Chiral Soliton Model Research Articles

Planar Diagrams versus Chiral Solitons

It is noted that the sum of planar diagrams in QCD 4 is not a sum of poles, contrary to the literature. Implications for chiral soliton models are discussed

The pion-nucleon sigma commutator in chiral models of the nucleon

A new set of symmetry-breaking terms to describe the effects of current quark masses in confining chiral soliton models is proposed. We calculate the pion-nucleon sigma commutator in such models and obtain values in the range 30–40 MeV, to which the valence quarks and pion cloud make roughly equal contributions. We also note that the values for the commutator extracted from lattice QCD calculations agree well with the valence contribution, rather than the full σ πN.

Strange systems of baryons in chiral soliton models

Strange systems of baryons in chiral soliton models

The Phase Shifts for Λ-N Elastic Scattering

A chiral soliton model with the gluon field, chiral doublet -field and chiral singlet ω-meson field is employed to study Λ-nucleon elastic scattering phase shifts within the framework of the relativistic two-quark-cluster theory. The phase shifts are sensitive to the strange quark in the Λ-hyperon.

Splitting of the neutron and proton electric polarizabilities in a hedgehog model

Proton and neutron proper (static) electric polarizabilities, α n and α p, are calculated in a chiral soliton model with quarks and mesons. Semiclassical methods ( 1 N c expansion, cranking, linear response theory) are used. We find α n> α p, and the splitting effect is of the order of 1 N c . Its magnitude, 5.4×10 10−4 fm, agrees with recent experimental data. The average nucleon po larizability is of the order of N c. The numerical value of this quantity obtained from our semiclassical method is roughly a factor of three larger than the experimental value. This is because the contribution of pion-Δ intermediate states is artificially enhanced in hedgehog models.

The two-point approximation for the Casimir energy in the self-consistent chiral soliton model of the nucleon

The two-point approximation for strongly non-local effective actions is studied in the particular case of the chiral soliton model of the nucleon. Sea-quark effects are included self-consistently (within the approximation), and a self-consistent soliton obtained with observables differing (for physically relevant quark masses) by about 20% from those found from the corresponding exact calculation. The theory is defined with a momentum-space cut-off, and the effect of different choices of cut-off is investigated. An analytically much simpler (pole) form of the basic approximation is also described, which leads to a simple algebraic self-consistent equation for the soliton profile function, the solution of which is essentially indistinguishable from the full two-point approximation. This pole form of the approximation therefore provides a reasonably accurate, practical and efficient approach to such non-local problems.

Nucleon-antinucleon annihilation in the chiral soliton model

We investigate the annihilation process of nucleons in the chiral soliton model by the path integral method. A soliton-antisoliton pair is shown to decay into mesons at a range of about 1 fm, defined by the S S potential. The contribution of the annihilation channel to the elastic scattering is discussed.

Canonical quantization in chiral-soliton model with a hidden local symmetry.

Quantum aspects of an SU(2) chiral soliton with a hidden local symmetry and zero winding number are investigated in the collective-coordinate approach. This model allows us to examine various procedures of canonical quantization. We consider first the minimal or intrinsic formulation, where the hidden symmetry is eliminated. We examine particle motion on a sphere ${S}^{2}$ in terms of a minimal set of two independent coordinates {${q}^{b}, b=1, 2$}. Second, the embedding or immersion formulation is examined, where a curved manifold is embedded in a Euclidean space. Third, we consider the canonical quantization with the hidden local symmetry. A remark is given on the existence of a "pionlike" quantum soliton.

Slowly rotating skyrmions in broken SU(3)

We study static baryon properties for chiral soliton models is broken SU (3) when the assumption of slow rotations is literally taken into account.

