Nucleon and Delta Elastic and Transition Form Factors
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1 Nucleon and Delta Elastic and Transition Form Factors Based on: - Phys. Rev. C88 (013) 0301(R), - Few-Body Syst. 54 (013) 1-33, - Few-body Syst. 55 (014) Jorge Segovia Instituto Universitario de Física Fundamental y Matemáticas Universidad de Salamanca, Spain Ian C. Cloët and Craig D. Roberts Argonne National Laboratory, USA Sebastian M. Schmidt Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Germany Fachbereich Theoretische Physik / Institut für Physik Karl-Franzens-Universität Graz March 10th, 015 Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 1/37
2 The challenge of QCD Quantum Chromodynamics is the only known example in nature of a nonperturvative fundamental quantum field theory QCD have profound implications for our understanding of the real-world: Explain how quarks and gluons bind together to form hadrons. Origin of the 98% of the mass in the visible universe. Given QCD s complexity: The best promise for progress is a strong interplay between experiment and theory. Emergent phenomena ւ Quark and gluon confinement Colored particles have never been seen isolated ց Dynamical chiral symmetry breaking Hadrons do not follow the chiral symmetry pattern Neither of these phenomena is apparent in QCD s Lagrangian yet! They play a dominant role determining characteristics of real-world QCD Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors /37
3 Emergent phenomena: Confinement Confinement is associated with dramatic, dynamically-driven changes in the analytic structure of QCD s propagators and vertices (QCD s Schwinger functions) Dressed-propagator for a colored state: An observable particle is associated with a pole at timelike-p. When the dressing interaction is confining: Real-axis mass-pole splits, moving into a pair of complex conjugate singularities. No mass-shell can be associated with a particle whose propagator exhibits such singularity. Dressed-gluon propagator: Confined gluon. IR-massive but UV-massless. m G 4Λ QCD (Λ QCD 00MeV). Any -point Schwinger function with an inflexion point at p > 0: Breaks the axiom of reflexion positivity No physical observable related with Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 3/37
4 Emergent phenomena: Dynamical chiral symmetry breaking Spectrum of a theory invariant under chiral transformations should exhibit degenerate parity doublets π J P = 0 m = 140MeV cf. σ J P = 0 + m = 500MeV ρ J P = 1 m = 775MeV cf. a 1 J P = 1 + m = 160MeV N J P = 1/ + m = 938MeV cf. N(1535) J P = 1/ m = 1535MeV Splittings between parity partners are greater than 100-times the light quark mass scale: m u/m d 0.5, m d = 4MeV Dynamical chiral symmetry breaking Mass generated from the interaction of quarks with the gluon-medium. Quarks acquire a HUGE constituent mass. Responsible of the 98% of the mass of the proton. (Not) spontaneous chiral symmetry breaking Higgs mechanism. Quarks acquire a TINY current mass. Responsible of the % of the mass of the proton M(p) [GeV] Rapid acquisition of mass is effect of gluon cloud p [GeV] m = 0 (Chiral limit) m = 30 MeV m = 70 MeV Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 4/37
5 Electromagnetic form factors of nucleon excited states A central goal of Nuclear Physics: understand the structure and properties of protons and neutrons, and ultimately atomic nuclei, in terms of the quarks and gluons of QCD. Unique window into its quark and gluon structure Distinctive information on the roles played by confinement and DCSB in QCD Elastic and transition form factors ւ ց CEBAF Large Acceptance Spectrometer (CLAS) Most accurate results for the electroexcitation amplitudes of the four lowest excited states. They have been measured in a range of Q up to: 8.0GeV for (13)P 33 and N(1535)S GeV for N(1440)P 11 and N(150)D 13. The majority of new data was obtained at JLab. High-Q reach by experiments Probe the excited nucleon structures at perturbative and non-perturbative QCD scales Upgrade of CLAS up to 1GeV CLAS1 (New generation experiments in 015) Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 5/37
