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## Craig Roberts Physics Division

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**Revealing and mapping parton**dressing and correlations through diverse hadron structure measurements Craig Roberts Physics Division**Collaborators: 2011-Present**Students Early-career scientists • Adnan BASHIR (U Michoácan); • Stan BRODSKY (SLAC); • Gastão KREIN (São Paulo) • Roy HOLT (ANL); • Mikhail IVANOV (Dubna); • Yu-xin LIU (PKU); • Michael RAMSEY-MUSOLF (UW-Mad) • Alfredo RAYA (U Michoácan); • Sebastian SCHMIDT (IAS-FZJ & JARA); • Robert SHROCK (Stony Brook); • Peter TANDY (KSU); • Tony THOMAS (U.Adelaide) • Shaolong WAN (USTC) Craig Roberts: Mapping Parton Structure and Correlations (63p) Rocio BERMUDEZ (U Michoácan); Chen CHEN (ANL, IIT, USTC); Xiomara GUTIERREZ-GUERRERO (U Michoácan); Trang NGUYEN (KSU); Khépani Raya (U Michoácan); Hannes ROBERTS (ANL, FZJ, UBerkeley); Chien-Yeah SENG (UW-Mad) Kun-lun WANG (PKU); Lei CHANG (FZJ); J. JavierCOBOS-MARTINEZ (U.Sonora); Ian CLOËT (ANL); Bruno EL-BENNICH (São Paulo); Mario PITSCHMANN (ANL & UW-Mad); Si-xue QIN(U. Frankfurt am Main); Jorge SEGOVIA (ANL); David WILSON (ODU);**Table of Contents**Craig Roberts: Mapping Parton Structure and Correlations (63p) Introduction Pion valence-quark distribution Pion valence-quark parton distribution amplitude Charged pion elastic form factor Nucleon form factors Nucleon structure functions at large-x Epilogue**Science Challenges for the coming decade: 2013-2022**Craig Roberts: Mapping Parton Structure and Correlations (63p) • Exploit opportunities provided by new data on hadron elastic and transition form factors • Chart infrared evolution of QCD’s coupling and dressed-masses • Reveal correlations that are key to nucleon structure • Expose the facts or fallacies in modern descriptions of hadron structure**Science Challenges for the coming decade: 2013-2022**Craig Roberts: Mapping Parton Structure and Correlations (63p) • Precision experimental study of valence region, and theoretical computation of distribution functions and distribution amplitudes • Computation is critical • Without it, no amount of data will reveal anything about the theory underlying the phenomena of strong interaction physics**Overarching Science Challenges for the coming decade:**2013-2022 Discover meaning of confinement, and its relationship to DCSB – the origin of visible mass Craig Roberts: Mapping Parton Structure and Correlations (63p)**What is QCD?**Craig Roberts: Mapping Parton Structure and Correlations (63p)**QCD is a Theory**(not an effective theory) Craig Roberts: Mapping Parton Structure and Correlations (63p) • Very likely a self-contained, nonperturbativelyrenormalisable and hence well defined Quantum Field Theory This is not true of QED – cannot be defined nonperturbatively • No confirmed breakdown over an enormous energy domain: 0 GeV < E < 8000 GeV • Increasingly likely 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**Contrast: so-called Effective Field Theories**Can Cannot • QCD appears valid at all energy scales that have been tested so far: no breakdown below • E ≈ 60000 mπ • Cannot be used to test QCD • Any mismatch between • EF-Theory and experiment owes to an error in the formulation of one or conduct of the other Craig Roberts: Mapping Parton Structure and Correlations (63p) EFTs applicable over a very restricted energy domain; e.g., ChPT known to breakdown for E > 2mπ Can be used to help explore how features of QCD influence observables**Strong-interaction: QCD**• Nature’sonly (now known) example of a truly nonperturbative, fundamental theory • A-priori, no idea as to what such a theory • can produce Craig Roberts: Mapping Parton Structure and Correlations (63p) • Asymptotically free • Perturbation theory is valid and accurate tool at large-Q2 • Hence chiral limit is defined • Essentiallynonperturbative for Q2 < 2 GeV2**What is Confinement?