The shape of the $\Delta$ baryon in a covariant spectator quark model

Abstract

Using a covariant spectator quark model that describes the recent lattice QCD data for the $\Delta$ electromagnetic form factors and all available experimental data on $\gamma N\to \Delta$ transitions, we analyze the charge and magnetic dipole distributions of the $\Delta$ baryon and discuss its shape. We conclude that the quadrupole moment of the $\Delta$ is a good indicator of the deformation and that the ${\Delta }^{+}$ charge distribution has an oblate shape. We also calculate transverse moments and find that they do not lead to unambiguous conclusions about the underlying shape.

arXiv commentExtended introduction, references added, other small modifications. To appear in Phys. Rev. D. 14 pages, 8 figures

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• Axial form factors of the octet baryons in a covariant quark model
• Spectroscopy of Light Baryons: $\Delta$ Resonances
• ${\gamma }^{\ast }N\to N^{\ast }(1520)$ form factors in the timelike regime
• Using the Single Quark Transition Model to predict nucleon resonance amplitudes
• Semirelativistic approximation to the ${\gamma }^{\ast }N\to N(1520)$ and ${\gamma }^{\ast }N\to N(1535)$ transition form factors
• ${\gamma }^{\ast }N\to N(1710)$ transition at high momentum transfer
• $N^{\ast }$ Form Factors based on a Covariant Quark Model
• Parametrizations of the ${\gamma }^{\ast }N\to \Delta (1232)$ quadrupole form factors and Siegert's theorem
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• New low-$Q^2$ measurements of the ${\gamma }^{\ast }N\to \Delta (1232)$ Coulomb quadrupole form factor, pion cloud parametrizations and Siegert's theorem
• Combined parametrization of the neutron electric form factor and the ${\gamma }^{\ast }N\to \Delta (1232)$ quadrupole form factors
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• A covariant model for the ${\gamma }^{\ast }N\to N^{\ast }(1520)$ reaction
• 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
• Spectroscopy and Radiative Decays of ${\Omega }_{ccc}$ and ${\Omega }_{bbb}$ Baryons in a Quark-Diquark Model