6 Theory tool: Dyson-Schwinger equations Confinement and Dynamical Chiral Symmetry Breaking (DCSB) can be identified with properties of dressed-quark and -gluon propagators and vertices (Schwinger functions) Dyson-Schwinger equations (DSEs) The quantum equations of motion of QCD whose solutions are the Schwinger functions. Propagators and vertices. Generating tool for perturbation theory. No model-dependence. Nonperturbative tool for the study of continuum strong QCD. Any model-dependence should be incorporated here. Allows the study of the interaction between light quarks in the whole range of momenta. Analysis of the infrared behaviour is crucial to disentangle confinement and DCSB. Connect quark-quark interaction with experimental observables. It is via the Q evolution of form factors that one gains access to the running of QCD s coupling and masses from the infrared into the ultraviolet. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 6/37
7 The simplest example of DSEs: The gap equation The quark propagator is given by the gap equation: S 1 (p) = Z (iγ p +m bm )+Σ(p) Σ(p) = Z 1 Λ General solution: q g D µν(p q) λa γµs(q)λa Γν(q,p) S(p) = Z(p ) iγ p +M(p ) Kernel involves: D µν(p q) - dressed gluon propagator Γ ν(q,p) - dressed-quark-gluon vertex M(p) [GeV] Each of which satisfies its own Dyson-Schwinger equation Infinitely many coupled equations Coupling between equations necessitates truncation Rapid acquisition of mass is effect of gluon cloud p [GeV] m = 0 (Chiral limit) m = 30 MeV m = 70 MeV M(p ) exhibits dynamical mass generation Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 7/37
8 Ward-Takahashi identities (WTIs) Symmetries should be preserved by any truncation Highly nontrivial constraint Failure implies loss of any connection with QCD Symmetries in QCD are implemented by WTIs Relate different Schwinger functions For instance, axial-vector Ward-Takahashi identity: These observations show that symmetries relate the kernel of the gap equation a one-body problem with that of the Bethe-Salpeter equation a two-body problem Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 8/37
9 Bethe-Salpeter and Faddeev equations Hadrons are studied via Poincaré covariant bound-state equations Mesons A -body bound state problem in quantum field theory. Properties emerge from solutions of Bethe-Salpeter equation: Γ(k;P) = d 4 q (π) 4 K(q,k;P)S(q+P)Γ(q;P)S(q) The kernel is that of the gap equation. iγ = iγ is is K Baryons A 3-body bound state problem in quantum field theory. Structure comes from solving the Faddeev equation. Faddeev equation: Sums all possible quantum field theoretical exchanges and interactions that can take place between the three dressed-quarks. p q p d a Ψ P = p q p d Γ a q Γ b b Ψ P Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 9/37
10 Diquarks inside baryons The attractive nature of quark-antiquark correlations in a color-singlet meson is also attractive for 3 c quark-quark correlations within a color-singlet baryon Diquark correlations: Empirical evidence in support of strong diquark correlations inside the nucleon. A dynamical prediction of Faddeev equation studies. In our approach: Non-pointlike color-antitriplet and fully interacting. Thanks to G. Eichmann. Diquark composition of the Nucleon (N) and Delta ( ) pseudoscalar and vector diquarks Ignored wrong parity larger mass-scales Positive parity states ւ ց Dominant right parity shorter mass-scales scalar and axial-vector diquarks N 0 +, 1 + diquarks only 1 + diquark Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 10/37
11 Baryon-photon vertex (in the quark-diquark picture) One must specify how the photon couples to the constituents within the hadrons: Nature of the coupling of the photon to the quark. Nature of the coupling of the photon to the diquark. Six contributions to the current One-loop diagrams Two-loop diagrams 1 Coupling of the photon to the dressed quark. Coupling of the photon to the dressed diquark: Elastic transition. Induced transition. 3 Exchange and seagull terms. Ingredients in the contributions 1 Ψ i,f Faddeev amplitudes. Single line Quark prop. 3 Double line Diquark prop. 4 Γ Diquark BS amplitudes. 5 X µ Seagull vertices. Q P i Ψ Ψ P f f i P i Ψ Ψ P f f i Q P i Ψ Ψ P f f i axial vector scalar Q P f i Ψ Ψ P f i P Γ Γ Q f i Ψ Ψ P f i Xµ Γ Q µ P i Ψ Ψ P f f i Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 11/37 X Γ Q