**Craig Roberts: Mapping Parton Structure and Correlations (63p)**Light quarks & Confinement**• Folklore “The color field lines between a quark and an anti-quark form flux tubes. Craig Roberts: Mapping Parton Structure and Correlations (63p) 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.” Hall-DConceptual-DR(5)**Light quarks & Confinement**Craig Roberts: Mapping Parton Structure and Correlations (63p) • Problem: 16 tonnes of force makes a lot of pions.**Light quarks & Confinement**Craig Roberts: Mapping Parton Structure and Correlations (63p) Problem: 16 tonnes of force makes a lot of pions.**G. Bali et al., PoS LAT2005 (2006) 308**Light quarks & Confinement Craig Roberts: Mapping Parton Structure and Correlations (63p) 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**Confinement**Confined particle Normal particle complex-P2 complex-P2 timelike axis: P2<0 s ≈ 1/Im(m) ≈ 1/2ΛQCD≈ ½fm • Real-axis mass-pole splits, moving into pair(s) of complex conjugate singularities • State described by rapidly damped wave & hence state cannot exist in observable spectrum Craig Roberts: Mapping Parton Structure and Correlations (63p) • 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**Light quarks & Confinement**Craig Roberts: Mapping Parton Structure and Correlations (63p) • In the study of hadrons, attention should turn from potential models toward the continuum bound-state problem in quantum field theory • Such approaches offer the possibility of posing simultaneously the questions • What is confinement? • What is dynamical chiral symmetry breaking? • How are they related? Is it possible that two phenomena, so critical in the Standard Model and tied to the dynamical generation of a mass-scale in QCD, can have different origins and fates?**Dynamical ChiralSymmetry Breaking**Craig Roberts: Mapping Parton Structure and Correlations (63p)**Dynamical ChiralSymmetry Breaking**Craig Roberts: Mapping Parton Structure and Correlations (63p) • DCSB is a fact in QCD • Dynamical, not spontaneous • Add nothing to QCD , no Higgs field, nothing! • Effect achieved purely through the dynamics of gluons and quarks. • It’s the most important mass generating mechanism for visible matter in the Universe. • Responsible for approximately 98% of the proton’s mass. • Higgs mechanism is (almost) irrelevant to light-quarks.**DCSB**C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50 M. Bhagwat & P.C. Tandy, AIP Conf.Proc. 842 (2006) 225-227 • In QCD, all “constants” of quantum mechanics are actually strongly momentum dependent: couplings, number density, mass, etc. • So, a quark’s mass depends on its momentum. • Mass function can be calculated and is depicted here. • Continuum- and Lattice-QCD Mass from nothing! • are in agreement: the vast bulk of the light-quark mass comes from a cloud of gluons, dragged along by the quark as it propagates. Craig Roberts: Mapping Parton Structure and Correlations (63p)**In QCD, Gluons, too, become massive**Craig Roberts: Mapping Parton Structure and Correlations (63p) Not just quarks … Gluons also have a gap equation … 1/k2behaviour signals essential singularity in the running coupling: Impossible to reach in perturbation theory**Valence quarks**Parton structure of hadrons Craig Roberts: Mapping Parton Structure and Correlations (63p)**Parton Structure of Hadrons**Craig Roberts: Mapping Parton Structure and Correlations (63p) • Valence-quark structure of hadrons • Definitive of a hadron – it’s how we tell a proton from a neutron • Expresses charge; flavour; baryon number; and other Poincaré-invariant macroscopic quantum numbers • Via evolution, determines background at LHC • Sea-quark distributions • Flavour content, asymmetry, intrinsic: yes or no? • Any nontrivial answers are essentially nonperturbative features of QCD**Parton Structure of Hadrons**Craig