Nucleon structure functions from relativistic constituent quarks

We investigate the connection between the Breit and infinite momentum frames and show that when the nucleon matrix element of the time component of the electromagnetic current, which yields ${G}_{E}$ in the Breit frame, is boosted to the infinite momentum (or light-front) frame, the quantity ${F}_{1}$ is obtained.

On the group-structure of theories in the infinite momentum frame

Nucleon structure functions at moderate Q2: Relativistic constituent quarks and spectator mass spectrum

Baryons in the large N limit of two-dimensional Gross-Neveu models are reconsidered. The time-dependent Dirac-Hartree-Fock approach is used to boost a baryon to any inertial frame and shown to yield the covariant energy-momentum relation. Momentum distributions are computed exactly in arbitrary frames and used to interpolate between the rest frame and the infinite momentum frame, where they are related to structure functions. Effects from the Dirac sea depend sensitively on the occupation fraction of the valence level and the bare fermion mass and do not vanish at infinite momentum. In the case of the kink baryon, they even lead to divergent quark and antiquark structure functions at x=0.

The parton picture of elementary particles

Baryon spectra and electroweak nucleon form factors in constituent quark models

Results for the proton and neutron electric and magnetic form factors as well as the nucleon axial form factor are presented for constituent quark models, based on either one-gluon-exchange and Goldstone-boson-exchange dynamics. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. The only input to the calculations is the nucleon wave function of the corresponding constituent quark model. A comparison is given to results of the instanton-induced constituent quark model treated with the Bethe-Salpeter equation.

The authors argue that it is inappropriate to use SU(3) flavour symmetry in analysing the recent EMC measurement of the proton spin structure function and then present a light-cone, quark-proton model analysis without using SU(3). The nucleon is described as a bound state of three relativistic quarks on the light-cone. The constituent quarks have their own internal structure in terms of valence quarks, a quark-antiquark sea and gluons. The EMC result, taken in conjunction with the Bjorken sum rule, gives, separately, the valence quark and an effective sea contribution to the proton spin, demonstrating explicit cancellation of the valence and sea contributions.

Spin-dependent structure functions ${g}_{1}^{p}{(x,Q}^{2})$ and ${g}_{2}^{p}{(x,Q}^{2})$ for the proton have been derived at the valency quark level in a relativistic independent quark model with an effective potential in equally mixed scalar-vector harmonic form. The level of accuracy of the functional form, so derived at the model scale of a low ${Q}^{2},$ has been tested through a reasonable verification of the relevant sum rules due to Ellis and Jaffe in the case of ${g}_{1}^{p}{(x,Q}^{2})$ as well as Burkhardt and Cottingham in the case of ${g}_{2}^{p}{(x,Q}^{2}).$The twist-2 and the twist-3 components of ${g}_{2}^{p}{(x,Q}^{2})$ have also been separated at this level without effecting any further ${Q}^{2}$ evolution. But ${g}_{1}^{p}{(x,Q}^{2})$ has been evolved from a reference scale of ${Q}_{0}^{2}\ensuremath{\simeq}0.1{\mathrm{GeV}}^{2}$ to ${Q}^{2}=10.7{\mathrm{GeV}}^{2}$ to find a satisfactory comparison with the available experimental data.

The constituent quarks are interpreted as bound states, which have an internal structure. The quark distributions of the proton are related to those of the constituent quarks. The experiments support this hypothesis. Likewise the spin structure of the proton is related to the spin structure of the constituent quarks. We find that about 30% of the spin of a constituent quark is given by the valence quark, and 70% are provided by the gluons.

Nucleon and pion electromagnetic form factors in a light-front constituent quark model

Electroexcitation of nucleon resonances

A systematic procedure is described which permits the structure functions of nucleons to be calculated from a nonrelativistic constituent quark model. Transformation from the nucleon rest frame to the light cone or infinite momentum frame is accomplished based on work of Susskind, which does not require the weak binding and nonrelativistic kinematical approximations used in previous work. The light-cone distribution functions so obtained are then subjected to QCD evolution, giving predictions for the quark momentum densities. The model incorporates SU(6) breaking by the QCD-inspired one gluon exchange potential originated by De R\'ujula, Georgi, and Glashow, with the parameters fixed by Isgur and Karl from the N-\ensuremath{\Delta} mass splitting. In contrast with some previous work, the parameter values which fit the baryon mass spectrum are here shown to also give rather good agreement with the deep-inelastic flavor and spin asymmetries in the valence region.

We discuss the predictions of the Goldstone-boson-exchange constituent-quark model for the proton and neutron electric and magnetic form factors as well as the nucleon axial and induced pseudoscalar form factors. The results are calculated in a covariant framework using the point-form approach to relativistic quantum mechanics. The only input into the calculations is the nucleon wave function from the constituent-quark model. A remarkably consistent picture, with all aspects of the electroweak nucleon structure close to existing experimental data, is obtained.

Renormalizable coupled scalar and Dirac field theories are quantized in equal-${x}^{+}$ surfaces (called light fronts). Schwinger's action principle is employed to deduce the correct canonical equal-${x}^{+}$ (anti-) commutation relations. These theories are shown to be Lorentz-invariant. Generalized Schwinger conditions for a quantum field theory to be Lorentz-invariant are given and discussed in an appendix. Spectral sum rules are derived. Leading singularities of Green's functions and products of field operators near the light cone are studied and the implications to current algebra sum rules are discussed. We also discuss some of the delicate features of the light-front formulation.