In this paper we present the derivation as well as the numerical results for the electromagnetic form factors of the nucleon within the chiral quark soliton model in the semiclassical quantization scheme. The model is based on semibosonized SU(2) Nam
bu -- Jona-Lasinio lagrangean, where the boson fields are treated as classical ones. Other observables, namely the nucleon mean squared radii, the magnetic moments, and the nucleon--$Delta$ splitting are calculated as well. The calculations have been done taking into account the quark sea polarization effects. The final results, including rotational $1/N_c$ corrections, are compared with the existing experimental data, and they are found to be in a good agreement for the constituent quark mass of about 420 MeV. The only exception is the neutron electric form factor which is overestimated.
We calculate the axial form factor in the chiral quark soliton (semibosonized Nambu - Jona-Lasinio) model using the semiclassical quantization scheme in the next to leading order in angular velocity. The obtained axial form factor is in a good absolu
te (without additional scaling) agreement with the experimental data. Both the value at the origin and the $q$-dependence of the form factor as well as the axial m.s.radius are fairly well reproduced.
We extract the isovector tensor nucleon form factors, which play an important role in understanding the transverse spin structure of the nucleon when related to the quark helicity-flip generalized parton distributions via their first moments. We empl
oy the light-cone QCD sum rules to leading order in QCD and include distribution amplitudes up to twist 6 in order to calculate the three tensor form factors $H_T$, $E_T$ and $tilde{H}_T$. Our results agree well with those from other approaches in the low and high momentum-transfer regions.
Vector and axial form factors in the quark resonance model are analyzed with a combination of theoretical and phenomenological arguments. The new form of form factors is deduced from $Delta$(1232) excitation models and available data. The vector part
is shown to agree with the resonant contribution to electron-proton inclusive $F_2$ data. The axial part is obtained by finding a simultaneous fit to ANL and BNL $frac{d sigma}{d Q^2}$ neutrino scattering data. The best fit corresponds to $C_5^A(0)=0.88$ in the Rarita Schwinger formalism.
The electromagnetic form factors provide important hints for the internal structure of the nucleon and continue to be of major interest for experimentalists. For an intermediate range of momentum transfers the form factors can be calculated on the la
ttice. However, reliability of the results is limited by systematic errors due to the required extrapolation to physical quark masses. Chiral effective field theories predict a rather strong quark mass dependence in a range which was yet unaccessible for lattice simulations. We give an update on recent results from the QCDSF collaboration using gauge configurations with Nf=2, non-perturbatively O(a)-improved Wilson fermions at very small quark masses down to 340 MeV pion mass, where we start to probe the relevant quark mass region.