBERTS (ANL, FZJ, UBerkeley);10. Chien-Yeah SENG (UM-Amherst) ;11. Kun-lun WANG (PKU);12. Shu-sheng XU (Nanjing U) ;13. Chen CHEN (USTC);14. J. Javier COBOS-MARTINEZ (U.Sonora);15. Mario PITSCHMANN (Vienna);16. Si-xue QIN (U. Frankfurt am Main, PKU);17. Jorge SEGOVIA (ANL);18. David WILSON (ODU);
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
22. Adnan BASHIR (U Michoácan);23. Stan BRODSKY (SLAC);24. Gastão KREIN (São Paulo) ;25. Roy HOLT (ANL);26. Yu-xin LIU (PKU);27. Hervé Moutarde (CEA, Saclay) ;28. Michael RAMSEY-MUSOLF (UM-Amherst) ;29. Alfredo RAYA (U Michoácan);30. Jose Rodriguez Qintero (U. Huelva) ;31. Sebastian SCHMIDT (IAS-FZJ & JARA);32. Robert SHROCK (Stony Brook);33. Peter TANDY (KSU);34. Tony THOMAS (U.Adelaide) ;35. Shaolong WAN (USTC) ;36. Hong-Shi ZONG (Nanjing U)
Students, Postdocs, Asst. Profs.
19. Lei Chang (U. Adelaide) ;20. Ian Cloet (ANL) ;21. Bruno El-Bennich (São Paulo);
3
Physics is an
empirical science
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
4
It’s not physics unless it can be tested
empirically.
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
5
It’s not proven
unless it’s verified
experimentally.574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
6
Top Open Questions in
Physics574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
7
Understand the 4% of material that we know
exists 574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
8
Key Questions for the Future
What is confinement? Where is the mass of the nucleon? Where is the nucleon's magnetic moment? What is the nucleon? What is a hadron? …
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Examples of Emergent Phenomena in QCD, the strong-interaction sector of
the Standard Model
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
9
Key Questions for the Future
What is confinement? Where is the mass of the nucleon? Where is the nucleon's magnetic moment? What is the nucleon? What is a hadron? …
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
One cannot properly know what lies beyond the Standard Model unless one first knows what is in the Standard Model
10
Jefferson Lab574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
11
Thomas Jefferson National Accelerator Facility (JLab) One of the primary reasons for building CEBAF/JLab
Prediction: at energy-scales greater than some a priori unknown minimum value, Λ, cross-sections and form factors will behave as
power = ( number valence-quarks – 1 + Δλ ) Δλ=0,1, depending on whether helicity is conserved
or flipped … prediction of 1/k2 vector-boson exchange
logarithm = distinctive feature & concrete prediction of QCD Initially imagined that Λ = 1GeV! So, JLab was initially built to reach 4GeV.
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Parton model scaling
QCD scaling violations
e.g. S. J. Brodsky and G. R. Farrar, Phys. Rev. Lett. 31, 1153 (1973)
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
12
Thomas Jefferson National Accelerator Facility (JLab) 1994 – 2004
o An enormous number of fascinating experimental results
o Including an empirical demonstration that the distribution of charge and magnetisation within the proton are completely different,
o Suggesting that quark-quark correlations play a crucial role in nucleon structure
But no sign of parton model scaling and certainly not of scaling violations
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Particle physics paradigm
Particle physics paradigm
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
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Thomas Jefferson National Accelerator Facility (JLab)
2004 … Mission Need Agreed on upgrade of CEBAF (JLab's accelerator) to 12GeV
2014 … 12GeV commissioning beams now being delivered to the experimental halls
Final cost of upgrade isapproximately $370-Million
Physics of JLab at 12GeV arXiv:1208.1244 [hep-ex]
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
14
Critical Theory Needs for JLab12 Experiment – Goal: accurate measurement of pion form factor
to 6 GeV2; and it can produce a 10% measurement at 9 GeV2
Experiment – Goal: Accurate measurement of nucleon elastic and transition form factors to 15 GeV2
Experiment – Goal: Hadron tomography in momentum and configuration space
Critical need for success of Laboratory’s programme – Insightful computational framework
• Capable of computing hadron wave functions• Capable of predicting and unifying meson & nucleon
elastic and transition form factors on 0<Q2<15 GeV2
• Possessing direct connection to QCD, so that connection with established predictions of (perturbative) QCD can be established
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
15
Contemporary Theory
Dyson-Schwinger equations– Insightful computational framework – Established connection
with predictions of (perturbative) QCD– Capable of predicting and unifying meson & nucleon
elastic and transition form factors on 0<Q2<20 GeV2
… and beyond– Capable of predicting pointwise behaviour of hadronic
parton distribution functions/amplitudes… valence-quark domain is understood
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
16
Significant Progress on All Fronts
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Novel understanding of gluon and quarkconfinement and its consequencesis emerging from quantum field theory
Arriving at a clear picture of how hadron masses emerge dynamically in a universe with light quarks
Dynamical Chiral Symmetry Breaking (DCSB) Realistic computations of ground-state hadron wave functions
with a direct connection to QCD are now available Quark-quark correlations are crucial in hadron structure
and accumulating empirical evidence in support of this prediction
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
17
What is Confinement?