12 Contact-interaction (CI) framework Symmetry preserving Dyson-Schwinger equation treatment of a vector vector contact interaction Gluon propagator: Contact interaction. g D µν(p q) = δ µν 4πα IR m G Truncation scheme: Rainbow-ladder. Γ a ν (q,p) = (λa /)γ ν Quark propagator: Gap equation. Form Factors: Two-loop diagrams not incorporated. Exchange diagram It is zero because our treatment of the contact interaction model Γ Pf i Ψ Ψ P f i Γ Q S 1 (p) = iγ p +m+σ(p) = iγ p +M M 0.4GeV. Implies momentum independent constituent quark mass. Implies momentum independent BSAs. Baryons: Faddeev equation. m N = 1.14GeV m = 1.39GeV (masses reduced by meson-cloud effects) P f Seagull diagrams They are zero Γ i Ψ Ψ P i f Xµ Q µ P i Ψ Ψ P f f i Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 1/37 X Γ Q
13 Series of papers establishes its strengths and limitations CI framework has judiciously been applied to a large body of hadron phenomena. Produces results in qualitative agreement with those obtained using most-sophisticated interactions. 1 Features and flaws of a contact interaction treatment of the kaon C. Chen, L. Chang, C.D. Roberts, S.M. Schmidt S. Wan and D.J. Wilson Phys. Rev. C (013). arxiv:11.1 [nucl-th] Spectrum of hadrons with strangeness C. Chen, L. Chang, C.D. Roberts, S. Wan and D.J. Wilson Few Body Syst (01). arxiv: [nucl-th] 3 Nucleon and Roper electromagnetic elastic and transition form factors D.J. Wilson, I.C. Cloët, L. Chang and C.D. Roberts Phys. Rev. C 85, 0505 (01). arxiv:111.1 [nucl-th] 4 π- and ρ-mesons, and their diquark partners, from a contact interaction H.L.L. Roberts, A. Bashir, L.X. Gutierrez-Guerrero, C.D. Roberts and D.J. Wilson Phys. Rev. C 83, (011). arxiv: [nucl-th] 5 Masses of ground and excited-state hadrons H.L.L. Roberts, L. Chang, I.C. Cloët and C.D. Roberts Few Body Syst. 51, 1-5 (011). arxiv: [nucl-th] 6 Abelian anomaly and neutral pion production H.L.L. Roberts, C.D. Roberts, A. Bashir, L.X. Gutierrez-Guerrero and P.C. Tandy Phys. Rev. C 8, 0650 (010). arxiv: [nucl-th] Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 13/37
14 Weakness of the contact-interaction framework A truncation which produces Faddeev amplitudes that are independent of relative momentum: Underestimates the quark orbital angular momentum content of the bound-state. Eliminates two-loop diagram contributions in the EM currents. Produces hard form factors. Momentum dependence in the gluon propagator QCD-based framework Contrasting the results obtained for the same observables one can expose those quantities which are most sensitive to the momentum dependence of elementary quantities in QCD. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 14/37
15 QCD-kindred framework Gluon propagator: 1/k -behaviour. Truncation scheme: Rainbow-ladder. Γ a ν (q,p) = (λa /)γ ν Quark propagator: Gap equation. S 1 (p) = Z (iγ p +m bm )+Σ(p) = [ 1/Z(p ) ][ iγ p +M(p ) ] M(p = 0) 0.33GeV. Implies momentum dependent constituent quark mass. Implies momentum dependent BSAs. Baryons: Faddeev equation. m N = 1.18GeV m = 1.33GeV (masses reduced by meson-cloud effects) Form Factors: Two-loop diagrams incorporated. Exchange diagram Play an important role Γ Pf i Ψ Ψ P f i Γ Q Seagull diagrams They are less important P Γ f i Ψ Ψ P f i X µ Q µ P i Ψ Ψ P f f i X Γ Q Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 15/37
16 The Nucleon s electromagnetic current The electromagnetic current can be generally written as: J µ(k,q) = ie Λ +(P f )Γ µ(k,q)λ +(P i ) Incoming/outgoing nucleon momenta: P i = P f = m N. Photon momentum: Q = P f P i, and total momentum: K = (P i +P f )/. The on-shell structure is ensured by the Nucleon projection operators. Vertex decomposes in terms of two form factors: Γ µ(k,q) = γ µf 1 (Q )+ 1 m N σ µνq νf (Q ) The electric and magnetic (Sachs) form factors are a linear combination of the Dirac and Pauli form factors: G E (Q ) = F 1 (Q ) Q 4mN F (Q ) G M (Q ) = F 1 (Q )+F (Q ) They are obtained by any two sensible projection operators. Physical interpretation: G E Momentum space distribution of nucleon s charge. G M Momentum space distribution of nucleon s magnetization. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 16/37
