E2/M1E2/M1 Ratio for the γN→Δ\gamma N\rightarrow \Delta Transition in the Chiral Quark Soliton Model

We calculate the electric quadrupole to magnetic dipole transition ratio $E2/M1$ for the reaction \gamma N \ra \Delta(1232) in the chiral quark soliton model. The calculated $E2/M1$ ratio is in a good agreement with the very new experimental data. We obtain non-zero negative value for the electric quadrupole $N-\Delta$ transition moment, which suggests an oblate deformed charge structure of the nucleon or/and the delta isobar. Other observables related to this quantity, namely the $N-\Delta$ mass splitting, the isovector charge radius, and isovector magnetic moment, are properly reproduced as well.Comment: 11 pages, revtex, a figure included as a postscript fil

B=1 Soliton of the Nambu - Jona-Lasinio model in medium}

The solitonic sector of the Nambu - Jona-Lasinio model with baryon number one is solved in the presence of an external medium. The calculations fully include the polarization of both the Dirac sea and the medium as well as the Pauli blocking effect. We found that with an increasing density the medium destabilizes the soliton. At finite medium density the soliton mass gets reduced whereas the mean square baryon radius shows an increase - a swelling of the soliton. At some critical density of about two times nuclear matter density there is no localized solution - the soliton disappears.Comment: PHYSTEX, 14 pages, 5 figures (available upon request), Preprint RUB-TPII-26/9

B=3 Tetrahedrally Symmetric Solitons in the Chiral Quark Soliton Model

In this paper, B=3 soliton solutions with tetrahedral symmetry are obtained numerically in the chiral quark soliton model using the rational map ansatz. The solution exhibits a triply degenerate bound spectrum of the quark orbits in the background of tetrahedrally symmetric pion field configuration. The corresponding baryon density is tetrahedral in shape. Our numerical technique is independent on the baryon number and its application to $B \geq 4$ is straightforward.Comment: 4 pages, 3 figure

1/Nc1/N_c Rotational Corrections to gAg_A and Isovector Magnetic Moment of the Nucleon

The $1/N_c$ rotational corrections to the axial vector constant and the isovector magnetic moment of the nucleon are studied in the Nambu -- Jona-Lasinio model. We follow a semiclassical quantization procedure in terms of path integrals in which we can include perturbatively corrections in powers of angular velocity $\Omega \sim \frac 1{N_c}$. We find non-zero $1/N_c$ order corrections from both the valence and the Dirac sea quarks. These corrections are large enough to resolve the long-standing problem of a strong underestimation of both $g_A$ and $\mu^{IV}$ in the leading order. The axial constant $g_A$ is well reproduced, whereas the isovector magnetic moment $\mu^{IV}$ is still underestimated by 25 \%.Comment: (Revtex), 10 pages (3 figures available on request), report RUB-TPII-53/9

Light-flavor sea-quark distributions in the nucleon in the SU(3) chiral quark soliton model (I) -- phenomenological predictions --

Theoretical predictions are given for the light-flavor sea-quark distributions including the strange quark ones on the basis of the flavor SU(3) version of the chiral quark soliton model. Careful account is taken here of the SU(3) symmetry breaking effects due to the mass difference between the strange and nonstrange quarks. This effective mass difference $\Delta m_s$ between the strange and nonstrange quarks is the only one parameter necessary for the flavor SU(3) generalization of the model. A particular emphasis of study is put on the {\it light-flavor sea-quark asymmetry} as exemplified by the observables $\bar{d} (x) - \bar{u} (x), \bar{d} (x) / \bar{u} (x), \Delta \bar{u} (x) - \Delta \bar{d} (x)$ as well as on the {\it particle-antiparticle asymmetry} of the strange quark distributions represented by $s (x) - \bar{s} (x), s (x) / \bar{s} (x), \Delta s (x) - \Delta \bar{s} (x)$ etc. As for the unpolarized sea-quark distributions, the predictions of the model seem qualitatively consistent with the available phenomenological information provided by the NMC data for $\bar{d} (x) - \bar{u} (x)$, the E866 data for $\bar{d} (x) / \bar{u} (x)$, the CCFR data and Barone et al.'s fit for $s (x) / \bar{s} (x)$ etc. The model is shown to give several unique predictions also for the spin-dependent sea-quark distribution, such that $\Delta s (x) \ll \Delta \bar{s}(x) \lesssim 0$ and $\Delta \bar{d}(x) < 0 < \Delta \bar{u}(x)$, although the verification of these predictions must await more elaborate experimental investigations in the near future.Comment: 36 pages, 20 EPS figures. The revised version accepted for publication in Phys. Rev. D. The title has been changed, and the body of the paper has been divided into two pieces, i.e.. the present one which discusses the main phenomenological predictions of the model and the other one which describes the detailed formulation of the flavor SU(3) chiral quark soliton model to predict light-flavor quark and antiquark distribution functions in the nucleo

Pion light-cone wave function and pion distribution amplitude in the Nambu-Jona-Lasinio model