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
18
Light quarks & Confinement
A unit area placed midway between the quarks and perpendicular to the line connecting them intercepts a constant number of field lines, independent of the distance between the quarks. This leads to a constant force between the quarks – and a large force at that, equal to about 16 metric tons.”
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Folklore … JLab Hall-D Conceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes.
19
Light quarks & Confinement
Problem: Pions … They’re unnaturally light16 tonnes of force makes a lot of them.
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
20
Light quarks & Confinement
Problem: 16 tonnes of force makes a lot of pions.
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
21
Light quarks & Confinement In the presence of
light quarks, pair creation seems to occur non-localized and instantaneously
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
G. Bali et al., PoS LAT2005 (2006) 308
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Light quarks & Confinement In the presence of
light quarks, pair creation seems to occur non-localized and instantaneously
No flux tube in a theory with light-quarks.
Flux-tube is not the correct paradigm for confinement in hadron physics
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
G. Bali et al., PoS LAT2005 (2006) 308
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
23
What is Dressing?574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE
LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
24
Quark Gap Equation574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
25
Dynamical Chiral Symmetry Breaking
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
DCSB is a fact in QCD– Dynamical, not spontaneous
• Add nothing to QCD , No Higgs field, nothing! Effect achieved purely throughquark+gluon dynamics.
– It’s the most important mass generating mechanism for visible matter in the Universe. • Responsible for ≈98% of the proton’s mass.• Higgs mechanism is (almost) irrelevant to light-quarks.
26
In QCD: Gluons alsobecome massive! Not just quarks …
Gluons also have a gap equation …
Gluons are cannibals – a particle species whose members become massive by eating each other!
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
22
422 )(
kkm
g
gg
Present level of uncertainty using phenomenology and theory ∼ 30%
Power-law suppressed in ultraviolet, so invisible in perturbation theory
Gluon mass-squared function
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
27
Massive Gauge Bosons! Gauge boson cannibalism
… a new physics frontier … within the Standard Model Asymptotic freedom means
… ultraviolet behaviour of QCD is controllable Dynamically generated masses for gluons and quarks means
that QCD dynamically generates its own infrared cutoffs– Gluons and quarks with
wavelength λ > 2/mass ≈ 1 fm decouple from the dynamics … Confinement?!
How does that affect observables?– It will have an impact in
any continuum study– Must play a role in gluon saturation ...
In fact, perhaps it’s a harbinger of gluon saturation?574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
28
Confinement is dynamical!
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Confinement QFT Paradigm: – Confinement is expressed through a dramatic
change in the analytic structure of propagators for coloured states
– It can almost be read from a plot of the dressed-propagator for a coloured state
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
29
Normal particleConfined particle
σ ≈ 1/Im(m) ≈ 1/2ΛQCD ≈ ½fm
Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities, (or qualitatively analogous structures chracterised by a dynamically generated mass-scale)
Propagation described by rapidly damped wave & hence state cannot exist in observable spectrum
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
30
Quark Fragmentation A quark begins to
propagate in spacetime But after each “step” of
length σ, on average, an interaction occurs, so that the quark loses its identity, sharing it with other partons
Finally, a cloud of partons is produced, which coalesces into colour-singlet final states
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
meson
meson
meson
meson
Baryon
σ
Real-world confinement is a dynamical phenomenon, surrounded by mystery!
