Craig Roberts Physics Division Collaborators 2012Present Rocio BERMUDEZ U Michoácan Shi CHAO Nanjing U Ming hui DING PKU Fei GAO PKU S HERNÁNDEZ ID: 536582
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Slide1
Strong coupling QCD – the ins and outs of bound-states
Craig Roberts, Physics Division
Slide2
Collaborators: 2012-Present
Rocio
BERMUDEZ (U
Michoácan
)
;Shi CHAO (Nanjing U) ;Ming-hui DING (PKU);Fei GAO (PKU) ;S. HERNÁNDEZ (U Michoácan);Cédric MEZRAG (CEA, Saclay) ;Trang NGUYEN (KSU);Khépani RAYA (U Michoácan);Hannes ROBERTS (ANL, FZJ, UBerkeley);Chien-Yeah SENG (UM-Amherst) ;Kun-lun WANG (PKU);Shu-sheng XU (Nanjing U) ;Chen CHEN (USTC);J. Javier COBOS-MARTINEZ (U.Sonora);Mario PITSCHMANN (Vienna);Si-xue QIN (U. Frankfurt am Main, PKU);Jorge SEGOVIA (ANL);David WILSON (ODU);
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
2
Adnan BASHIR (U Michoácan);Stan BRODSKY (SLAC);Gastão KREIN (São Paulo) ;Roy HOLT (ANL);Yu-xin LIU (PKU);Hervé Moutarde (CEA, Saclay) ;Michael RAMSEY-MUSOLF (UM-Amherst) ;Alfredo RAYA (U Michoácan);Jose Rodriguez Qintero (U. Huelva) ;Sebastian SCHMIDT (IAS-FZJ & JARA);Robert SHROCK (Stony Brook);Peter TANDY (KSU);Tony THOMAS (U.Adelaide) ;Shaolong WAN (USTC) ;Hong-Shi ZONG (Nanjing U)
Students, Postdocs, Asst. Profs.
Lei Chang (U. Adelaide
)
;
Ian
Cloet
(ANL)
;
Bruno
El-
Bennich
(São Paulo);Slide3
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-states3Slide4
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
4Slide5
It’s not
proven
unless
it’s verified
experimentally.
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states5Slide6
Top Open Questions in 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
6Slide7
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
7Slide8
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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states8Examples of Emergent Phenomena in QCD, the strong-interaction sector of the Standard ModelSlide9
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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states9One cannot properly know what lies beyond the Standard Model unless one first knows what is in the Standard ModelSlide10
Jefferson Lab
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
10Slide11
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 QCDInitially imagined that Λ = 1GeV! So, JLab was initially built to reach 4GeV.574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states11Parton model scalingQCD scaling violations
e.g. S. J. Brodsky and G. R. Farrar, Phys. Rev.
Lett
. 31, 1153 (1973)Slide12
Thomas Jefferson National Accelerator Facility (
JLab)
1994 – 2004 An enormous number of fascinating experimental resultsIncluding an empirical demonstration that the distribution of charge and
magnetisation
within the proton are completely different,
Suggesting that quark-quark correlations play a crucial role in nucleon structureBut no sign of parton model scaling and certainly not of scaling violations574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states12Particle physics paradigmParticle physics paradigmSlide13
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 hallsFinal cost of upgrade is
approximately $370-Million
Physics of
JLab at 12GeV arXiv:1208.1244 [hep-ex]574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states13Slide14
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 GeV2Experiment – Goal: Hadron tomography in momentum and configuration spaceCritical need for success of Laboratory’s programme Insightful computational framework Capable of computing hadron wave functionsCapable of predicting and unifying meson & nucleon elastic and transition form factors on 0<Q2<15 GeV2Possessing 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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states14Slide15
Contemporary Theory
Dyson-Schwinger equations
Insightful computational framework Established connection with predictions of (perturbative) QCDCapable of predicting and unifying meson & nucleon elastic and transition form factors on
0<Q
2
<20 GeV2 … and beyondCapable of predicting pointwise behaviour of hadronic parton distribution functions/amplitudes … valence-quark domain is understood574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states15Slide16
Significant Progress on All
Fronts574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
16
Novel understanding of gluon
and quark confinement and its consequences is emerging from quantum field theoryArriving 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 availableQuark-quark correlations are crucial in hadron structure and accumulating empirical evidence in support of this predictionSlide17
What is Confinement?
