1 Craig Roberts, Physics DivisionExposing the valence-quark structure of the pion and nucleon 35+5 Craig Roberts, Physics Division Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All"
2 Collaborators: 2012-PresentStudents, Postdocs, Asst. Profs. Collaborators: 2012-Present Shi CHAO (Nanjing U) ; Ming-hui DING (PKU); Fei GAO (PKU) ; S. HERNÁNDEZ (U Michoácan); Cédric MEZRAG (CEA, Saclay) ; Khépani RAYA (U Michoácan); 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 (ANL, U. Frankfurt am Main, PKU); Jorge SEGOVIA (Salamanca); David WILSON (ODU); Adnan BASHIR (U Michoácan); Daniele BINOSI (ECT*) Stan BRODSKY (SLAC); Roy HOLT (ANL); G. Krein (São Paulo IFT) Yu-xin LIU (PKU); Hervé MOUTARDE (CEA, Saclay) ; Joannis PAPAVASILLIOU (U.Valencia) 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) Lei Chang (U. Adelaide) ; Ian Cloet (ANL) ; Bruno El-Bennich (São Paulo); Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp) Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All"
3 Emergent Phenomena in QCD, Key Questions 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? … Examples of Emergent Phenomena in QCD, the strong-interaction sector of the Standard Model Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
4 Significant Progress Novel understanding of gluon and quarkconfinement and its consequences is 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 Accumulating empirical evidence in support of this prediction Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
5 Quark Gap Equation QNP 2015 - 4 Mar. 2015 (60pp)Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
6 Dynamical Chiral Symmetry BreakingDCSB is a fact in QCD Dynamical, not spontaneous Add 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. Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
7 Gluons, too, have a gap equationNon-perturbative comparison of QCD effective charges, A.C. Aguilar, D. Binosi, J. Papavassiliou and J. Rodriguez-Quintero, Phys. Rev. D80 (2009) Gluons, too, have a gap equation Pinch-technique + background field method … reordering of diagrammatic summations in the self-energy – Πμν – ensures that subclusters are individually transverse and gluon-loop and ghost-loop contributions are separately transverse STIs → WGTIs Enables systematic analysis and evaluation of truncations and straightforward comparison of results with those of lQCD Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
8 RGI Running InteractionBridging a gap between continuum-QCD and ab initio predictions of hadron observables, D. Binosi, L. Chang, J.Papavassiliou, C.D. Roberts, arXiv: [nucl-th], Phys. Lett. B742 (2015) RGI Running Interaction Input to the DSE analysis = lQCD result for the ghost dressing function at a given renormalisation scale, ζ Solve ghost gap equation self-consistently such that αS(ζ) reproduces lQCD result Gluon-ghost vertex in ghost gap equation is computed from its own DSE in the one-loop dressed approximation. Continuum- and lattice-QCD solutions agree on solution for the gluon self energy d̂(k2)= α(ζ) Δ̂(k2; ζ) Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
9 In QCD: Gluons also become massive!Bridging a gap between continuum-QCD and ab initio predictions of hadron observables, D. Binosi, L. Chang, J.Papavassiliou, C.D. Roberts, arXiv: [nucl-th], Phys. Lett. B742 (2015) In QCD: Gluons also become massive! Running gluon mass Gluons are cannibals – a particle species whose members become massive by eating each other! Gluon mass-squared function Power-law suppressed in ultraviolet, so invisible in perturbation theory Interaction model for the gap equation, S.-x.Qin, L.Chang, Y-x.Liu, C.D.Roberts and D. J. Wilson, arXiv: [nucl-th], Phys. Rev. C 84 (2011) (R) [5 pages] Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
10 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? Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
11 Top down & Bottom up Bridging a gap between continuum-QCD& ab initio predictions of hadron observables D. Binosi (Italy), L. Chang (Australia), J. Papavassiliou (Spain), C. D. Roberts (US), arXiv: [nucl-th] , Phys. Lett. B 742 (2015) 183 Top down & Bottom up Modern kernels and interaction, developed at ANL and Peking U. One parameter, fitted to ground-state properties without reference to gauge- sector studies. Modern top-down and bottom-up results agree within 3% ! Top-down approach – ab initio computation of the interaction via direct analysis of the gauge-sector gap equations Bottom-up scheme – infer interaction by fitting data within a well-defined truncation of the matter sector DSEs that are relevant to bound-state properties. Serendipitous collaboration, conceived at one-week ECT* Workshop on DSEs in Mathematics and Physics, has united these two approaches Top-down result = gauge-sector prediction – Interaction predicted by modern analyses of QCD's gauge sector coincides with that required to describe ground-state observables using the sophisticated matter-sector ANL-PKU DSE truncation Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