17 Electromagnetic form factors of the Nucleon (Revisited) Bibliography: Current quark mass dependence of nucleon magnetic moments and radii I.C. Cloet et al., Few-Body Syst. 4 (008) arxiv: [nucl-th]. Survey of nucleon electromagnetic form factors I.C. Cloet et al., Few-Body Syst. 46 (01) arxiv: [nucl-th]. Revealing dressed-quarks via the proton s charge distribution I.C. Cloet et al., Phys. Rev. Lett. 111 (013) arxiv: [nucl-th]. Modifications: Photon-diquark vertices revisited in order to accomodate γ and Nγ : Photon axial-axial diquark transition. Photon axial-scalar diquark transition. Anomalous magnetic moment of the dressed quark. Results: (a) Cloet Segovia Segovia-AMM 3.5 (b) Cloet Segovia Segovia-AMM 0.6 G E G M Q (GeV ) Q (GeV ) Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 17/37
18 Sachs electric and magnetic form factors (I) Q dependence of proton form factors: G E p 0.5 G M p x Q m N x Q m N Proton static properties: Observations: r E r E M N r M r M M N µ Theory (0.61fm) (4.31) (0.53fm) (3.16).50 Experiment (0.88fm) (4.19) (0.84fm) (4.00).79 The QCD-kindred results are in fair agreement with experiment. The contact-interaction results are typically too hard Qualitative agreenent. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 18/37
19 Sachs electric and magnetic form factors (II) Q dependence of neutron form factors: G E n 0.04 G M n x Q m N x Q m N Neutron static properties: re re M N rm rm M N µ Theory (0.8fm) (1.99) (0.70fm) (4.95) 1.83 Experiment (0.34fm) (1.6) (0.89fm) (4.4) 1.91 Observations: The QCD-kindred results are in fair agreement with experiment GE n is small and hence is much affected by subdominant effects that we have neglected. The defects of a contact-interaction are expressed with greatest force in the neutron electric form factor. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 19/37
20 Unit-normalised ratio of Sachs electric and magnetic form factors Both CI and QCD-kindred frameworks predict a zero crossing in µ pg p E /Gp M Μ p G E p GM p Q GeV Μ n G E n GM n Q GeV The possible existence and location of the zero in µ pg p E /Gp M is a fairly direct measure of the nature of the quark-quark interaction M(p) (GeV) α =.0 α = 1.8 α = 1.4 α = p (GeV) Μ N G E N GM N Q GeV Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 0/37
21 Flavour separation x d F 1 p,x u F1 p The presence of strong diquark correlations within the nucleon is sufficient to explain the empirically verified behaviour of the flavour-separated form factors x Q M N x u u F pκp x Q M N x d d F pκp x Q M N Observations: F d 1p is suppressed respect Fu 1p at large Q. Valence content of the proton = uud Imagine only scalar diquarks: u[ud] 0 +. d-quark contribution comes from only photon-diquark diagram. u-quark contribution comes from photon-quark and photon-diquark diagrams. The location of the zero in F1p d depends on the relative probability of finding 1+ and 0 + diquarks in the proton. One would expect same behaviour in F more contributions playing an important role like anomalous magnetic moment They are not the key to explaining the data s basic features. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 1/37
22 The s electromagnetic current The small-q behaviour of the elastic form factors is a necessary element in computing the γ N transition form factors The electromagnetic current can be generally written as: J µ,λω (K,Q) = Λ +(P f )R λα (P f )Γ µ,αβ (K,Q)Λ +(P i )R βω (P i ) Vertex decomposes in terms of four form factors: [ ] [ ] Γ µ,αβ (K,Q) = (F1 +F )iγµ F K µ δ αβ (F3 m +F 4 )iγµ F 4 QαQ β K µ m 4m The multipole form factors: G E0 (Q ), G M1 (Q ), G E (Q ), G M3 (Q ), are functions of F1, F, F 3 and F 4. They are obtained by any four sensible projection operators. Physical interpretation: G E0 and G M1 Momentum space distribution of s charge and magnetization. G E and G M3 Shape deformation of the -baryon. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors /37
23 No experimental data Since one must deal with the very short -lifetime (τ τ π +): Little is experimentally known about the elastic form factors. Lattice-regularised QCD results are usually used as a guide. Lattice-regularised QCD produce -resonance masses that are very large: Approach m π m ρ m Unquenched I Unquenched II Unquenched III Hybrid Quenched I Quenched II Quenched III We artificially inflate the mass of the -baryon (right panels on the next...) Black-solid line: DSEs + QCD-kindred interaction (with/without m 1.7GeV) Blue-dashed line: DSEs + contact interaction (with/without m 1.7GeV) Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 3/37