We compute the pion light-cone wave function and the pion quark distribution amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars regularization method and as a result the distribution amplitude satisfies proper normalization and crossing properties. In the chiral limit we obtain the simple results, namely phi_pi(x)=1 for the pion distribution amplitude, and = -M / f_pi^2 for the second moment of the pion light-cone wave function, where M is the constituent quark mass and f_pi is the pion decay constant. After the QCD Gegenbauer evolution of the pion distribution amplitude good end-point behavior is recovered, and a satisfactory agreement with the analysis of the experimental data from CLEO is achieved. This allows us to determine the momentum scale corresponding to our model calculation, which is close to the value Q_0 = 313 MeV obtained earlier from the analogous analysis of the pion parton distribution function. The value of is, after the QCD evolution, around (400 MeV)^2. In addition, the model predicts a linear integral relation between the pion distribution amplitude and the parton distribution function of the pion, which holds at the leading-order QCD evolution.Comment: mistake in Eq.(38) correcte

Baryons as non-topological chiral solitons

The present review gives a survey of recent developments and applications of the Nambu--Jona-Lasinio model with $N_f=2$ and $N_f=3$ quark flavors for the structure of baryons. The model is an effective chiral quark theory which incorporates the SU(N$_f$)$_L\otimes$SU(N$_f$)$_R\otimes$U(1)$_V$ approximate symmetry of Quantum chromodynamics. The approach describes the spontaneous chiral symmetry breaking and dynamical quark mass generation. Mesons appear as quark-antiquark excitations and baryons arise as non-topological solitons with three valence quarks and a polarized Dirac sea. For the evaluation of the baryon properties the present review concentrates on the non-linear Nambu--Jona-Lasinio model with quark and Goldstone degrees of freedom which is identical to the Chiral quark soliton model obtained from the instanton liquid model of the QCD vacuum. In this non-linear model, a wide variety of observables of baryons of the octet and decuplet is considered. These include, in particular, electromagnetic, axial, pseudoscalar and pion nucleon form factors and the related static properties like magnetic moments, radii and coupling constants of the nucleon as well as the mass splittings and electromagnetic form factors of hyperons. Predictions are given for the strange form factors, the scalar form factor and the tensor charge of the nucleon.Comment: 104 pages, 27 figures as uuencoded and compressed postscript files , hardcopy available upon request; Prog.Part.Nucl.Phys. 37 (1996) (in print

Solution of the Kwiecinski evolution equations for unintegrated parton distributions using the Mellin transform

The Kwiecinski equations for the QCD evolution of the unintegrated parton distributions in the transverse-coordinate space (b) are analyzed with the help of the Mellin-transform method. The equations are solved numerically in the general case, as well as in a small-b expansion which converges fast for b Lambda_QCD sufficiently small. We also discuss the asymptotic limit of large bQ and show that the distributions generated by the evolution decrease with b according to a power law. Numerical results are presented for the pion distributions with a simple valence-like initial condition at the low scale, following from chiral large-N_c quark models. We use two models: the Spectral Quark Model and the Nambu--Jona-Lasinio model. Formal aspects of the equations, such as the analytic form of the b-dependent anomalous dimensions, their analytic structure, as well as the limits of unintegrated parton densities at x -> 0, x -> 1, and at large b, are discussed in detail. The effect of spreading of the transverse momentum with the increasing scale is confirmed, with growing asymptotically as Q^2 alpha(Q^2). Approximate formulas for for each parton species is given, which may be used in practical applications.Comment: 18 pages, 6 figures, RevTe

Real and Virtual Compton Scattering off the Nucleon

A review is given of the very recent developments in the fields of real and virtual Compton scattering off the nucleon. Both real and virtual Compton scattering reactions are discussed at low outgoing photon energy where one accesses polarizabilities of the nucleon. The real Compton scattering at large momentum transfer is discussed which is asymptotically a tool to obtain information on the valence quark wave function of the nucleon. The rapid developments in deeply virtual Compton scattering and associated meson electroproduction reactions at high energy, high photon virtuality and small momentum transfer to the nucleon are discussed. A unified theoretical description of those processes has emerged over the last few years, which gives access to new, generalized parton distributions. The experimental status and perspectives in these fields are also discussed.Comment: 25 pages, 17 figure

Magnetic Oscillations in Dense Cold Quark Matter with Four-Fermion Interactions

The phase structures of Nambu-Jona-Lasinio models with one or two flavours have been investigated at non-zero values of $\mu$ and $H$, where $H$ is an external magnetic field and $\mu$ is the chemical potential. In the phase portraits of both models there arise infinitely many massless chirally symmetric phases, as well as massive ones with spontaneously broken chiral invariance, reflecting the existence of infinitely many Landau levels. Phase transitions of first and second orders and a lot of tricritical points have been shown to exist in phase diagrams. In the massless case, such a phase structure leads unavoidably to the standard van Alphen-de Haas magnetic oscillations of some thermodynamical quantities, including magnetization, pressure and particle density. In the massive case we have found an oscillating behaviour not only for thermodynamical quantities, but also for a dynamical quantity as the quark mass. Besides, in this case we have non-standard, i.e. non-periodic, magnetic oscillations, since the frequency of oscillations is an $H$-dependent quantity.Comment: latex, 29 pages, 8 figure