An EIC will enable “3D” measurements relating to fragmentation and insight into real-world confinement
31
Symmetry preserving analyses in continuum
QCD574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Pion’s Goldberger-Treiman relation
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
32
Pion’s Bethe-Salpeter amplitudeSolution of the Bethe-Salpeter equation
Dressed-quark propagator
Axial-vector Ward-Takahashi identity entails
Owing to DCSB& Exact inChiral QCD
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Miracle: two body problem solved, almost completely, once solution of one body problem is known
Maris, Roberts and Tandynucl-th/9707003, Phys.Lett. B420 (1998) 267-273
B(k2)
33
This is the most fundamental
expression of Goldstone’s Theorem and DCSB574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE
LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states
fπ Eπ(p2) = B(p2)
34
Enigma of mass
The quark level Goldberger-Treiman relation shows that DCSB has a very deep and far reaching impact on physics within the strong interaction sector of the Standard Model; viz.,
Goldstone's theorem is fundamentally an expression of equivalence between the one-body problem and the two-body problem in the pseudoscalar channel.
This emphasises that Goldstone's theorem has a pointwise expression in QCD
Hence, pion properties are an almost direct measure of the dressed-quark mass function.
Thus, enigmatically, the properties of the massless pion are the cleanest expression of the mechanism that is responsible for almost all the visible mass in the universe.
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
fπ Eπ(p2) = B(p2)
35
Dynamical Chiral Symmetry Breaking
Vacuum Condensates?574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Universal Conventions
Wikipedia: (http://en.wikipedia.org/wiki/QCD_vacuum)“The QCD vacuum is the vacuum state of quantum chromodynamics (QCD). It is an example of a non-perturbative vacuum state, characterized by many non-vanishing condensates such as the gluon condensate or the quark condensate. These condensates characterize the normal phase or the confined phase of quark matter.”
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
36
37
“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!
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
u
u
ud
u ud
du
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
38
However, just like gluons and quarks, and for the same reasons:Condensates are confined within hadrons. There are no in-vacuum condensates.
Historically, DCSB has come to be associated with the presumed existence of spacetime-independent condensates that permeate the Universe.
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
39
Confinement contains
condensates574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
40
“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!
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
u
u
ud
u ud
du
41
New Paradigm Vacuum = perturbative hadronic fluctuations
but no nonperturbative condensates Hadrons = complex, interacting systems
within which perturbative behaviour is restricted to just 2% of the interior
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
u
u
ud
u ud
du
“EMPTY space may really be empty. Though quantum theory suggests that a vacuum should be fizzing with particle activity, it turns out that this paradoxical picture of nothingness may not be needed. A calmer view of the vacuum would also help resolve a nagging inconsistency with dark energy, the elusive force thought to be speeding up the expansion of the universe.”
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
42
“Void that is truly empty solves dark energy puzzle”Rachel Courtland, New Scientist 4th Sept. 2010
Cosmological Constant: Putting QCD condensates back into hadrons reduces the mismatch between experiment and theory by a factor of 1046
Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard Model
experiment*103
8 4620
4
HG QCDNscondensateQCD
Paradigm shift:In-Hadron Condensates
“The biggest embarrassment in
theoretical physics.”
43
Pion’s Wave Function574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
44
Pion’s valence-quark Distribution Amplitude
Last two years, methods have been developed that enable direct computation of meson light-front wave functions
φπ(x) = twist-two parton distribution amplitude = projection of the pion’s Poincaré-covariant wave-function onto the light-front
Results have been obtained with rainbow-ladder DSE kernel, simplest symmetry preserving form; and the best DCSB-improved kernel that is currently available.
xα (1-x)α, with α≈0.5574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].
45
Pion’s valence-quark Distribution Amplitude
Continuum-QCD prediction: marked broadening of φπ(x), which owes to DCSB
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Asymptotic
RL
DB
Imaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv:1301.0324 [nucl-th], Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages].
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
46
Features of Ground-state PDAs
A diverse array of studies since Caraguatatuba (2012) have shown that ground-state meson PDAs are broad, concave functions
Camel-humped distributions – popular with some for many years – are physically unreasonable because they correspond to bound-state amplitudes that disfavour equal momentum partitioning between valence-quark degrees of freedom
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Concave function: no line segment lies above any point on the graph
arXiv:1301.0324 [nucl-th], arXiv:1306.2645 [nucl-th], arXiv:1311.1390 [nucl-th], arXiv:1405.0289 [nucl-th], arXiv:1406:3353 [nucl-th]
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
47
Pion electromagnetic form factor
2013: existing data and theory – no hint of a trend toward the so-called asymptotic pQCD prediction?