12 Significant steps toward Bridging a gap between continuum-QCD & ab initio predictions of hadron observables D. Binosi (Italy), L. Chang (Australia), J. Papavassiliou (Spain), C. D. Roberts (US), arXiv: [nucl-th] , Phys. Lett. B 742 (2015) 183 Top down & Bottom up Modern kernels and interaction, developed at ANL and Peking U. One parameter, fitted to ground-state properties without reference to gauge- sector studies. Modern top-down and bottom-up results agree within 3% ! Top-down approach – ab initio computation of the interaction via direct analysis of the gauge-sector gap equations Bottom-up scheme – infer interaction by fitting data within a well-defined truncation of the matter sector DSEs that are relevant to bound-state properties. Serendipitous collaboration, conceived at one-week ECT* Workshop on DSEs in Mathematics and Physics, has united these two approaches Significant steps toward parameter-free prediction of hadron properties Top-down result = gauge-sector prediction – Interaction predicted by modern analyses of QCD's gauge sector coincides with that required to describe ground-state observables using the sophisticated matter-sector ANL-PKU DSE truncation Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
13 What is Confinement? QNP 2015 - 4 Mar. 2015 (60pp)Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
14 Confinement is dynamical!QNP Mar (60pp) Craig Roberts: Exposing the valence-quark structure of the pion and nucleon
15 Confinement QFT Paradigm:Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp) Confinement QFT Paradigm: Confinement is expressed through a dramatic change in the analytic structure of propagators for coloured states It can be read from a plot of the dressed-propagator for a coloured state Confined particle Normal particle Propagation described by rapidly damped wave & hence state cannot exist in observable spectrum 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)
16 Quark Fragmentation A quark begins to propagate in spacetimeBut 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 An EIC will enable “3D” measurements relating to fragmentation and insight into real-world confinement meson meson meson Baryon meson Real-world confinement is a dynamical phenomenon, surrounded by mystery! σ Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
17 Symmetry preserving analyses in continuum QCDCraig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
18 Pion’s Goldberger -Treiman relationMaris, Roberts and Tandy nucl-th/ , Phys.Lett. B420 (1998) Pion’s Goldberger -Treiman relation Pion’s Bethe-Salpeter amplitude Solution of the Bethe-Salpeter equation Dressed-quark propagator Axial-vector Ward-Takahashi identity entails B(k2) Miracle: two body problem solved, almost completely, once solution of one body problem is known Owing to DCSB & Exact in Chiral QCD Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
19 The most fundamental expression of Goldstone’s Theorem and DCSBfπ Eπ(p2) = B(p2) The most fundamental expression of Goldstone’s Theorem and DCSB QNP Mar (60pp) Craig Roberts: Exposing the valence-quark structure of the pion and nucleon
20 fπ Eπ(p2) = B(p2) Enigma of massThis identity is why the pion is massless in the chiral limit 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. Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
21 Pion’s Wave Function QNP 2015 - 4 Mar. 2015 (60pp)Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
22 Pion’s valence-quark Distribution AmplitudeImaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv: [nucl-th], Phys. Rev. Lett. 110 (2013) (2013) [5 pages]. 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, which precisely matches gauge sector prediction xα (1-x)α, with α≈0.5 Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
23 Pion’s valence-quark Distribution AmplitudeImaging dynamical chiral symmetry breaking: pion wave function on the light front, Lei Chang, et al., arXiv: [nucl-th], Phys. Rev. Lett. 110 (2013) (2013) [5 pages]. Pion’s valence-quark Distribution Amplitude Continuum-QCD prediction: marked broadening of φπ(x), which owes to DCSB Asymptotic DB RL Real-world PDAs are squat and fat Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
24 Lattice-QCD & Pion’s valence-quark Distribution AmplitudeDistribution amplitudes of light-quark mesons from lattice QCD, J. Segovia, et al., arXiv: [nucl-th] , Phys. Lett. B 731 (2014) pp Lattice-QCD & Pion’s valence-quark Distribution Amplitude Isolated dotted curve = conformal QCD Green curve & band = result inferred from the single pion moment computed in lattice-QCD Blue dashed curve = DSE prediction obtained with DB kernel Precise agreement between DSE prediction & informed analysis of lQCD result Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