Roberts: Mapping Parton Structure and Correlations (63p) • Light front provides a link with quantum mechanics • If a probability interpretation is ever valid, it’s in the infinite-momentum frame • Enormous amount of intuitively expressive information about hadrons & processes involving them is encoded in • Parton distribution functions • Generalisedparton distribution functions • Transverse-momentum-dependent parton distribution functions • Information will be revealed by the measurement of these functions – so long as they can be calculated Success of programme demands very close collaboration between experiment and theory**Parton Structure of Hadrons**Craig Roberts: Mapping Parton Structure and Correlations (63p) • Need for calculation is emphasised by Saga of pion’s valence-quark distribution: • 1989: uvπ ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD; • 2001: DSE- QCD predicts uvπ ~ (1-x)2 argues that distribution inferred from data can’t be correct;**Parton Structure of Hadrons**Craig Roberts: Mapping Parton Structure and Correlations (63p) • Need for calculation is emphasised by Saga of pion’s valence-quark distribution: • 1989: uvπ ~ (1-x)1 – inferred from LO-Drell-Yan & disagrees with QCD; • 2001: DSE- QCD predicts uvπ ~ (1-x)2 argues that distribution inferred from data can’t be correct; • 2010: NLO reanalysis including soft-gluon resummation, inferred distribution agrees with DSE and QCD**Pion’s valence-quark Distribution Amplitude**Pion’s Bethe-Salpeter wave function Whenever a nonrelativistic limit is realistic, this would correspond to the Schroedinger wave function. Craig Roberts: Mapping Parton Structure and Correlations (63p) Exact expression in QCD for the pion’s valence-quark parton distribution amplitude Expression is Poincaré invariant but a probability interpretation is only valid in the light-front frame because only therein does one have particle-number conservation. Probability that a valence-quark or antiquark carries a fraction x=k+ / P+ of the pion’s light-front momentum { n2=0, n.P = -mπ}**Pion’s valence-quark Distribution Amplitude**Pion’s Bethe-Salpeter wave function Craig Roberts: Mapping Parton Structure and Correlations (63p) Moments method is ideal for φπ(x): entails Contact interaction (1/k2)ν , ν=0 Straightforward exercise to show ∫01 dxxmφπ(x) = fπ1/(1+m) , hence φπ(x)= fπ Θ(x)Θ(1-x)**Pion’s valence-quark Distribution Amplitude**Craig Roberts: Mapping Parton Structure and Correlations (63p) The distribution amplitude φπ(x) is actually dependent on the momentum-scale at which a particular interaction takes place; viz., φπ(x)= φπ(x,Q) One may show in general that φπ(x) has an expansion in terms of Gegenbauer–α=3/2 polynomials: Only even terms contribute because the neutral pion is an eigenstate of charge conjugation, so φπ(x)=φπ(1-x) Evolution, analogous to that of the parton distribution functions, is encoded in the coefficients an(Q)**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]. Pion’s valence-quark Distribution Amplitude Craig Roberts: Mapping Parton Structure and Correlations (63p) • However, practically, in reconstructing φπ(x) from its moments, it is better to use Gegenbauer–α polynomials and then rebuild the Gegenbauer–α=3/2 expansion from that. • Better means – far more rapid convergence because Gegenbauer–α=3/2 is only accurate near ΛQCD/Q=0. • One nontrivial Gegenbauer–α polynomial provides converged reconstruction cf. more than SEVEN Gegenbauer–α=3/2 polynomials • 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=0.3**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]. Pion’s valence-quark Distribution Amplitude • This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB. • Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result Asymptotic DB RL Craig Roberts: Mapping Parton Structure and Correlations (63p) Both kernels agree: marked broadening