Jlab 12 will allow an extension of the Fπ measurement up to a value of Q2 of about 6 (GeV/c)2
& 10% measurement at 9 GeV2
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Projected JLab reach
Result imagined by many to be QCD prediction
Evaluated with φπ = 6x(1-x)
E12-06-101 and E12-07-105
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
48
Pion electromagnetic form factor Understanding – Part 1
– Compare data with the real QCD prediction; i.e. the result calculated using the broad pion PDA predicted by modern analyses of continuum QCD
Understanding – Part 2– Algorithm used to
compute the PDA can also be employed to compute Fπ(Q2) directly, to arbitrarily large Q2
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Real QCD prediction – obtained with realistic, computed PDA
Predictions: JLab will see maximum Experiments to 8GeV2 will see
parton model scaling and QCD scaling violations for the first time in a hadron form factor
Pion electromagnetic form factor at spacelike momentaL. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv:1307.0026 [nucl-th], Phys. Rev. Lett. 111, 141802 (2013)
maximum
Agreement within 15%
49
When is asymptotic PDA valid?
PDA is a wave function not directly observable
but PDF is. φπ
asy(x) can only be a good approximation to the pion's PDA when it is accurate to write
uvπ (x) ≈ δ(x)
for the pion's valence-quark distribution function.
This is far from valid at currently accessible scales
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Q2=27 GeV2
This is not δ(x)!
Explanation and Prediction of Observables using Continuum Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv:1310.2651 [nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line]
Basic features of the pion valence-quark distribution function, L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
50
When is asymptotic PDA valid? When is asymptopia reached?
If uvπ(x) ≈ δ(x), then
<x> = ∫01 dx x uv
π(x) = 0;
i.e., the light-front momentum fraction carried by valence-quarks is ZERO Asymptopia is reached when <x> is “small”
As usual, the computed valence-quark distribution produces (π = u+dbar)
2<x>2GeV = 44% When is <x> small?
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
NLO evolution of PDF, computation of <x>. Even at LHC energies, light-front fraction of
the π momentum:<x>dressed valence-quarks = 21%
<x>glue = 54%, <x>sea-quarks = 25%
LHC: 16TeV
Evolution in QCD is LOGARITHMIC
JLab 2GeV
Explanation and Prediction of Observables using Continuum Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv:1310.2651 [nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line]
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
51
At the “Planck scale”
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Evolution in QCD is LOGARITHMIC
In the truly asymptotic domain, way, way beyond LHC energy scales, gluons and sea-quarks share the momentum of a hadron, each with roughly 50% of the momentum
Explanation and Prediction of Observables using Continuum Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv:1310.2651 [nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line]
EIC Reach
52
GPDs & TMDs574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
53
PDFs … only describe hadron light-front structure incompletely because inclusive deep inelastic scattering (DIS) measurements do not yield information about the distribution of partons in the plane perpendicular to the bound-state's total momentum; i.e., within the light front.
Generalised Parton Distributions (GPDs)– Spatial tomography of hadrons– Measured in DVCS
Transverse Momentum-dependent Distributions (TMDs)– Momentum tomography of hadrons– Measured in SIDIS
A new generation of experiments – more than ½ beam time at JLab – aims to provide the empirical information necessary to develop a phenomenology of nucleon Wigner distributions.
GPDs & TMDs
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
54
Principal problem with phenomenology– If one wishes to use measured GPDs as a means by which to
validate our basic perception of strong interactions in the Standard Model, then data fitting is inadequate.
Instead, it is necessary to compute GPDs using a framework that possesses a direct connection with QCD.
