Soliton Models for the Nucleon and Predictions for the Nucleon Spin Structure

In these lectures the three flavor soliton approach for baryons is reviewed. Effects of flavor symmetry breaking in the baryon wave--functions on axial current matrix elements are discussed. A bosonized chiral quark model is considered to outline the computation of spin dependent nucleon structure functions in the soliton picture.Comment: 12 pages, Lectures presented at the Advanced Study Institute Symmetry and Spin, Prague, 2001, to appear in the proceedings. References correcte

Wave-Packet Scattering off the Kink-Solution

We investigate the propagation of a wave--packet in the $\phi^4$ model. We solve the time-dependent equation of motion for two distinct initial conditions: The wave-packet in a trivial vacuum background and in the background of the kink soliton solution. We extract the scattering matrix from the wave-packet in the kink background at very late times and compare it with the result from static potential scattering in the small amplitude approximation. We vary the size of the initial wave-packet to identify non-linear effects as, for example, the replacement of the center of the kink.Comment: 15 pages, 7 figures (from 14 eps files), 4 tables, Int. J. Mod. Phys. A, in prin

On the strange vector form factors of the nucleon in the NJL soliton model

Within the Nambu--Jona--Lasinio model strange degrees of freedom are incorporated into the soliton picture using the collective approach of Yabu and Ando. The form factors of the nucleon associated with the nonet vector current are extracted. The numerical results provide limits for the strange magnetic moment: $-0.05\le\mu_s\le0.25$. For the strange magnetic form factor of the nucleon the valence quark and vacuum contributions add coherently while there are significant cancellations for the strange electric form factor.Comment: 9 pages, one figure, postscript file submitted as uuencoded compressed fil

Chiral Quark Model

In this talk I review studies of hadron properties in bosonized chiral quark models for the quark flavor dynamics. Mesons are constructed from Bethe--Salpeter equations and baryons emerge as chiral solitons. Such models require regularization and I show that the two--fold Pauli--Villars regularization scheme not only fully regularizes the effective action but also leads the scaling laws for structure functions. For the nucleon structure functions the present approach serves to determine the regularization prescription for structure functions whose leading moments are not given by matrix elements of local operators. Some numerical results are presented for the spin structure functions.Comment: Talk presented at the workshop QCD 2002, IIT Kanpur, Nov. 2002, 10 pages, proceedings style files include

Fermion Energies in the Background of a Cosmic String

We provide a thorough exposition, including technical and numerical details, of previously published results on the quantum stabilization of cosmic strings. Stabilization occurs through the coupling to a heavy fermion doublet in a reduced version of the standard model. We combine the vacuum polarization energy of fermion zero-point fluctuations and the binding energy of occupied energy levels, which are of the same order in a semi-classical expansion. Populating these bound states assigns a charge to the string. We show that strings carrying fermion charge become stable if the electro-weak bosons are coupled to a fermion that is less than twice as heavy as the top quark. The vacuum remains stable in our model, because neutral strings are not energetically favored. These findings suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model.Comment: 38 pages, 6 figures, version accepted for publication in Phys Rev

One-dimensional infinite component vector spin glass with long-range interactions

We investigate zero and finite temperature properties of the one-dimensional spin-glass model for vector spins in the limit of an infinite number m of spin components where the interactions decay with a power, \sigma, of the distance. A diluted version of this model is also studied, but found to deviate significantly from the fully connected model. At zero temperature, defect energies are determined from the difference in ground-state energies between systems with periodic and antiperiodic boundary conditions to determine the dependence of the defect-energy exponent \theta on \sigma. A good fit to this dependence is \theta =3/4-\sigma. This implies that the upper critical value of \sigma is 3/4, corresponding to the lower critical dimension in the d-dimensional short-range version of the model. For finite temperatures the large m saddle-point equations are solved self-consistently which gives access to the correlation function, the order parameter and the spin-glass susceptibility. Special attention is paid to the different forms of finite-size scaling effects below and above the lower critical value, \sigma =5/8, which corresponds to the upper critical dimension 8 of the hypercubic short-range model.Comment: 27 pages, 27 figures, 4 table

Nucleon Structure Functions from a Chiral Soliton in the Infinite Momentum Frame

We study the frame dependence of nucleon structure functions obtained within a chiral soliton model for the nucleon. Employing light cone coordinates and introducing collective coordinates together with their conjugate momenta, translational invariance of the solitonic quark fields (which describe the nucleon as a localized object) is restored. This formulation allows us to perform a Lorentz boost to the infinite momentum frame of the nucleon. The major result is that the Lorentz contraction associated with this boost causes the leading twist contribution to the structure functions to properly vanish when the Bjorken variable $x$ exceeds unity. Furthermore we demonstrate that for structure functions calculated in the valence quark approximation to the Nambu--Jona--Lasinio chiral soliton model the Lorentz contraction also has significant effects on the structure functions for moderate values of the Bjorken variable $x$.Comment: 16 pages, 1 figure, revised version to be published in Int. J. Mod. Phys.

Instability of the hedgehog shape for the octet baryon in the chiral quark soliton model

In this paper the stability of the hedgehog shape of the chiral soliton is studied for the octet baryon with the SU(3) chiral quark soliton model. The strangeness degrees of freedom are treated by a simplified bound-state approach, which omits the locality of the kaon wave function. The mean field approximation for the flavor rotation is applied to the model. The classical soliton changes shape according to the strangeness. The baryon appears as a rotational band of the combined system of the deformed soliton and the kaon.Comment: 24 pages, LaTeX, 8 eps file