24 G E0 and G M1 with(out) an inflated quark core mass G E G E x Q m x Q m G M G M x Q m x Q m Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 4/37
25 G E and G M3 with(out) an inflated quark core mass 0 0 G E 4 G E x Q m x Q m 1 G M3 0 1 G M x Q m x Q m Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 5/37
26 Static electromagnetic properties of the (13) + Approach G M1 (0) G E (0) G M3 (0) DSE-QCD-kindred DSE-contact Exp ±.0±4 - - The. Average 3.5 ± ± 1.9 No consensus Lattice-QCD (hybrid) +3.0± /N c +N ± Faddeev equation > 0 Covariant χpt+qlqcd ± ± ±.1 QCD-SR +4.± ±0. 0.7±0. χqsm General Param. Method QM+exchange-currents /N c +m s-expansion +3.8± RQM HBχPT +.8 ± ± nrcqm Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 6/37
27 The γ N reaction Two ways in order to analyze the structure of the -resonances ւ π-mesons as a probe complex BUT: B( γn) 1% ց photons as a probe relatively simple This became possible with the advent of intense, energetic electron-beam facilities Reliable data on the γ p + transition: Available on the entire domain 0 Q 8GeV. Isospin symmetry implies γ n 0 is simply related with γ p +. γ p + data has stimulated a great deal of theoretical analysis: Deformation of hadrons. The relevance of pqcd to processes involving moderate momentum transfers. The role that experiments on resonance electroproduction can play in exposing non-perturbative phenomena in QCD: The nature of confinement and Dynamical Chiral Symmetry Breaking. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 7/37
28 The γ N transtion current (I) The electromagnetic current can be generally written as: J µλ (K,Q) = Λ +(P f )R λα (P f )iγ 5 Γ αµ(k,q)λ +(P i ) Incoming nucleon: P i = m N, and outgoing delta: P f = m. Photon momentum: Q = P f P i, and total momentum: K = (P i +P f )/. The on-shell structure is ensured by the N- and -baryon projection operators. The composition of the 4-point function Γ αµ is determined by Poincaré covariance: Convenient to work with orthogonal momenta Simplify its structure considerably Not yet the case for K and Q (m m N ) 0 K Q 0 We take instead ˆK µ = TQ µν ˆK ν and ˆQ Vertex decomposes in terms of three (Jones-Scadron) form factors: [ λm Γ αµ = k (GM λ G E )γ 5ε αµγδ ˆK γ ˆQ δ GE TQ αγ TK γµ iς ] GC + λ ˆQ αˆk µ, m Magnetic dipole G M Electric quadrupole G E Coulomb quadrupole G C Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 8/37
29 The γ N transtion current (II) The Jones-Scadron form factors are: G M = 3(s +s 1 ), G E = s s 1, G C = s 3. G M,Ash = G M,J S GM,Ash vs G M,J S ( 1+ Q (m +m N ) ) 1 The scalars are obtained from the following Dirac traces and momentum contractions: ς(1 + d) s 1 = n T K d ˆK µν λ ς Tr[γ5J µλγ ν], s = n λ+ λ m T K µλ Tr[γ5J µλ], s 3 = 3n λ+ (1 + d) ˆK λ m d ˆK µ λ ς Tr[γ5J µλ]. We have used the following notation: 1 4d n =, λ ± = (m ±m N ) +Q Q 4ikλ m (m, ς = +m N ) (m + m N ), d = m m N (m + m N ), λm = ( 3 λ +λ, k = 1 + m ). m N G. Eichmann et al., Phys. Rev. D85 (01) Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 9/37
30 Experimental results and theoretical expectations I.G. Aznauryan and V.D. Burkert Prog. Part. Nucl Phys. 67 (01) 1-54 G* M,Ash /3G D R EM (%) The R EM ratio is measured to be minus a few percent R SM (%) The R SM ratio does not seem to settle to a constant at large Q Q (GeV ) Q (GeV ) SU(6) predictions p µ + = n µ 0 p µ + = n µ n CQM predictions (Without quark orbital angular momentum) R EM 0. R SM 0. pqcd predictions (For Q ) GM 1/Q4. R EM +100%. R SM constant. Experimental data do not support theoretical predictions Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 30/37
31 Q -behaviour of G M,Jones Scadron (I) Transition cf. elastic magnetic form factors ΜΜ G M GM ΜΜ G M GM x Q m x Q m Fall-off rate of G M,J S (Q ) in the γ p + must follow that of G M (Q ). With isospin symmetry: p µ + = n µ 0 so same is true of the γ n 0 magnetic form factor. These are statements about the dressed quark core contributions Outside the domain of meson-cloud effects, Q 1.5GeV Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 31/37