This observation is highlighted by experience drawn from the simpler case of the pion's valence-quark PDF (L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29)– Phenomenology contradicted QCD predictions– Many claimed QCD was challenged– Until nonperturbative continuum-QCD predictions appeared …– Data reanalysed … now the PDF is seen as a success for QCD
GPDs & TMDs
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
55
GPDs unify PDFs and elastic form factors, and extend both into a new domain
GPDs – unify & extend
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
56
Rainbow-ladder (RL) truncation– δn
xP(ℓ):= δ(n ℓ - x n P)⋅ ⋅ , ℓ+R =ηbar ℓ++η ℓP, ℓ-
R= η ℓ- + ηbarℓP,
ℓ± = ℓ ± Δ/2, ℓP = ℓ - P. Triangle corresponds to the textbook handbag diagram
– Certainly guarantees connection between H(x,ξ,t) and Fπ(t), at same order of truncation
However, handbag diagram is not complete set of diagrams in RL truncation of valence-quark PDF and hence it’s not adequate for H(x,ξ,t)
Correction for PDF is known … Extension of Hπ(x,ξ,t) to all ξ ≠ 0 is not yet known but ξ =0 can be handled
Pion valence-quark GPD
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Basic features of the pion valence-quark distribution function, L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
57
Completely general expression:
Use fact that H(x,ξ,t) can be written as a Radon transform, owing to its general properties:
Then … compute handbag diagram plus first-guess correction … inspect the result … read off the surviving Radon amplitude, F(α,β,t) … obtain
Hπ(x,ξ,t) is then completely determined … not just a limited number of moments but the entire function
Pion valence-quark GPD
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Sketching the pion's valence-quark generalised parton distribution, C. Mezrag, L. Chang, H. Moutarde, C.D. Roberts, J. Rodriguez-Quintero, F. Sabatié, S.M. Schmidt in progress
ξ =0
uvπ(x)
computed directly from triangle diagram
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
58
GPD in impact parameter space:
A true quantum mechanics density …… describes the probability of finding a parton within the light-front at a transverse position |bperp| from the hadron's centre of transverse momentum (CoTM)
Computed result … … not a guess
Pion valence-quark GPD
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Sketching the pion's valence-quark generalised parton distribution, C. Mezrag, L. Chang, H. Moutarde, C.D. Roberts, J. Rodriguez-Quintero, F. Sabatié, S.M. Schmidt in progress
qπ(x
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
59
GPD in impact parameter space:
Peaked at (xVm, |bperp|=0) … peak
becomes sharper as resolving scale, ζ, increases
Broad at |bperp| =0, becomes even broader as ζ increases
Narrowing as x → 1 … increasing ζ: xV
m → 0; GPD becomes even narrower … there can’t be many partons carrying x 1; i.e., all the ≃hadron’s light-front momentum
Pion valence-quark GPD
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Sketching the pion's valence-quark generalised parton distribution, C. Mezrag, L. Chang, H. Moutarde, C.D. Roberts, J. Rodriguez-Quintero, F. Sabatié, S.M. Schmidt in progress
qπ(x
60
Baryon Bound-States
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
61
Baryon Structure
Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarks
Confinement and DCSB are readily expressed Prediction: strong diquark correlations exist within baryons as
a dynamical consequence of DCSB in QCD– The same mechanism that produces an almost massless pion from
two dynamically-massive quarks forces a strong correlation between two quarks in colour-antitriplet channels within a baryon
Diquark correlations are not pointlike– Typically, r0+ ~ rπ & r1+ ~ rρ
(actually 10% larger)– They have soft form factors
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
62
Baryon Structure
Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarks
Confinement and DCSB are readily expressed Prediction: strong diquark correlations exist within baryons as
a dynamical consequence of DCSB in QCD– The same mechanism that produces an almost massless pion from
two dynamically-massive quarks forces a strong correlation between two quarks in colour-antitriplet channels within a baryon
Diquark correlations are not pointlike– Typically, r0+ ~ rπ & r1+ ~ rρ
(actually 10% larger)– They have soft form factors
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Nucleon wave function can be calculated …
prediction of nucleon properties is possible
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Visible Impacts of DCSB
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
63
Apparently small changes in M(p) within the domain 1<p(GeV)<3have striking effect on the proton’s electric form factor
The possible existence and location of the zero is determined by behaviour of Q2F2
p(Q2), proton’s Pauli form factor Like the pion’s PDA, Q2F2
p(Q2) measures the rate at which dressed-quarks become parton-like: F2
p=0 for bare quark-partons Therefore, GE
p can’t be zero on the bare-parton domain
I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution, arXiv:1304.0855 [nucl-th], Phys. Rev. Lett. 111 (2013) 101803
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Visible Impacts of DCSB
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp 64
Follows that the possible existence and location
of a zero in the ratio of proton elastic form factors
[μpGEp(Q2)/GMp(Q2)] are a direct measure of the nature of the quark-quark interaction in the Standard Model.
