Electromagnetic form factors of the baryon octet in the perturbative chiral quark model

We apply the perturbative chiral quark model at one loop to analyze the electromagnetic form factors of the baryon octet. The analytic expressions for baryon form factors, which are given in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, axial nucleon coupling, strong pion-nucleon form factor), and the numerical results for baryon magnetic moments, charge and magnetic radii are presented. Our results are in good agreement with experimental data.Received: 7 January 2003, Revised: 4 November 2003, Published online: 15 April 2004PACS: 12.39.Ki Relativistic quark model - 13.40.Gp Electromagnetic form factors - 14.20.Dh Protons and neutrons - 14.20.Jn Hyperons     

The fuzzy bag and baryonic properties with center of mass and recoil corrections

The fuzzy bag is a hadronic model which has features both of the bag model (energy-momentum conservation, QCD vacuum energy) and of relativistic potential models (confinement achieved through a potential). It is also a chiral model, with the unique property that the pion field is suppressed in the interior of the bag by means of a scalar potential, and yet chiral symmetry is preserved. This scalar potential allows one to control how far the pion field can penetrate in the interior of the bag. We calculate the masses of the fundamental baryon octet taking into account the center of mass, one-gluon exchange and one-pion exchange corrections. We also calculate the nucleon axial charge, charge radii and magnetic moments including center of mass and recoil corrections. The agreement with experiment is excellent, and the results indicate that the pion field is suppressed only very close to the center of the bag. Received: 14 January 2003 / Published online: 5 May 2003 RID="a" ID="a" e-mail: pilotto@if.ufrgs.br     

Nucleon charge form factors and chiral quark models

Calculations of the proton and neutron charge form factors G_E^p,n(q²) are presented, based on chiral bag as well as confining Dirac potential models with chiral pion-quark coupling. Special emphasis is placed on a detailed treatment of the charged pion cloud contribution to the nucleon current. The role of a finite extension of the pion-quark vertex in truncating the summation over intermediate quark bag states is studied. Quark core radii (including recoil corrections) are constrained by a simultaneous calculation of the nucleon axial form factor. The proton charge form factor is well reproduced for $\text{|q}{}^2\text{|}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 0.7}\text{GeV}$ with quark core rms radii between 0.5–0.6 fm. About $\text{1}\text{3}$ of the proton charge is carried by the pion cloud in this model. The neutron charge form factor is obtained with the correct sign and overall q² dependence but needs further refinements, probably at the level of the isoscalar form factor.     

Non-locality effects on the pion nucleon form factor

We investigate effects of the non-locality in the elementary pion quark coupling on theπNN form factor in the framework of the chiral bag model. We show that this nonlocality leads to shorter ranged form factors thereby reducing the discrepancy between large bag-model confinement radii and empirically found small-ranged cut-off parameters.     

A single quark model for single pion photoproduction at threshold

Single pion photoproduction is studied in a single quark model in which a quark absorbs the photon and then emits the pion, propagating as a quark between the two interactions. Two different chiral bag models are used which allow for the coupling of the quarks to the pion. Surprisingly, the single quark model reproduces the results of phenomenological models and agrees with the experimental amplitudes to within 30% at threshold.     

Properties of the nucleon in the nuclear medium within a chiral quark-meson theory

The modifications of the nucleon structure due to the presence of an external baryon medium are investigated in a chiral quark meson theory. To that end the Nambu-Jona-Lasinio (NJL) model is combined with the projected chiral soliton model. The medium effects are incorporated using the medium modified values of the pion decay constant and the pion and sigma masses at finite density. These values are evaluated within the NJL model. Using functional integral techniques the latter is solved in a quark continuum at finite density. The effective meson values serve to fix the parameters of the linear chiral sigma model which is solved in a variational projected mean field approach in order to obtain the nucleon properties. All nucleon properties show modifications in the medium except for the pion nucleon coupling constant. The proton radius shows an increase of 19% and the nucleon mass a decrease of 17% if the medium reaches nuclear matter density. The magnetic moments and axial vector coupling constant are less modified. All form factors show remarkable reduction at finite transfer momenta.     

Pion-nucleon scattering: Chiral symmetry and unitarity

The chiral quark models which have been constructed over the past five years generally preserve chiral symmetry in the tree approximation. However, unitarity is then violated. We examine the problem of going beyond the tree approximation for s-wave pion-nucleon scattering within the context of the cloudy bag model.     

Chiral Bag Model at Finite Temperature

By taking the thermodynamical contributions of the pion mesons cloud outside the bag into account,the chiral bag model is extended to finite temperature.The temperature dependence of the radius of the chiral bag and the critical temperature of quark deconfinement are given.     

The nucleon as a topological chiral soliton

We consider a version of the chiral bag model in which the interior quark sector is joined to an exterior meson sector through the requirement of continuity of the axial vector current at the bag surface. The negative energy quark sea plays a crucial role in this model, which reduces to the Skyrme soliton in the limit as the bag radius R→0. The “leakage” of baryon number and energy through the bag results in a remarkable insensitivity of these quantities to the bag radius. Although low-energy phenomenology should display a similar insensitivity, we suggest that a bag radius of 0.44 fm is advantageous on technical grounds. This choice of R should minimize the importance of gluon corrections, vacuum fluctuation effects, and inherent uncertainties in the effective lagrangian.     