of φπ(x), which owes to DCSB**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]. Pion’s valence-quark Distribution Amplitude These computations are the first to directly expose DCSB – pointwise – on the light-front; i.e., in the infinite momentum frame. • This may be claimed because PDA is computed at a low renormalisation scale in the chiral limit, whereat the quark mass function owes entirely to DCSB. • Difference between RL and DB results is readily understood: B(p2) is more slowly varying with DB kernel and hence a more balanced result Asymptotic DB RL Craig Roberts: Mapping Parton Structure and Correlations (63p) Both kernels agree: marked broadening of φπ(x), which owes to DCSB**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]. Pion’s valence-quark Distribution Amplitude C.D. Roberts, Prog. Part. Nucl. Phys. 61 (2008) 50 Dilation of pion’s wave function is measurable in pion’s electromagnetic form factor at JLab12 A-rated:E12-06-10 • Established a one-to-one connection between DCSB and the pointwise form of the pion’s wave function. • Dilation measures the rate at which dressed-quark approaches the asymptotic bare-parton limit • Experiments at JLab12 can empirically verify the behaviour of M(p), and hence chart the IR limit of QCD Craig Roberts: Mapping Parton Structure and Correlations (63p)**Pion distribution amplitude from lattice-QCD,**I.C. Cloëtet al. (in progress) Lattice comparisonPion’s valence-quark PDA V. Braun et al., PRD 74 (2006) 074501 • Lattice-QCD • => one nontrivial moment: • <(2x-1)2> = 0.27 ± 0.04 • Legend • Solid = DB (Best) DSE • Dashed = RL DSE • Dotted (black) = 6 x (1-x) • Dot-dashed = midpoint lattice; and the yellow shading exhibits band allowed by lattice errors • DBα=0.31 but 10% a2<0 • RL α=0.29 and 0% a2 φπ~ xα (1-x)α α=0.35 +0.32 = 0.67 - 0.24 = 0.11 Craig Roberts: Mapping Parton Structure and Correlations (63p) Employ the generalised-Gegenbauer method described previously (and in Phys. Rev. Lett. 110 (2013) 132001 (2013) [5 pages]).**Pion distribution amplitude from lattice-QCD,**I.C. Cloëtet al. (in progress) Lattice comparisonPion’s valence-quark PDA Craig Roberts: Mapping Parton Structure and Correlations (63p) • Establishes that contemporary DSE- and lattice-QCD computations, at the same scale, agree on the pointwise form of the pion's PDA, φπ(x). • This unification of DSE- and lattice-QCD results expresses a deeper equivalence between them, expressed, in particular, via the common behaviour they predict for the dressed-quark mass-function, which is both • a definitive signature of dynamical chiral symmetry breaking • and the origin of the distribution amplitude's dilation.**Pion distribution amplitude from lattice-QCD,**I.C. Cloëtet al. (in progress) When is asymptotic PDA valid? asymptotic 4 GeV2 100 GeV2 • Consequently, the asymptotic distribution, • φπasy(x), is a poor approximation to the pion's PDA • at all such scales that are either currently accessible or • foreseeable in experiments on pion elastic and transition form factors. • Thus, related expectations based on φπasy(x) should be revised. Craig Roberts: Mapping Parton Structure and Correlations (63p) Under leading-order evolution, the PDA remains broad to Q2>100 GeV2 Feature signals persistence of the influence of dynamical chiral symmetry breaking.**Pion distribution amplitude from lattice-QCD,**I.C. Cloëtet al. (in progress) When is asymptotic PDA valid? Q2=27 GeV2 This is not δ(x)! Craig Roberts: Mapping Parton Structure and Correlations (63p) 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**Pion electromagnetic form factor at spacelikemomenta, Lei**Changet al. (in progress) Charged pionelastic form factor • P. Maris & P.C. Tandy,Phys.Rev. C62 (2000) 055204: numerical procedure is practically useless for Q2>4GeV2, so prediction ends! • Algorithm developed for pion PDA overcomes this obstacle • Solves the practical problem of continuing from Euclidean metric formulation to Minkowski space Craig Roberts: Mapping Parton Structure and Correlations (63p)**Pion electromagnetic form factor at spacelikemomenta, Lei**Changet al. (in progress) Charged pionelastic form factor • Improved DSE interaction kernel, based on DSE and lattice-QCD studies of gluon sector • S.