Eur. Phys. J. A (2008) 36: 329-348
https://doi.org/10.1140/epja/i2008-10599-0

Regular Article - Theoretical Physics

A covariant model for the nucleon and the Δ

¹ Thomas Jefferson National Accelerator Facility, 23606, Newport News, VA, USA
² Centro de Fısica Teórica de Partıculas, Av. Rovisco Pais, 1049-001, Lisboa, Portugal
³ Department of Physics, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisboa, Portugal
⁴ College of William and Mary, 23185, Williamsburg, VA, USA

^* e-mail: ramalho@jlab.org

Received: 21 March 2008
Accepted: 26 May 2008
Published online: 12 June 2008

Abstract

The covariant spectator formalism is used to model the nucleon and the Δ(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 magnetic form factor, G _M ^* , for the γN → Δ transition, can be described using manifestly covariant nucleon and Δ wave functions with 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 gives electric, G _E ^* , and Coulomb, G ^* _C , transition form factors that are identically zero, showing that these form factors are sensitive to wave function components with L > 0 .