I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution, arXiv:1304.0855 [nucl-th], Phys. Rev. Lett. 111 (2013) 101803
65
Electric Charge Proton: if one accelerates the
rate at which the dressed-quark sheds its cloud of gluons to become a parton, then zero in Gep is pushed to larger Q2
Opposite for neutron! Explained by presence of
diquark correlations
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
J. Segovia, I.C. Cloët, C.D. Roberts, S.M. Schmidt: Nucleon and Δ Elastic and Transition Form Factors, arXiv:1408.2919 [nucl-th], Few Body Systems (in press)
These features entail that at x≈ 5 the electric form factor of the neutral neutron will become larger than that of the unit-charge proton!
JLab12 will probe this prediction
Leads to Prediction neutron:protonGEn(Q2) > GEp(Q2) at Q2 > 4GeV2
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
66
Far valence domain x≃1
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
67
Far valence domain x≃1
Endpoint of the far valence domain: x 1, is especially significant≃– All familiar PDFs vanish at x=1; but ratios of any two need not– Under DGLAP evolution, the value of such a ratio is invariant.
Thus, e.g., – limx→1 dv(x)/uv(x)
is unambiguous, scale invariant, nonperturbative feature of QCD. keen discriminator between frameworks that claim to explain nucleon structure.
Furthermore, Bjorken-x=1 corresponds strictly to the situation in which the invariant mass of the hadronic final state is precisely that of the target; viz., elastic scattering. Structure functions inferred experimentally on x 1 ≃
are determined theoretically by target's elastic form factors.
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Nucleon spin structure at very high-xCraig D. Roberts, Roy J. Holt and Sebastian M. SchmidtarXiv:1308.1236 [nucl-th], Phys. Lett. B 727 (2013) pp. 249–254
68
Neutron Structure Function at high-x
Valence-quark distributions at x=1– Fixed point under DGLAP evolution– Strong discriminator between theories
Algebraic formula
– P1p,s = contribution to the proton's charge arising from diagrams
with a scalar diquark component in both the initial and final state
– P1p,a = kindred axial-vector diquark contribution
– P1p,m = contribution to the proton's charge arising from diagrams
with a different diquark component in the initial and final state.
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36D. J. Wilson, I. C. Cloët, L. Chang and C. D. RobertsarXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
Measures relative strength of axial-vector/scalar diquarks in proton
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
69
Neutron StructureFunction at high-x
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
d/u=1/2
SU(6) symmetry
pQCD, uncorrelated Ψ
0+ qq only, d/u=0
Deep inelastic scattering – the Nobel-prize winning quark-discovery experiments
Reviews: S. Brodsky et al.
NP B441 (1995) W. Melnitchouk & A.W.Thomas
PL B377 (1996) 11 N. Isgur, PRD 59 (1999) R.J. Holt & C.D. Roberts
RMP (2010)
d/u=0.28
DSE: “realistic”
Distribution of neutron’s momentum amongst quarks on the valence-quark domain
DSE: “contact”d/u=0.18
Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) 117501
x>0.9
Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) 252001
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36D. J. Wilson, I. C. Cloët, L. Chang and C. D. RobertsarXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
70
Neutron StructureFunction at high-x
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
d/u=1/2
SU(6) symmetry
pQCD, uncorrelated Ψ
0+ qq only, d/u=0
Deep inelastic scattering – the Nobel-prize winning quark-discovery experiments
Reviews: S. Brodsky et al.
NP B441 (1995) W. Melnitchouk & A.W.Thomas
PL B377 (1996) 11 N. Isgur, PRD 59 (1999) R.J. Holt & C.D. Roberts
RMP (2010)
d/u=0.28
DSE: “realistic”
Distribution of neutron’s momentum amongst quarks on the valence-quark domain
DSE: “contact”d/u=0.18
Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) 117501
x>0.9
Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) 252001
I.C. Cloët, C.D. Roberts, et al.arXiv:0812.0416 [nucl-th], Few Body Syst. 46 (2009) 1-36D. J. Wilson, I. C. Cloët, L. Chang and C. D. RobertsarXiv:1112.2212 [nucl-th], Phys. Rev. C85 (2012) 025205 [21 pages]
NB. d/u|x=1= 0 means there are
no valence d-quarks in the proton!