-x. Qin, L. Chang et al. Phys.Rev. C84 (2011) 042202(R) • New prediction in better agreement with available data than old DSE result • Prediction extends from Q2=0 to arbitrarily large Q2, without interruption, unifying both domains DSE 2000 … Breakdown here Craig Roberts: Mapping Parton Structure and Correlations (63p)**Pion electromagnetic form factor at spacelikemomenta, Lei**Changet al. (in progress) Charged pionelastic form factor • Unlimited domain of validity emphasised in this figure • Depict prediction on domain 0<Q2<20GeV2 but have computed the result to Q2=100GeV2. • If it were necessary, reliable results could readily be obtained at even higher values. DSE 2013 Craig Roberts: Mapping Parton Structure and Correlations (63p)**Pion electromagnetic form factor at spacelikemomenta, Lei**Changet al. (in progress) Charged pionelastic form factor ρ-meson pole VMD • Predict a maximum at 6GeV2, which lies within domain that is accessible to JLab12 • Difficult, however, to distinguish DSE prediction from Amendolia-1986 monopole • What about comparison with perturbative QCD? Amendoliaet al. DSE 2013 maximum A-rated:E12-06-10 Craig Roberts: Mapping Parton Structure and Correlations (63p)**Pion electromagnetic form factor at spacelikemomenta, Lei**Changet al. (in progress) Charged pionelastic form factor • Prediction of pQCD obtained when the pion valence-quark PDA has the form appropriate to the scale accessible in modern experiments is markedly different from the result obtained using the asymptotic PDA • Near agreement between the pertinent perturbative QCD prediction and DSE-2013 prediction is striking. DSE 2013 15% pQCD obtained with φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment pQCD obtained withφπasy(x) • Single DSE interaction kernel, determined fully by just one parameter and preserving the one-loop renormalisation group behaviour of QCD, has unified the Fπ(Q2) and φπ(x) (and numerous other quantities) Craig Roberts: Mapping Parton Structure and Correlations (63p)**Pion electromagnetic form factor at spacelikemomenta, Lei**Changet al. (in progress) Charged pionelastic form factor • Leading-order, leading-twist QCD prediction, obtained with φπ(x) evaluated at a scale appropriate to the experiment underestimates DSE-2013 prediction by merely an approximately uniform 15%. • Small mismatch is explained by a combination of higher-order, higher-twist corrections & and shortcomings in the rainbow-ladder truncation. DSE 2013 15% pQCD obtained φπ(x;2GeV), i.e., the PDA appropriate to the scale of the experiment pQCD obtained withφπasy(x) • Hence, one should expect dominance of hard • contributions to the pion form factor for Q2>8GeV2. • Nevertheless, the normalisation of the form factor is fixed by a pion wave-function whose dilation with respect to φπasy(x) is a definitive signature of DCSB Craig Roberts: Mapping Parton Structure and Correlations (63p)**R.T. Cahill et al.,**Austral. J. Phys. 42 (1989) 129-145 Structure of Hadrons SUc(3): Craig Roberts: Mapping Parton Structure and Correlations (63p) • Dynamical chiral symmetry breaking (DCSB) – has enormous impact on meson properties. • Must be included in description and prediction of baryon properties. • DCSB is essentially a quantum field theoretical effect. In quantum field theory • Meson appears as pole in four-point quark-antiquark Green function → Bethe-Salpeter Equation • Nucleon appears as a pole in a six-point quark Green function → Faddeev Equation. • Poincaré covariant Faddeev equation sums