A Covariant model for the nucleon and the $\Delta$

Abstract

The covariant spectator formalism is used to model the nucleon and the $\Delta$(1232) as a system of three constituent quarks with their own electromagnetic structure. The definition of the ``fixed-axis'' polarization states for the diquark emitted from the initial state vertex and absorbed into the final state vertex is discussed. The helicity sum over those states is evaluated and seen to be covariant. Using this approach, all four electromagnetic form factors of the nucleon, together with the {\it magnetic} form factor, $G_M^{\ast }$, for the $\gamma N\to \Delta$ transition, can be described using manifestly covariant nucleon and $\Delta$ wave functions with {\it zero} orbital angular momentum $L$, but a successful description of $G_M^{\ast }$ near $Q^2=0$ requires the addition of a pion cloud term not included in the class of valence quark models considered here. We also show that the pure $S$-wave model gives electric, $G_E^{\ast }$, and coulomb, $G_C^{\ast }$, transition form factors that are identically zero, showing that these form factors are sensitive to wave function components with $L>0$.

20 pages, 5 figures, 2 tables

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• Nucleon resonances in Compton scattering
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• Axial form factors of the octet baryons in a covariant quark model
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• Spin and angular momentum in the nucleon
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• Using the Single Quark Transition Model to predict nucleon resonance amplitudes
• The shape of the $\Delta$ baryon in a covariant spectator quark model
• Semirelativistic approximation to the ${\gamma }^{\ast }N\to N(1520)$ and ${\gamma }^{\ast }N\to N(1535)$ transition form factors
• A chiral quark model for meson electro-production in the region of D-wave resonances
• Two-photon exchange effect on deuteron electromagnetic form factors
• ${\gamma }^{\ast }N\to N(1710)$ transition at high momentum transfer
• Parametrizations of the ${\gamma }^{\ast }N\to \Delta (1232)$ quadrupole form factors and Siegert's theorem
• $N^{\ast }$ Form Factors based on a Covariant Quark Model
• Improved empirical parametrizations of the ${\gamma }^{\ast }N\to \Delta (1232)$ and ${\gamma }^{\ast }N\to N(1520)$ helicity amplitudes and the Siegert's theorem
• Electromagnetic form factors of the ${\Omega }^{-}$ baryon in the spacelike and timelike regions
• New low-$Q^2$ measurements of the ${\gamma }^{\ast }N\to \Delta (1232)$ Coulomb quadrupole form factor, pion cloud parametrizations and Siegert's theorem
• Covariant model for the Dalitz decay of the $N(1535)$ resonance
• A covariant model for the decuplet to octet Dalitz decays
• Low-$Q^2$ empirical parametrizations of the $N^{\ast }$ helicity amplitudes
• A Study of deuteron electromagnetic form factors with light-front approach
• Estiamte of the two-photon exchange effect on deuteron electromagnetic form factors
• Combined parametrization of the neutron electric form factor and the ${\gamma }^{\ast }N\to \Delta (1232)$ quadrupole form factors
• Meson cloud contributions to the Dalitz decays of decuplet to octet baryons
• Electroweak form factors of baryons in dense nuclear matter
• Quark model calculations of transition form factors at high photon virtualities
• A covariant model for the negative parity resonances of the nucleon
• A Relativistic Model for the Electromagnetic Structure of Baryons from the 3rd Resonance Region