JLab12 can solve this enigma
71
Spin structure on x≃1574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
72
Quark helicity at large Bjorken-x
Correlations between dressed-quarks within the proton have an enormous impact on nucleon spin structure
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Nucleon spin structure at very high-xCraig D. Roberts, Roy J. Holt and Sebastian M. SchmidtarXiv:1308.1236 [nucl-th], Phys. Lett. B 727 (2013) pp. 249–254
73
Quark helicity at large Bjorken-x
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Existing data cannot distinguish between modern pictures of nucleon structure
Empirical results for nucleon longitudinal spin asymmetries on x ≃ 1 promise to add greatly to our capacity for discriminating between contemporary pictures of nucleon structure.
Nucleon spin structure at very high-xCraig D. Roberts, Roy J. Holt and Sebastian M. SchmidtarXiv:1308.1236 [nucl-th], Phys. Lett. B 727 (2013) pp. 249–254
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
74
TMDs Eight leading-twist TMDs Three of these are nonzero in the collinear limit
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
75
TMDs … Transversity … Tensor Charge
Intrinsic, defining property of the nucleon … just as significant as axial-charge
No gluon transversity distribution Value of tensor charge places constraints on some extensions of
the Standard Model <PRD85 (2012) 054512> Current knowledge of transversity:
SIDIS @HERMES, COMPASS, JLab Future SIDIS at JLab (SoLId), EIC, …
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Direction of motion
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
76
TMDs … Transversity … Tensor Charge
Presence of diquark correlations in the proton wave function suppresses δu by 50% cf. SU(6) quark model prediction
Axial-vector correlation is crucial, e.g.: δd is only nonzero because the proton wave function contains axial-vector correlations; and axial-vector suppresses δu
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Direction of motion
DSE latticemodels
Data fits
Pitschmann et al., arXiv:1411.xxxx – Nucleon tensor charges and electric dipole moments
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
77
Future574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
78
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
79
Future Strong self-interactions amongst gluons are a unique feature of QCD
– Plausibly, they make QCD the only known nonperturbatively well-defined theory in Nature
Gluon cannibalism produces nonperturbatively massive gauge bosons and dressed-quarks– It is responsible for 98% of the mass of visible matter in the Universe
In this Universe, all readily accessible matter is defined by light quarks– Confinement is therefore a complex, dynamical phenomenon
unrelated to static potentials in quantum mechanical models This is the Standard Model Frontier:
– Predict– Measure – Explain
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
All the phenomena driven by the gluons that bind us all
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
80
Index Key Questions for the Future Critical Theory Needs for JLab12 QCD is a Theory Light quarks & Confinement Quark Gap Equation In QCD: Gluons also become massive! Confinement What is an hadron? Enigma of mass Confinement contains condensates Pion’s valence-quark Distribution Am
plitude Pion electromagnetic form factor When is asymptotic PDA valid? Pion valence -quark GPD Baryon Structure Visible Impacts of DCSB
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Electric Charge Flavor separation of proton form facto
rs Far valence domain x 1≃ TMDs … Transversity … Tensor Charge Future
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
81
What is QCD?
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
82
Very likely a self-contained, nonperturbatively renormalisable and hence well defined Quantum Field TheoryThis is not true of QED – cannot be defined nonperturbatively
No confirmed breakdown over an enormous energy domain: 0 GeV < E < 8 TeV
Increasingly probable that any extension of the Standard Model will be based on the paradigm established by QCD – Extended Technicolour: electroweak symmetry breaks via a
fermion bilinear operator in a strongly-interacting non-Abelian theory. (Andersen et al. “Discovering Technicolor” Eur.Phys.J.Plus 126 (2011) 81)
– Higgs sector of the SM becomes an effective description of a more fundamental fermionic theory, similar to the Ginzburg-Landau theory of superconductivity
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
(not an effective theory)QCD is a Theory
wikipedia.org/wiki/Technicolor_(physics)
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
83
Calories for quarks One of the most important figures in the Standard Model of Particle Physics
98% of the mass in this room & visible mass in the Universe owes to the phenomenon that produces this behaviour
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
84
Just one of the terms that are summed in a solution of the simplest, sensible gap equation
Where does the mass come from?
