A covariant model for the nucleon and the Δ

Abstract

The covariant spectator formalism is used to model the nucleon and the ∆(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 → ∆ transition, can be described using manifestly covariant nucleon and ∆ 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.

Origin of model relations among transverse-momentum dependent parton distributions

“…[53][54][55] and the comment in Ref. [26] that in this approach the partons do not necessarily occupy the lowest-energy available orbital (with quantum numbers J P ¼ 1 2 þ and L z ¼ 0.…”

Improved empirical parametrizations of theγ*N→Δ(1232)andγ*N<

“…Using the properties of Dirac and Rarita-Schwinger spinors, we can conclude that (ū 3 γ 5 u) = 2 3 |q| 2M ∝ |q| and (ū 3 u) = − 2 3 = O(1), near the pseudo-threshold [19,20]. Applying those results, one obtains S 1/2 = O(|q| 2 ) for ∆(1232) resonance and S 1/2 = O(|q|) for N (1520) resonance.…”

“…The four form factors are not all independent, only three of them are independent. Using the current conservation condition, q · J = 0, we can conclude that [19,20] …”

“…Instead of the elementary form factors G i , alternatively we can use the multipole form factors: magnetic dipole (G M ), electric quadrupole (G E ) and Coulomb quadrupole (G C ), defined as [12,19,20] …”

Baryons as relativistic three-quark bound states

“…Another covariant approach is the covariant spectator model of Ref. [541], which has been actively explored for a range of observables including various elastic and transition form factors of octet and decuplet baryons [542][543][544][545][546][547]; a recent overview can be found in Ref. [548].…”