25 When is asymptotic PDA valid?Explanation and Prediction of Observables using Continuum Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv: [nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line] 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 Basic features of the pion valence-quark distribution function, L. Chang et al., Phys. Lett. B 737 (2014) pp. 23–29 Q2=27 GeV2 This is not δ(x)! Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
26 When is asymptotic PDA valid?Explanation and Prediction of Observables using Continuum Strong QCD, Ian C. Cloët and Craig D. Roberts, arXiv: [nucl-th], Prog. Part. Nucl. Phys. 77 (2014) pp. 1–69 [on-line] When is asymptotic PDA valid? When is asymptopia reached? If uvπ(x) ≈ δ(x), then
27 PDAs & Hard Exclusive ProcessesLepage & Brodsky, Phys. Lett. B 87 (1979) ; Phys. Rev. D 22 (1980) Efremov & Radyushkin, Phys. Lett. B 94 (1980) PDAs & Hard Exclusive Processes In the theory of strong interactions, the cross-sections for many hard exclusive hadronic reactions can be expressed in terms of the PDAs of the hadrons involved Example: pseudoscalar-meson elastic electromagnetic form factor αS(Q2) is the strong running coupling, φπ(u) is the meson’s twist-two valence-quark PDA fP is the meson's leptonic decay constant It was promised that JLab would verify this fundamental prediction Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
28 Pion electromagnetic form factorIn 2001 – seven years after beginning operations, Jefferson Lab provided the first high precision pion electroproduction data for Fπ between Q2 values of 0.6 and 1.6 (GeV/c)2. JLab Data Result imagined by many to be QCD prediction Evaluated with φπ = 6x(1-x) 2006 & 2007 – new result, at Q2=2.45 (GeV/c)2 Authors of the publications stated: “still far from the transition to the Q2 region where the pion looks like a simple quark-antiquark pair” disappointment and surprise Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
29 Pion electromagnetic form factorFactor of three discrepancy Year 2000 prediction for Fπ(Q2) P.Maris & P.C. Tandy, Phys.Rev. C62 (2000) Problem … used brute-force computational method … unable to compute for Q2>4GeV2 JLab Data Result imagined by many to be QCD prediction Evaluated with φπ = 6x(1-x) Shape of prediction suggested to many that one might never see parton model scaling and QCD scaling violations Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
30 New Algorithm New InsightsQNP Mar (60pp) Craig Roberts: Exposing the valence-quark structure of the pion and nucleon
31 Pion electromagnetic form factorSolution – 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 Real QCD prediction – obtained with realistic, computed PDA Result imagined by many to be QCD prediction Evaluated with φπ = 6x(1-x) Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
32 Pion electromagnetic form factorAgreement within 15% Solution – 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 Solution – Part 2 Algorithm used to compute the PDA can also be employed to compute Fπ(Q2) directly, to arbitrarily large Q2 maximum 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 momenta L. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt and P. C. Tandy, arXiv: [nucl-th], Phys. Rev. Lett. 111, (2013) Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
33 Implications Verify the theory of factorisation in hard exclusive processes, with dominance of hard contributions to the pion form factor for Q2>8GeV2. Notwithstanding that, normalisation of Fπ(Q2) is fixed by a pion wave-function whose dilation with respect to φπasy(x)=6x(1-x) is a definitive signature of DCSB Empirical measurement of the strength of DCSB in the Standard Model – the origin of visible mass Paves the way for a dramatic reassessment of pictures of proton & neutron structure, which is already well underway Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
34 GPDs & TMDs QNP 2015 - 4 Mar. 2015 (60pp)Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
35 GPDs – unify & extend GPDs unify PDFs and elastic form factors, and extend both into a new domain Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
36 GPDs & TMDs Principal problem with phenomenologyIf 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) Data-based 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 Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
37 Pion valence -quark GPDSketching the pion's valence-quark generalised parton distribution, C. Mezrag et al., arXiv: [nucl-th], PLB 741 (2015) pp. 190–196 Pion valence -quark GPD 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 qπ(x Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