32 Q -behaviour of G M,Jones Scadron (II) GM,J S cf. Experimental data and dynamical models G M,JS Observations: x Q m All curves are in marked disagreement at infrared momenta. Similarity between Solid-black and Dot-Dashed-green. Solid-black: QCD-kindred interaction. Dashed-blue: Contact interaction. Dot-Dashed-green: Dynamical + no meson-cloud The discrepancy at infrared comes from omission of meson-cloud effects. Both curves are consistent with data for Q 0.75m 1.14GeV. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 3/37
33 Q -behaviour of G M,Ash Presentations of experimental data typically use the Ash convention G M,Ash (Q ) falls faster than a dipole 1.0 N M n G M,Ash x Q m No sound reason to expect: GM,Ash /G M constant Jones-Scadron should exhibit: GM,J S /G M constant Meson-cloud effects Up-to 35% for Q.0m. Very soft disappear rapidly. G M,Ash vs G M,J S A factor 1/ Q of difference. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 33/37
34 Electric and coulomb quadrupoles R EM = R SM = 0 in SU(6)-symmetric CQM. Deformation of the hadrons involved. Modification of the structure of the transition current. R SM R SM : Good description of the rapid fall at large momentum transfer x Q m R EM R EM : A particularly sensitive measure of orbital angular momentum correlations x Q m Zero Crossing in the transition electric form factor Contact interaction at Q 0.75m 1.14GeV QCD-kindred interaction at Q 3.5m 4.93GeV Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 34/37
35 Large Q -behaviour of the quadrupole ratios Helicity conservation arguments in pqcd should apply equally to both the results obtained within our QCD-kindred framework and those produced by an internally-consistent symmetry-preserving treatment of a contact interaction R EM Q = 1, R SM Q = constant 1.0 R SM, R EM Observations: x Q m Ρ Truly asymptotic Q is required before predictions are realized. R EM = 0 at an empirical accessible momentum and then R EM 1. R SM constant. Curve contains the logarithmic corrections expected in QCD. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 35/37
36 Summary Unified study of nucleon and elastic and transition form factors that compares predictions made by: Contact-interaction, QCD-kindred interaction, within the framework of Dyson-Schwinger equations. The comparison clearly establishes Experiments are sensitive to the momentum dependence of the running couplings and masses in the strong interaction sector of the Standard Model. Experiment-theory collaboration can effectively constrain the evolution to infrared momenta of the quark-quark interaction in QCD. New experiments using upgraded facilities will leave behind meson-cloud effects and will gain access to the region of transition between nonperturbative and perturbative behaviour of QCD s running coupling and masses. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 36/37
37 Conclusions The NγN elastic form factors: G p E (Q )/G p M (Q ) possesses a zero at Q 10GeV. Any change in the interaction which shifts a zero in the proton ratio to larger Q relocates a zero in G n E (Q )/G n M (Q ) to smaller Q. The presence of strong diquark correlations within the nucleon is sufficient to understand empirical extractions of the flavour-separated form factors. The γ elastic form factors: The elastic form factors are very sensitive to m, particularly G E and G M3 form factors. Lattice-regularised QCD produce -resonance masses that are very large, the form factors obtained therewith should be interpreted carefully. The Nγ transition form factors: G p M,J S falls asymptotically at the same rate as Gp M. This is compatible with isospin symmetry and pqcd predictions. Data do not fall unexpectedly rapid once the kinematic relation between Jones-Scadron and Ash conventions is properly account for. Strong diquark correlations within baryons produce a zero in the transition electric quadrupole at Q 5GeV. Limits of pqcd, R EM 1 and R SM constant, are apparent in our calculation but truly asymptotic Q is required before the predictions are realized. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 37/37
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