all possible exchanges and interactions that can take place between three dressed-quarks • Tractable equation is based on the observation that an interaction which describes colour-singlet mesons also generates nonpointlike quark-quark (diquark) correlations in the colour-antitriplet channel**R.T. Cahill et al.,**Austral. J. Phys. 42 (1989) 129-145 Faddeev Equation quark exchange ensures Pauli statistics quark diquark composed of strongly-dressed quarks bound by dressed-gluons Craig Roberts: Mapping Parton Structure and Correlations (63p) • Linear, Homogeneous Matrix equation • Yields wave function (Poincaré Covariant FaddeevAmplitude) thatdescribes quark-diquark relative motion within the nucleon • Scalar and Axial-Vector Diquarks . . . • For nucleon, both have “correct” parity and “right” masses • In Nucleon’s Rest Frame Amplitude has s−, p− & d−wave correlations**SU(2)isospin symmetry of hadrons might emerge from mixing**half-integer spin particles with their antiparticles. Structure of Hadrons Craig Roberts: Mapping Parton Structure and Correlations (63p) Remarks • Diquark correlations are not inserted by hand Such correlations are a dynamical consequence of strong-coupling in QCD • The same mechanism that produces an almost masslesspion from two dynamically-massive quarks; i.e., DCSB, forces a strong correlation between two quarks in colour-antitriplet channels within a baryon – an indirect consequence of Pauli-Gürsey symmetry • Diquark correlations are not pointlike • Typically, r0+ ~ rπ & r1+ ~ rρ(actually 10% larger) • They have soft form factors**Structure of Hadrons**Craig Roberts: Mapping Parton Structure and Correlations (63p) • Elastic form factors • Provide vital information about the structure and composition of the most basic elements of nuclear physics. • They are a measurable and physical manifestation of the nature of the hadrons' constituents and the dynamics that binds them together. • Accurate form factor data are driving paradigmatic shifts in our pictures of hadrons and their structure; e.g., • role of orbital angular momentum and nonpointlikediquark correlations • scale at which p-QCD effects become evident • strangeness content • meson-cloud effects • etc.**L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458**[nucl-th] Phys. Rev. Lett. 106 (2011) 072001 Photon-nucleon current Vertex must contain the dressed-quark anomalous magnetic moment • In a realistic calculation, the last three diagrams represent 8-dimensional integrals, which can be evaluated using Monte-Carlo techniques Oettel, Pichowsky, Smekal Eur.Phys.J. A8 (2000) 251-281 Craig Roberts: Mapping Parton Structure and Correlations (63p) Composite nucleon must interact with photon via nontrivial current constrained by Ward-Green-Takahashi identities DSE → BSE → Faddeev equation plus current → nucleon form factors**I.C. Cloët, C.D. Roberts, et al.**arXiv:0812.0416 [nucl-th] L. Chang, Y. –X. Liu and C.D. RobertsarXiv:1009.3458 [nucl-th] Phys. Rev. Lett. 106 (2011) 072001 • DSE result Dec 08 • DSE result • – including the • anomalous • magnetic • moment distribution • Highlights again the • critical importance of • DCSB in explanation of • real-world observables. Craig Roberts: Mapping Parton Structure and Correlations (63p)**I.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing**dressed-quarks via the proton's charge distribution, arXiv: 1304.0855 [nucl-th] Visible Impacts of DCSB • Apparently small changes in M(p) within the domain 1<p(GeV)<3 • have striking effect on the proton’s electric form factor • The possible existence and location of the zero is determined by behaviour of Q2F2p(Q2) • Like the pion’s PDA, Q2F2p(Q2) measures the rate at which dress-ed-quarks become parton-like: • F2p=0 for bare quark-partons • Therefore, GEp can’t be zero on the bare-parton domain Craig Roberts: Mapping Parton Structure and Correlations (63p)