Deceptively simply picture Corresponds to the sum of a countable infinity of diagrams.
NB. QED has 12,672 α5 diagrams Impossible to compute this in perturbation theory.
The standard algebraic manipulation tools are just inadequate
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
αS23
85
GMOR Relation
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
86
GMOR Relation
Valuable to highlight the precise form of the Gell-Mann–Oakes–Renner (GMOR) relation: Eq. (3.4) in Phys.Rev. 175 (1968) 2195
o mπ is the pion’s mass o Hχsb is that part of the hadronic Hamiltonian density which
explicitly breaks chiral symmetry. The operator expectation value in this equation is evaluated
between pion states. Un-approximated form of the GMOR relation doesn’t make
any reference to a vacuum condensate574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)
87
GMOR is synonymous with “Vacuum Quark
Condensate”574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
88
GMOR Relation
Demonstrated algebraically that the so-called Gell-Mann – Oakes – Renner relation is the following statement
Namely, the mass of the pion is completely determined by the pion’s scalar form factor at zero momentum transfer Q2 = 0. viz., by the pion’s scalar charge
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)
89
Hadron Charges
Matrix elements associated with hadron form factors Scalar charge of a hadron is an intrinsic property of
that hadron … no more a property of the vacuum than the hadron’s electric charge, axial charge, tensor charge, etc. …
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
90
What is a hadron?574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC
ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
91
What is an hadron? Answer depends on your frame of reference,
even though truly observable quantities do not! Light-front (infinite momentum frame)
– Hadron is viewed as collection of infinitely many weakly interacting partons
– Bound-state complexity is “factorised off” and parametrised in nonperturbative distribution amplitudes
– Wave functions are complex but operators are simple “Human” frames
– Hadron structure is expressed in Schwinger functions • propagators and bound-state wave functions
– Computable using known methods in quantum field theory and expressed in terms of dressed-gluons and quarks, each of which is a complex, coherent collections of partons.
– Wave functions are simple but operators are complex
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
92
What is an hadron? Answer depends on your frame of reference,
even though truly observable quantities do not! Light-front (infinite momentum frame)
– Hadron is viewed as collection of infinitely many weakly interacting partons
– Bound-state complexity is “factorised off” and parametrised in nonperturbative distribution amplitudes
– Wave functions are complex but operators are simple “Human” frames
– Hadron structure is expressed in Schwinger functions • propagators and bound-state wave functions
– Computable using known methods in quantum field theory and expressed in terms of dressed-gluons and quarks, each of which is a complex, coherent collections of partons.
– Wave functions are simple but operators are complex
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Descriptions are completely equivalent and hence one can choose whichever is most practical/useful/insightful, so long as frame-dependence of numerous interpretations is not forgotten.
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
93
Kinematics: – k, n are light-like four-vectors, satisfying k2=0=n2, k n=1⋅ ;– zperp represents that two-component part of z annihilated by both k, n; – P± = P ± Δ/2– ξ = -n Δ/2n P⋅ ⋅ = skewness: -1 ≤ ξ ≤ 1– t=-Δ2 is the momentum transfer– P2 = t/4-mπ
2, P Δ=0⋅
Poincaré invariance: – Support -1 ≤ x ≤ 1
GPD also depends on renormalisation scale ζ. Evolution equations are known: ERBL for |x|<ξ ; DGLAP for |x|>ξ (ξ >0)
Pion valence-quark GPD
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
94
Discovering Diquarks574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
95
Flavor separation of proton form factors
Very different behavior for u & d quarks Means apparent scaling in proton F2/F1 is purely accidental 574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE
LHC ERA. 79pp
Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 (2011) 252003
Q4F2q/k
Q4 F1q
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
96
Diquark correlations!
Poincaré covariant Faddeev equation – Predicts scalar and axial-vector
diquarks Proton's singly-represented d-quark
more likely to be struck in association with 1+ diquark than with 0+
– form factor contributions involving 1+ diquark are softer
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Cloët, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36Wilson, Cloët, Chang, Roberts, PRC 85 (2012) 045205
Doubly-represented u-quark is predominantly linked with harder 0+ diquark contributions
Interference produces zero in Dirac form factor of d-quark in proton– Location of the zero depends on the relative probability of finding
1+ & 0+ diquarks in proton– Correlated, e.g., with valence d/u ratio at x=1
d
u
=Q2/M2