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
17Slide18
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
18
Folklore … JLab Hall-D Conceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes. Slide19
Light quarks & Confinement
Problem: Pions … They’re unnaturally light
16 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
19Slide20
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
20Slide21
Light quarks & Confinement
In the presence of light quarks,
pair creation seems to occur non-localized and instantaneously574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
21
G. Bali et al., PoS LAT2005 (2006) 308Slide22
Light quarks & Confinement
In the presence of light quarks, pair creation seems to occur non-localized and instantaneouslyNo flux tube in a theory with light-quarks. Flux-tube is not the correct paradigm for confinement in
hadron physics574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
22
G. Bali et al., PoS LAT2005 (2006) 308Slide23
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
23Slide24
Quark Gap Equation
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24Slide25
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
25
DCSB is a fact in QCDDynamical, not spontaneousAdd nothing to QCD , No Higgs field, nothing! Effect achieved purely through quark+gluon dynamics.It’s the most important mass generating mechanism for visible matter in the Universe. Responsible for ≈98% of the proton’s mass.Higgs mechanism is (almost) irrelevant to light-quarks.Slide26
In Q
CD: 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-states26Present level of uncertainty using phenomenology and theory ∼ 30%Power-law suppressed in ultraviolet, so invisible in perturbation theory
Gluon mass-squared functionSlide27
Massive
Gauge Bosons!
Gauge boson cannibalism
… a new physics frontier … within the Standard Model
Asymptotic freedom means
… ultraviolet behaviour of QCD is controllableDynamically generated masses for gluons and quarks means that QCD dynamically generates its own infrared cutoffsGluons 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 studyMust 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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states27Slide28
Confinement is dynamical!
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
28Slide29
Confinement
QFT Paradigm:
Confinement is expressed through a dramatic
change in the analytic structure of propagators for
coloured
statesIt can almost be read from a plot of the dressed-propagator for a coloured state574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states29Normal particleConfined particleσ ≈ 1/Im(m) ≈ 1/2ΛQCD ≈ ½fmReal-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 spectrumSlide30
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 states574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states30mesonmesonmesonmesonBaryonσReal-world confinement is a dynamical phenomenon, surrounded by mystery!
An EIC will enable “3D” measurements relating to fragmentation and insight into real-world confinementSlide31
Symmetry preserving analyses in continuum QCD
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
31Slide32
Pion’s
Goldberger-Treiman relation
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
32
Pion’s
Bethe-Salpeter amplitude Solution of the Bethe-Salpeter equationDressed-quark propagatorAxial-vector Ward-Takahashi identity entailsOwing to DCSB& Exact inChiral QCD574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppMiracle: two body problem solved, almost completely, once solution of one body problem is knownMaris, Roberts and Tandynucl-th/9707003, Phys.Lett. B420 (1998) 267-273 B(k2)Slide33
This is the
most fundamental expression of Goldstone’s Theorem and 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
33
fπ Eπ(p2) = B(p2)Slide34
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 QCDHence, 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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states34fπ Eπ(p2) = B(p2)Slide35
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-states35Slide36
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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states36Slide37
“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!
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
37uuu
d
u
u
dduSlide38
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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states38Slide39
Confinement contains 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
39Slide40
“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!
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
40uuu
d
u
u
dduSlide41
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 interior574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states41u
u
u
d
uudduSlide42
“
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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states42“Void that is truly empty solves dark energy puzzle”Rachel Courtland, New Scientist 4th Sept. 2010Cosmological Constant: Putting QCD condensates back into hadrons reduces the mismatch between experiment and theory by a factor of 1046Possibly by far more, if technicolour-like theories are the correct paradigm for extending the Standard ModelParadigm shift:In-Hadron Condensates“The biggest embarrassment in theoretical physics.”Slide43
Pion’s
Wave Function
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
43Slide44
Pion’s valence-quark
Distribution AmplitudeLast two years, methods have been developed that enable direct computation of meson light-front wave functionsφπ
(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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states44Imaging 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].Slide45
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-states45AsymptoticRLDBImaging 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].Real-world PDAs are squat and fatSlide46
Features of
Ground-state PDAsA 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 freedom574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states46Concave function: no line segment lies above any point on the grapharXiv:1301.0324 [nucl-th], arXiv:1306.2645 [nucl-th], arXiv:1311.1390 [nucl-th], arXiv:1405.0289 [nucl-th], arXiv:1406:3353 [nucl-th]Slide47
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
F
π
measurement up to a value of Q2 of about 6 (GeV/c)2 & 10% measurement at 9 GeV2574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states47Projected JLab reachResult imagined by many to be QCD predictionEvaluated with φπ = 6x(1-x)E12-06-101 and E12-07-105 Slide48
Pion
electromagnetic form factorUnderstanding – 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 2Algorithm used to compute the PDA can also be employed to compute
F
π
(Q2) directly, to arbitrarily large Q2574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states48Real QCD prediction – obtained with realistic, computed PDA Predictions: JLab will see maximumExperiments to 8GeV2 will see parton model scaling and QCD scaling violations for the first time in a hadron form factorPion 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%
Slide49
When is
asymptotic PDA valid?
