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A covariant quark model, based both on the spectator formalism and on Vector Meson Dominance, and previously calibrated by the physical data, is here extended to the unphysical region of the lattice data by means of one single extra adjustable parameter - the constituent quark mass in the chiral limit. We calculated the Nucleon (N) and the Gamma N -> Delta form factors in the universe of values for that parameter described by quenched lattice QCD. A qualitative description of the Nucleon and Gamma N -> Delta form factors lattice data is achieved for light pion masses.
Within the dynamical model of Refs. [Phys. Rev. C54, 2660 (1996); C63, 055201 (2001)], we perform an analysis of recent data of pion electroproduction reactions at energies near the [Delta](1232) resonance. We discuss possible interpretations of the extracted bare and dressed [gamma] N → [Delta] form factors in terms of relativistic constituent quark models and Lattice QCD calculations. Possible future developments are discussed.
Starting with a spectator quark model developed for the nucleon (N) and the Delta in the physical pion mass region, we extend the predictions of the reaction gamma N -> Delta to the lattice QCD regime. The quark model includes S and D waves in the quark-diquark wavefunctions. Within this framework it is the D-wave part in the Delta wavefunction that generates nonzero valence contributions for the quadrupole form factors of the transition. Those contributions are however insufficient to explain the physical data, since the pion cloud contributions dominate. To separate the two effects we apply the model to the lattice regime in a region where the pion cloud effects are negligible, and adjust the D-state parameters directly to the lattice data. This process allows us to obtain a better determination of the D-state contributions. Finally, by adding a simple parametrization of the pion cloud we establish the connection between the experimental data and the lattice da.
Http://dx.doi.org/10.1140/epja/i2008-10599-0 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, $G_M^*$, for the $\gamma N \rightarrow \Delta$ transition, can be described using manifestly covariant nucleon and $\Delta$ wave functions with {\it zero\/} orbital angular momentum $L$, but a successful description of $G_M^*$ 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.
Using a covariant spectator quark model we estimate valence quark contributions to the F_1*(Q2) and F2*(Q2) transition form factors for the gamma N -> P11(1440) reaction. The Roper resonance, P11(1440), is assumed to be the first radial excitation of the nucleon. The present model requires no extra parameters except for those already fixed by the previous studies for the nucleon. Our results are consistent with the experimental data in the high Q2 region, and those from lattice QCD. We also estimate the meson cloud contributions, focusing on the low Q2 region, where they are expected to be dominant.
A constituent quark model based on the spectator formalism is applied to the gamma N -> N* transition for the three cases, where N* is the nucleon, the Delta and the Roper resonance. The model is covariant, and therefore can be used for the predictions at higher four-momentum transfer squared, Q2. The baryons are described as an off-mass-shell quark and a spectator on-mass-shell diquark systems. The quark electromagnetic current is described by quark form factors, which have a form inspired by the vector meson dominance. The valence quark contributions of the model are calibrated by lattice QCD simulations and experimental data. Contributions of the meson cloud to the inelastic processes are explicitly included.
The author demonstrates that a relativistic constituent quark model can give nucleon form factors that agree well with recent, accurate measurements. The relativistic features of the model and the specific form of the wave function are essential for the result.
We calculated all the electromagnetic observables for the nucleon and its lowest-lying Delta(1232) excitation within a constituent quark model for those two baryons based on the covariant spectator theory. Once the reactions gamma N \to N and gamma N \to Delta were described, we predicted without further adjusting of parameters the four electromagnetic Delta form factors: the electric charge G_{E0}, the magnetic dpole G_{M1}, the electric quadrupole G_{E2} and the magnetic octupole G_{M3}. The results are compatible with the available experimental data and recent lattice QCD data.
We consider the baryons as three constituent valence quark systems. Their dynamics is described by the covariant Spectator formalism [1,2] for a quark-diquark system, where the diquark is always on its mass-shell. The electromagnetic interaction is considered in the relativistic impulse interaction (RIA) where the photon couples with the quark through the current j M = j\y^ + 72 l°2mV (m *s ^ e n u c l e o n mass). The two form factors j'l and 72 account for all QCD mechanisms (qq pairs, pion cloud and gluon sea effects). Only the 71 form factor includes pion cloud effects in its isovector part. The nucleon wave function consists of spin-0 (isospin-0) and spin-1 (isospin-l) components written in terms of the diquark polarization vectors and the nucleon Dirac spinor [1]. Furthermore, it verifies the Dirac equation and generates the correct structure for its non-relativistic limit. Current conservation is also satisfied. The Jlab polarization data of the electromagnetic nucleon elastic form factors are described [3,4] when one assumes an S-state for the quark-diquark system [1], which means that the data does not signal any angular dependence in the wave function. The results show that spherical charge and matter distributions are compatible with the data, even when we consider Spin Direction Dependent density definitions [5]. The explicit consideration of the pion cloud effects definitively improves the description of the nucleon form factors [1]. We also calculated the N-Delta transition form factors. Preliminary results considering the Delta wave function as a mixture of a S and a D state explain the magnetic dipole G*M and the electric quadrupole G*E data [6]. Improvements are underway in order to describe also the Coulomb quadrupole form factor G£.
A covariant spectator quark model is applied to estimate the valence quark contributions to the$ F1*(Q2) and F2*(Q2) transition form factors for the gamma N -> P11(1440) reaction. The Roper resonance, P11(1440), is assumed to be the first radial excitation of the nucleon. The model requires no extra parameters except for those already fixed by the previous studies for the nucleon. The results are consistent with the experimental data in the high Q2 region, and those from the lattice QCD. Finally the model is also applied to estimate the meson cloud contributions from the CLAS and MAID analysis.