Divergence of the quark self-energy in the second quantized chiral bag model

When summing over the intermediate quark states of a spherical cavity, the quark self-energy of the chiral bag model, in lowest order of the pion coupling, is shown to generate a series of terms, each one growing linearly with the angular variable κ. However, there is a cancellation between terms for different κ, which finally leads to an overall linearly divergent series.     

The effective chiral Lagrangian from the theta term

We construct the effective chiral Lagrangian involving hadronic and electromagnetic interactions originating from the QCD term. We impose vacuum alignment at both quark and hadronic levels, including field redefinitions to eliminate pion tadpoles. We show that leading time-reversal-violating (TV) hadronic interactions are related to isospin-violating interactions that can in principle be determined from charge-symmetry-breaking experiments. We discuss the complications that arise from TV electromagnetic interactions. Some implications of the expected sizes of various pion-nucleon TV interactions are presented, and the pion-nucleon form factor is used as an example.     

Electromagnetic properties of relativistic quarks in confining potentials

We investigate electromagnetic properties of the quark core of nucleons in a model with massless quarks in confining potentials. We find quark core rms radii of 0.6 fm or smaller to be compatible with form factor data corrected for pion cloud effects. Relations between the magnetic form factor and the axial vector or pseudoscalar form factors will also be discussed.     

Form factors in the projected linear chiral sigma model

Several nucleon form factors are computed within the framework of the linear chiral soliton model. To this end variational means and projection techniques applied to generalized hedgehog quark-boson Fock states are used. In this procedure the Goldberger-Treiman relation and a virial theorem for the pion-nucleon form factor are well fulfilled demonstrating the consistency of the treatment. Both proton and neutron charge form factors are correctly reproduced, as well as the proton magnetic one. The shapes of the neutron magnetic and of the axial form factors are good but their absolute values at the origin are too large. The slopes of all the form factors at zero momentum transfer are in good agreement with the experimental data. The pion-nucleon form factor exhibits to great extent a monopole shape with a cut-off mass ofΛ=690 MeV. Electromagnetic form factors for the vertexγNΔ and the nucleon spin distribution are also evaluated and discussed.     

Gluon condensates,chiral symmetry breaking and pion wave-function

We consider here chiral symmetry breaking in quantum chromodynamics arising from gluon condensates in vacuum. Through coherent states of gluons simulating a mean field type of approximation, we show that the off-shell gluon condensates of vacuum generate a mass-like contribution for the quarks, giving rise to chiral symmetry breaking. We next note that spontaneous breaking of global chiral symmetry links the four component quark field operator to the pion wave function. This in turn yields many hadronic properties in the light quark sector in agreement with experiments, leading to the conclusion that low energy hadron properties are primarily driven by the vacuum structure of quantum chromodynamics.     

Meson-Cloud Effects in the Electromagnetic Nucleon Structure

We study how the electromagnetic structure of the nucleon is influenced by a pion cloud. To this aim we make use of a constituent-quark model with instantaneous confinement and a pion that couples directly to the quarks. To derive the invariant 1-photon-exchange electron-nucleon scattering amplitude we employ a Poincaré-invariant coupled-channel formulation which is based on the point-form of relativistic quantum mechanics. We argue that the electromagnetic nucleon current extracted from this amplitude can be reexpressed in terms of pure hadronic degrees of freedom with the quark substructure of the pion and the nucleon being encoded in electromagnetic and strong vertex form factors. These are form factors of bare particles, i.e. eigenstates of the pure confinement problem. First numerical results for (bare) photon-nucleon and pion-nucleon form factors, which are the basic ingredients of the further calculation, are given for a simple 3-quark wave function of the nucleon.     

Solution of a symmetry conserving chiral soliton model for nucleon and delta

The linear chiral soliton model is solved for nucleon and delta by constructing Fock states in the coherent pair approximation with correct spin and isospin properties. The quark configurations are those arising from theSU(2)×SU(2) coupling of three quarks in 1s-orbits. The overall Fock state is formed by the vector coupling of the quark configurations with the pion coherent state and thus avoids the use of the hedgehog ansatz. The sigma field is treated in the mean field approximation. Equations of motion for the quark, sigma and pion fields are solved in the static approximation. Soliton solutions are found with properties that are in reasonable agreement with those observed for the nucleon and delta including the axial vector coupling constant. With only components having zero and one unpaired pion in the coherent pair approximation the nucleon mass is found to be larger than that using the projected hedgehog approach.     

On a possible estimation of the constituent-quark parameters from Jefferson Lab experiments on the pion form factor

The charge form factor of the pion is calculated for the momentum transfer range of the Jefferson Lab experiments. The approach is based on the instant form of the relativistic Hamiltonian dynamics. It is shown that the form-factor dependence on the choice of the model for the quark wave function in the pion is weak, while the dependence on the constituent-quark mass is rather significant. It is possible to estimate the mass of the constituent quark and the sum of the anomalous magnetic moments of the u- and -quarks from the JLab experiments. Received: 3 April 2000 / Revised version: 25 February 2001 / Published online: 25 April 2001     

Pion decays and the pion electromagnetic form factor in a σ-model with quarks

We study in the one-loop approximation the decays of the pion and the pion electromagnetic form factor at low q² in the framework of a σ-model with quarks. The theory has a free parameters the quark and σ masses and the results are very insensitive to their values. We get good approximation for all processes considered except for the ratio of the axial to the vector form factor that appear in the electronic radiative decay of the charged pion. The reason is probably that our model includes the pion-pion interaction only in the isoscalar s-wave at the one-loop level.