Relativistic Quark Models

Abstract

The application of relativistic constituent quark models to the evaluation of the electromagnetic properties of the nucleon and its resonances is addressed. The role of the pair creation process in the Feynmann triangle diagram is discussed and the importance both of choosing the light-front formalism and of using a Breit frame where the plus component of the four-momentum transfer is vanishing, is stressed. The nucleon elastic form factors are calculated free of spurious effects related to the loss of rotational covariance. The effect of a finite constituent size is considered and the parameters describing the constituent form factors are fixed using only the nucleon data up to Q 2 ≃ 1 (GeV /c) 2 ; a constituent charge radius of ≃ 0.45 f m is obtained in this way. Above Q 2 ≃ 1 (GeV /c) 2 our parameter-free predictions are in good agreement with the experimental data, showing that soft physics may be dominant up to Q 2 ∼ 10 (GeV /c) 2 . Our new results for the longitudinal and transverse helicity amplitudes of the N − P 11 (1440) transition are presented.

Electromagnetic meson form factor from a relativistic coupled-channels approach

“…In the latter case the stronger fall-off produced by the PFSM is a welcome feature which brings the theoretical predictions from constituent quark models close to experiments [29]. For the usual front-form spectator current in the q + = 0 frame agreement with experiment is achieved only by introducing electromagnetic form factors for the constituent quarks [31].…”

“…The spin-rotation factor S is the | k M | → ∞ limit of the trace of the Wigner D function occurring in Eq. (31). In order to find explicit expressions for kq , m q q and S in terms of the integration variable k′ q and the momentum transfer Q we have to specify our kinematics.…”

Nucleon Electromagnetic Form Factors and Densities

“…The point-form spectator approximation (PFSA) using pointlike constituent quarks and a Goldstone boson exchange interaction fitted to spectroscopic data (dash-dot) lies well above the g p and well below the GEH data for large Q 2 [27]. Finally, a light-front calculation using one-gluon exchange and constituent-quark form factors fitted to Q 2 < 1 (GeV/c) 2 provides a good fit (solid) up to about 4 (GeV/c) 2 [28]. However, none of the available theoretical calculations provides a truly quantitative description for all four form factors over a wide range of Q 2 .…”

Measurements of the Electric Form Factor of the Neutron at Q²=0.45 and 1.13 (GeV/c)²

“…shows the theoretical predictions of the ratio of the form factors for selected models. In this figure, "VMD+pQCD" denotes the extended Gari-Krümpelmann model by Lomon[Lom01,Lom02]; "Chiral Soliton" denotes the chiral soliton model by Holzwarth[Hol96,Hol02] (results for model B2 are plotted); "OGE CQM" denotes the CQM on the light-front with one-gluon exchange interaction by Cardarelli and Simula[Car00] and Simula[Sim01]; "LFCBM" denotes light-front cloudy bag model by Miller[Mil02]; and "GBE CQM" denotes the CQM with Goldstone boson exchange interaction by Wagenbrunn et al[Wag01] and Boffi et al[Bof02]. The top panel inFigure 2…”