38 Pion valence -quark GPDSketching the pion's valence-quark generalised parton distribution, C. Mezrag et al., arXiv: [nucl-th], PLB 741 (2015) pp. 190–196 Pion valence -quark GPD 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: xVm → 0; GPD becomes even narrower … there can’t be many partons carrying x≃1; i.e., all the hadron’s light-front momentum qπ(x Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
39 Baryon Bound-States QNP 2015 - 4 Mar. 2015 (60pp)Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
40 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 Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
41 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 Nucleon wave function can be calculated … prediction of nucleon properties is possible Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
42 Visible Impacts of DCSBI.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution, arXiv: [nucl-th], Phys. Rev. Lett. 111 (2013) Visible Impacts of DCSB Apparently small changes in M(p) within the domain 1
43 Visible Impacts of DCSBI.C. Cloët, C.D. Roberts, A.W. Thomas: Revealing dressed-quarks via the proton's charge distribution, arXiv: [nucl-th], Phys. Rev. Lett. 111 (2013) Visible Impacts of DCSB 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. Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
44 Electric Charge GEn(Q2) > GEp(Q2) at Q2 > 4GeV2J. Segovia, I.C. Cloët, C.D. Roberts, S.M. Schmidt: Nucleon and Δ Elastic and Transition Form Factors, arXiv: [nucl-th], Few Body Syst. 55 (2014) 1185 [on-line] 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 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:proton GEn(Q2) > GEp(Q2) at Q2 > 4GeV2 Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
45 Discovering Diquarks QNP 2015 - 4 Mar. 2015 (60pp)Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
46 Flavor separation of proton form factorsVery different behavior for u & d quarks Means apparent scaling in proton F2/F1 is purely accidental Q4F2q/k Cates, de Jager, Riordan, Wojtsekhowski, PRL 106 (2011) Q4 F1q Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
47 Diquark correlations! Poincaré covariant Faddeev equationCloët, Eichmann, El-Bennich, Klähn, Roberts, Few Body Syst. 46 (2009) pp.1-36 Wilson, Cloët, Chang, Roberts, PRC 85 (2012) 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 u d =Q2/M2 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 Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
48 Diquark correlations u-quark = solid d-quark = dashed Plainly ,J. Segovia, I.C. Cloët, C.D. Roberts, S.M. Schmidt: Nucleon and Δ Elastic and Transition Form Factors, arXiv: [nucl-th], Few Body Syst. 55 (2014) 1185 [on-line] Diquark correlations u-quark = solid d-quark = dashed Plainly , presence of axial-vector diquark is crucial to agreement with data and is the origin of zero in F1d scalar diquark alone cannot describe data does not produce a zero 0+ only Complete 0+ & 1+ 1+ only J. Segovia et al., in progress Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
49 Far valence domain x≃1 QNP 2015 - 4 Mar. 2015 (60pp)Craig Roberts: Exposing the valence-quark structure of the pion and nucleon
50 Nucleon spin structure at very high-x Craig D. Roberts, Roy JNucleon spin structure at very high-x Craig D. Roberts, Roy J. Holt and Sebastian M. Schmidt arXiv: [nucl-th], Phys. Lett. B 727 (2013) pp. 249–254 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. Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
51 Neutron Structure Function at high-xI.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th], Few Body Syst. 46 (2009) 1-36 D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts arXiv: [nucl-th], Phys. Rev. C85 (2012) [21 pages] 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. Measures relative strength of axial-vector/scalar diquarks in proton Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
52 Neutron Structure Function at high-xI.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th], Few Body Syst. 46 (2009) 1-36 D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts arXiv: [nucl-th], Phys. Rev. C85 (2012) [21 pages] Neutron Structure Function at high-x x>0.9 d/u=1/2 SU(6) symmetry 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” pQCD, uncorrelated Ψ DSE: “contact” d/u=0.18 0+ qq only, d/u=0 (48) Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) Distribution of neutron’s momentum amongst quarks on the valence-quark domain Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