PDA is a wave function
not directly observable but PDF is.φπasy(x) can only be a good approximation to the pion's PDA when it is accurate to write 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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states49Q2=27 GeV2This 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. 23–29Slide50
When is
asymptotic PDA valid?
When is asymptopia reached?If uv
π
(x) ≈
δ(x), then <x> = ∫01 dx x uvπ(x) = 0; i.e., the light-front momentum fraction carried by valence-quarks is ZERO Asymptopia is reached when <x> is “small”As usual, the computed valence-quark distribution produces (π = u+dbar) 2<x>2GeV = 44%When is <x> small?574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states50NLO 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
2GeVExplanation 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]Slide51
At the
“Planck scale”
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states
51
Evolution in QCD is
LOGARITHMICIn 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 momentumExplanation 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 ReachSlide52
GPDs & TMDs
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
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52Slide53
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 hadronsMeasured in DVCS
Transverse Momentum-dependent Distributions (TMDs)Momentum tomography of hadronsMeasured in SIDISA 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 & TMDs574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states53Slide54
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 predictionsMany claimed QCD was challengedUntil nonperturbative continuum-QCD predictions appeared …Data reanalysed … now the PDF is seen as a success for QCDGPDs & TMDs574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states54Slide55
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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states
55Slide56
Rainbow-ladder (RL) truncation
δnxP(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 diagramCertainly guarantees connection between H(x,ξ,t) and Fπ(t), at same order of truncationHowever, 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 handledPion valence-quark GPD574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states56Basic features of the pion valence-quark distribution function, L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29Slide57
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 functionPion valence-quark GPD574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states57Sketching 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 progressξ =0uvπ(x)computed directly from triangle diagramSlide58
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 guessPion valence-quark GPD574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states58Sketching 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 progressqπ(xSlide59
GPD in impact parameter space:
Peaked at (xV
m, |bperp|=0) … peak becomes sharper as resolving scale,
ζ
, increases
Broad at |bperp| =0, becomes even broader as ζ increasesNarrowing as x → 1 … increasing ζ: xVm → 0; GPD becomes even narrower … there can’t be many partons carrying x≃1; i.e., all the hadron’s light-front momentumPion valence-quark GPD574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states59Sketching 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 progressqπ(xSlide60
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
60Slide61
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 QCDThe 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 pointlikeTypically, r0+ ~ rπ & r1+ ~ rρ (actually 10% larger)They have soft form factors574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states61Slide62
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 QCDThe 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 pointlikeTypically, r0+ ~ rπ & r1+ ~ rρ (actually 10% larger)They have soft form factors574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states62Nucleon wave function can be calculated … prediction of nucleon properties is possibleSlide63
Visible Impacts
of DCSB574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
63
Apparently small changes in M(p) within the domain 1<p(
GeV)<3 have striking effect on the proton’s electric form factorThe possible existence and location of the zero is determined by behaviour of Q2F2p(Q2), proton’s Pauli form factorLike the pion’s PDA, Q2F2p(Q2) measures the rate at which dressed-quarks become parton-like:F2p=0 for bare quark-partonsTherefore, GEp can’t be zero on the bare-parton domainI.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) 101803Slide64
Visible Impacts
of DCSB574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
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) 101803Slide65
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
Q
2
Opposite for neutron!Explained by presence of diquark correlations574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states65J. 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 predictionLeads to Prediction neutron:protonGEn(Q2) > GEp(Q2) at Q2 > 4GeV
2Slide66
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
66Slide67
Far valence domain x≃
1Endpoint of the far valence domain: x ≃ 1, is especially significantAll 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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states67Nucleon 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. 249–254Slide68
Neutron Structure Function at high-
xValence-quark distributions at x=1
Fixed point under DGLAP evolutionStrong discriminator between theoriesAlgebraic formula
P
1
p,s = contribution to the proton's charge arising from diagrams with a scalar diquark component in both the initial and final stateP1p,a = kindred axial-vector diquark contributionP1p,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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states68I.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 protonSlide69
Neutron Structure
Function at high-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
69
d/u=1/2SU(6) symmetrypQCD, uncorrelated Ψ0+ qq only, d/u=0Deep inelastic scattering – the Nobel-prize winning quark-discovery experimentsReviews: 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=0.28DSE: “realistic”Distribution of neutron’s momentum amongst quarks on the valence-quark domainDSE: “contact”d/u=0.18Melnitchouk, 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) 1-36
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]
Slide70
Neutron Structure
Function at high-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
70
d/u=1/2SU(6) symmetrypQCD, uncorrelated Ψ0+ qq only, d/u=0Deep inelastic scattering – the Nobel-prize winning quark-discovery experimentsReviews: 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=0.28DSE: “realistic”Distribution of neutron’s momentum amongst quarks on the valence-quark domainDSE: “contact”d/u=0.18Melnitchouk, 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) 1-36
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]
NB.
d/
u|
x
=1
= 0
means there are no valence d-quarks
in the proton!
