Nucleon and Delta Elastic and Transition Form Factors Based on: - - PowerPoint PPT Presentation

Nucleon and Delta Elastic and Transition Form Factors Based on: - Phys. Rev. C88 (2013) 032201(R), - Few-Body Syst. 54 (2013) 1-33, - Few-body Syst. 55 (2014) 1185-1222. Jorge Segovia Instituto Universitario de F´ ısica Fundamental y Matem´ aticas Universidad de Salamanca, Spain Ian C. Clo¨ et and Craig D. Roberts Argonne National Laboratory, USA Sebastian M. Schmidt Institute for Advanced Simulation, Forschungszentrum J¨ ulich and JARA, Germany Fachbereich Theoretische Physik / Institut f¨ ur Physik Karl-Franzens-Universit¨ at Graz March 10th, 2015 Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 1/37

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 ց Quark and gluon confinement Dynamical chiral symmetry breaking ↓ ↓ Colored particles Hadrons do not have never been seen follow the chiral isolated 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 2/37

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 2 . 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 ∼ 2 − 4Λ QCD (Λ QCD ≃ 200 MeV ). Any 2 -point Schwinger function with an inflexion point at p 2 > 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

Emergent phenomena: Dynamical chiral symmetry breaking Spectrum of a theory invariant under chiral transformations should exhibit degenerate parity doublets J P = 0 − J P = 0 + π m = 140 MeV cf. σ m = 500 MeV J P = 1 − J P = 1 + ρ m = 775 MeV cf. a 1 m = 1260 MeV J P = 1 / 2 + J P = 1 / 2 − N m = 938 MeV cf. N (1535) m = 1535 MeV Splittings between parity partners are greater than 100-times the light quark mass scale: m u / m d ∼ 0 . 5 , m d = 4 MeV ☞ Dynamical chiral symmetry breaking Rapid acquisition of mass is 0.4 Mass generated from the interaction of quarks with effect of gluon cloud the gluon-medium. Quarks acquire a HUGE constituent mass. 0.3 m = 0 (Chiral limit) M(p) [GeV] m = 30 MeV Responsible of the 98% of the mass of the proton. m = 70 MeV 0.2 ☞ (Not) spontaneous chiral symmetry breaking 0.1 Higgs mechanism. Quarks acquire a TINY current mass. 0 Responsible of the 2% of the mass of the proton. 0 1 2 3 p [GeV] Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 4/37

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. Elastic and transition form factors ւ ց High- Q 2 reach by Unique window into its quark and gluon structure experiments ↓ ↓ Distinctive information on the Probe the excited nucleon roles played by confinement structures at perturbative and and DCSB in QCD non-perturbative QCD scales 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 2 up to: 8 . 0 GeV 2 for ∆(1232) P 33 and N (1535) S 11 . 4 . 5 GeV 2 for N (1440) P 11 and N (1520) D 13 . ☞ The majority of new data was obtained at JLab. Upgrade of CLAS up to 12 GeV → CLAS12 (New generation experiments in 2015) Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 5/37

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 2 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

The simplest example of DSEs: The gap equation The quark propagator is given by the gap equation: Rapid acquisition of mass is 0.4 effect of gluon cloud S − 1 ( p ) = Z 2 ( i γ · p + m bm ) + Σ( p ) 0.3 � Λ g 2 D µν ( p − q ) λ a 2 γ µ S ( q ) λ a m = 0 (Chiral limit) M(p) [GeV] m = 30 MeV Σ( p ) = Z 1 2 Γ ν ( q , p ) m = 70 MeV q 0.2 General solution: 0.1 Z ( p 2 ) S ( p ) = i γ · p + M ( p 2 ) 0 0 1 2 3 Kernel involves: p [GeV] M ( p 2 ) exhibits dynamical D µν ( p − q ) - dressed gluon propagator Γ ν ( q , p ) - dressed-quark-gluon vertex mass generation Each of which satisfies its own Dyson-Schwinger equation ↓ Infinitely many coupled equations ↓ Coupling between equations necessitates truncation Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 7/37

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

Bethe-Salpeter and Faddeev equations Hadrons are studied via Poincar´ e covariant bound-state equations ☞ Mesons iS A 2-body bound state problem in quantum field theory. i Γ i Γ Properties emerge from solutions of K = Bethe-Salpeter equation: d 4 q � Γ( k ; P ) = (2 π ) 4 K ( q , k ; P ) S ( q + P ) Γ( q ; P ) S ( q ) iS The kernel is that of the gap equation. ☞ Baryons A 3-body bound state problem in quantum p q p q − a field theory. Γ P P Structure comes from solving the Faddeev Ψ a Ψ = b q equation. p d Γ b p d Faddeev equation: Sums all possible quantum field theoretical exchanges and interactions that can take place between the three dressed-quarks. Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 9/37

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 ( ∆ ) Positive parity states ւ ց pseudoscalar and vector diquarks scalar and axial-vector diquarks ↓ ↓ N ⇒ 0 + , 1 + diquarks Ignored Dominant → ∆ ⇒ only 1 + diquark wrong parity right parity larger mass-scales shorter mass-scales Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 10/37

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 − Coupling of the photon to the 1 Q Γ P P dressed quark. f i Ψ Ψ f i Γ Coupling of the photon to the 2 P P f dressed diquark: Ψ i Ψ f i Q ➫ Elastic transition. − Γ ➫ Induced transition. P P f i Ψ Ψ P P Exchange and seagull terms. f f i 3 Ψ Ψ i f i X µ Ingredients in the contributions Q Q Ψ i , f ≡ Faddeev amplitudes. 1 Single line ≡ Quark prop. 2 Q P P f Ψ i Ψ Double line ≡ Diquark prop. 3 f i axial vector scalar − X Γ ≡ Diquark BS amplitudes. µ 4 P P f Ψ i Ψ f i X µ ≡ Seagull vertices. 5 Q Γ Jorge Segovia (segonza@usal.es) Nucleon and Delta Elastic and Transition Form Factors 11/37