53 Neutron Structure Function at high-xI.C. Cloët, C.D. Roberts, et al. arXiv: [nucl-th], Few Body Syst. 46 (2009) 1-36 D. J. Wilson, I. C. Cloët, L. Chang and C. D. Roberts arXiv: [nucl-th], Phys. Rev. C85 (2012) [21 pages] Neutron Structure Function at high-x NB. d/u|x=1= 0 means there are no valence d-quarks in the proton! JLab12 can solve this enigma x>0.9 d/u=1/2 SU(6) symmetry 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” pQCD, uncorrelated Ψ DSE: “contact” d/u=0.18 0+ qq only, d/u=0 (48) Melnitchouk, Accardi et al. Phys.Rev. D84 (2011) Melnitchouk, Arrington et al. Phys.Rev.Lett. 108 (2012) Distribution of neutron’s momentum amongst quarks on the valence-quark domain Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
54 Spin structure on x≃1 QNP 2015 - 4 Mar. 2015 (60pp)Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
55 Quark helicity at large Bjorken-xNucleon spin structure at very high-x Craig D. Roberts, Roy J. Holt and Sebastian M. Schmidt arXiv: [nucl-th], Phys. Lett. B 727 (2013) pp. 249–254 Quark helicity at large Bjorken-x Correlations between dressed-quarks within the proton have an enormous impact on nucleon spin structure Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
56 Quark helicity at large Bjorken-xNucleon spin structure at very high-x Craig D. Roberts, Roy J. Holt and Sebastian M. Schmidt arXiv: [nucl-th], Phys. Lett. B 727 (2013) pp. 249–254 Quark helicity at large Bjorken-x 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. Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
57 TMDs … Transversity … Tensor ChargeDirection of motion 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
58 TMDs … Transversity … Tensor ChargeDirection of motion Pitschmann et al., arXiv: – Nucleon tensor charges and electric dipole moments 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 models Data fits DSE lattice Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
59 Summary Conformal anomaly ... gluons and quarks acquire mass dynamically Top-down and bottom-up DSE analyses agree on RGI interaction in QCD ⇒ parameter-free prediction of meson properties DCSB ⇒ reliable predictions of pseudoscalar meson pion properties Prediction = PDAs are squat and fat, at all sensible scales Prediction = factorisation in hard scattering formalism will be verified in pion form factor at JLab Prediction = DCSB, diquark correlations & their many consequences, e.g. zeros in GEp, GEn, F1d GEn > GEp on Q2 > 5 GeV2 Far valence domain … sensitive discriminator between pictures of nucleon Prediction = Nucleon tensor charge ... correlations within Faddeev amplitude are crucial ... connection with EDM of neutron and proton Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
60 Future All the phenomena driven by the gluons that bind us allStrong 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 All the phenomena driven by the gluons that bind us all Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
61 What is QCD? QNP 2015 - 4 Mar. 2015 (60pp)Craig Roberts: Exposing the valence-quark structure of the pion and nucleon
62 QCD is a Theory (not an effective theory)Very likely a self-contained, nonperturbatively renormalisable 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 < 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 wikipedia.org/wiki/Technicolor_(physics) Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
63 What is Confinement? QNP 2015 - 4 Mar. 2015 (60pp)Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
64 Light quarks & ConfinementFolklore … JLab Hall-D Conceptual Design Report(5) “The color field lines between a quark and an anti-quark form flux tubes. 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.” Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
65 Light quarks & ConfinementProblem: Pions … They’re unnaturally light so 16 tonnes of force makes a lot of them. Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
66 Light quarks & ConfinementProblem: 16 tonnes of force makes a lot of pions. Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
67 Light quarks & ConfinementG. Bali et al., PoS LAT2005 (2006) 308 Light quarks & Confinement In the presence of light quarks, pair creation seems to occur non-localized and instantaneously Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
68 Light quarks & ConfinementG. Bali et al., PoS LAT2005 (2006) 308 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 Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)
69 Table of Contents Dynamical Chiral Symmetry BreakingGluons are massive! Top down & Bottom up Confinement Pion’s Goldberger -Treiman relation Pion electromagnetic form factor Pion valence -quark GPD Baryon Structure Visible Impacts of DCSB Diquark correlations! Neutron Structure Function at high-x Quark helicity at large Bjorken-x TMDs … Transversity … Tensor Charge Summary Light quarks & Confinement Craig Roberts: Exposing the valence-quark structure of the pion and nucleon QNP Mar (60pp)