JLab12 can solve this enigmaSlide71
Spin structure on 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
71Slide72
Quark helicity
at large Bjorken-xCorrelations
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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
72Nucleon 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. 249–254Slide73
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
73
Existing data cannot distinguish between modern pictures of nucleon structureEmpirical 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. 249–254Slide74
TMDs
Eight leading-twist TMDsThree 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
74Slide75
TMDs … Transversity
… Tensor ChargeIntrinsic, defining property of the nucleon … just as significant as axial-chargeNo 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, JLabFuture SIDIS at JLab (SoLId), EIC, … 574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states75Direction of motionSlide76
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 δu574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states76Direction of motionDSElatticemodelsData fitsPitschmann
et
al., arXiv:1411.xxxx – Nucleon tensor charges and electric dipole momentsSlide77
Future
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
77Slide78
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
78Slide79
Future
Strong self-interactions amongst gluons are a unique feature of QCDPlausibly, they make QCD the only known nonperturbatively well-defined theory in NatureGluon
cannibalism produces nonperturbatively massive gauge bosons and dressed-quarksIt 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: PredictMeasure Explain574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states79All the phenomena driven by the gluons that bind us allSlide80
Index
Key Questions for the FutureCritical Theory Needs for JLab12QCD is a Theory
Light quarks & ConfinementQuark Gap Equation
In QCD: Gluons also become massive!
Confinement
What is an hadron?Enigma of massConfinement contains condensatesPion’s valence-quark Distribution AmplitudePion electromagnetic form factorWhen is asymptotic PDA valid?Pion valence -quark GPDBaryon StructureVisible Impacts of DCSB574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states80Electric ChargeFlavor separation of proton form factorsFar valence domain x≃1TMDs … Transversity … Tensor ChargeFutureSlide81
What is
Q
C
D
?
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states81Slide82
Very likely a self-contained, nonperturbatively
renormalisable and hence well defined Quantum Field Theory This is not true of QED – cannot be defined nonperturbativelyNo confirmed breakdown over an enormous energy domain: 0
GeV < E < 8 TeVIncreasingly probable that any extension of the Standard Model will be based on the paradigm established by
Q
C
D 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 superconductivity574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states82(not an effective theory)QCD is a Theory
wikipedia.org/wiki/Technicolor_(physics)Slide83
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
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states83Slide84
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 pictureCorresponds to the sum of a countable infinity of diagrams. NB. QED has 12,672 α5 diagramsImpossible to compute this in perturbation theory. The standard algebraic manipulation tools are just inadequate574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states84αS23Slide85
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
85Slide86
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 m
π
is the
pion’s mass 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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states86Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)Slide87
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
87Slide88
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 charge574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states88Expanding the concept of in-hadron condensatesLei Chang, Craig D. Roberts and Peter C. TandyarXiv:1109.2903 [nucl-th], Phys. Rev. C85 (2012) 012201(R)Slide89
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. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states89Slide90
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
90Slide91
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 partonsBound-state complexity is “factorised
off” and
parametrised
in nonperturbative distribution amplitudesWave functions are complex but operators are simple“Human” framesHadron 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 complex574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states91Slide92
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 partonsBound-state complexity is “factorised
off” and
parametrised
in nonperturbative distribution amplitudesWave functions are complex but operators are simple“Human” framesHadron 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 complex574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states92Descriptions 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.Slide93
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/2ξ = -n⋅Δ/2n⋅P = skewness: -1 ≤ ξ ≤ 1t=-Δ2 is the momentum transferP2 = t/4-mπ2, 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 GPD574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states93Slide94
Discovering
Diquarks
574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79pp
Craig Roberts: Strong-coupling QCD and the ins and outs of bound-states
94Slide95
Flavor separation of proton form factors
Very different behavior for
u &
d
quarks
Means apparent scaling in proton F2/F1 is purely accidental574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states95Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 (2011) 252003Q4F2q/kQ4 F1qSlide96
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 softer574. WE-Heraeus-Seminar: STRONG INTERACTIONS IN THE LHC ERA. 79ppCraig Roberts: Strong-coupling QCD and the ins and outs of bound-states96Cloët, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36Wilson, Cloët, Chang, Roberts, PRC 85 (2012) 045205Doubly-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 protonCorrelated, e.g., with valence d/u ratio at x=1du=Q2/M2