On exotic systems of baryons in chiral soliton models

The role of zero mode quantum corrections to the energy of baryonic systems with exotic quantum numbers (strangeness) is discussed. A simple expression for the contribution depending on strange inertia is obtained in the SU (3)-collective coordinate quantization approach and it is shown that this correction stabilizes the system the stronger the greater their baryon number is. Furthermore, systems are considered which could be interpreted in the quark model language as containing additional q q -pairs. It is argued that a strange skyrmion crystal should have additional binding in comparison with the SU (2)-quantized neutron crystal.

Regularization of the vacuum energy in the chiral-soliton model as an energy-eigenvalue sum.

In the chiral-soliton model with a finite ultraviolet cutoff, which describes the low-energy, large-{ital N}{sub {ital c}} limit of the strong interactions, we investigate the fermion vacuum energy, expressed as a sum over the eigenvalues of the relevant single-particle Dirac Hamiltonian, in order to clarify recent claims that it depends strongly on the regularization scheme, and can even exhibit vacuum instability. On the basis of a simple physically motivated criterion, we are able to determine which regulating functions can be considered as well behaved. Aided by a mapping of the problem onto an equivalent one in the proper-time formalism, we show that for these well-behaved regulators the vacuum energy does not depend significantly on the regularization scheme and there is no vacuum instability, in line with original expectations.

Hot nucleons

We present a systematic study of the nucleons' static and dynamic properties at finite temperatures. To describe the nucleon, we make use of the topological chiral soliton model based on a non-linear meson theory of interacting pions, ϱ- and ω-mesons. The nucleon properties are determined by the mesonic parameters. For the temperature dependence of these meson parameters, we use rigorous results from chiral perturbation theory as well as predictions from the Nambu-Jona-Lasinio model. We discuss bulk properties of the nucleon, electroweak form factors, strong and weak interaction regions. We stress the importance of these effects for the study of hadronic systems close to the chiral restoration phase transition. Furthermore, we derive an expression for the temperature dependence of the non-perturbative gluon condensate.

Chiral Soliton Model with Dynamical Restoration of Chiral Symmetry from Quark Flavour Dynamics

AbstractThe Nambu‐Jona‐Lasinio model as a particular model of quark flavour dynamics is bosonized in the low‐energy regime using a generalized heat kernel expansion with local mass scale. The resulting effective meson Lagrangian defines a chiral soliton model, the solutions of which show a partial restoration of chiral symmetry inside the soliton.

MESONS, SKYRMIONS AND BARYONS

We review the construction of low energy effective actions for QCD expressed in terms of mesons and baryons rather than quarks and gluons. The mesons consist of quark-antiquark pairs bound by effective gluon exchange, while the baryons contain three valence quarks, also bound by effective gluon exchange, but enveloped in a meson cloud (the “sea quarks”), which may take the form of a chiral soliton. Such a “chiral quark soliton model” offers a unified approach to the various superficially dissimilar models of baryons currently popular, in particular constituent quark models, chiral bags, and Skyrmions, permitting an objective assessment of which is likely to be the most useful for a given physical problem.

Discrete symmetries and statistics of solitons in the presence of topological actions

Abstract We show that the intrinsic charge conjugation or parity of a soliton-antisoliton pair in the chiral soliton model equals minus one if the solitons are fermions, and plus one if they are bosons. The result is intimately connected to the sign for rotating a soliton through 2π, or for interchanging two identical solitons, and holds in any theory where a topological term contributes to the statistics of solitons.

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.

Spin content of the nucleon in a non-topological chiral soliton model

The spin content of the proton is investigated by studying the flavor singlet axial structure of the nucleon in a non-topological chiral soliton model. In order to construct a nucleon state we used the generator coordinate projection method as well as a coherent state for the meson wave function. Using a standard set of parameters we found the value g 0A ≃ 0.44 for the flavor singlet axial vector coupling constant. This result is not far from that of a typical valence quark model.

Singlet axial-vector current and the "proton-spin" question.

As a preliminary we consider the phenomenology of the European Muon Collaboration experimental result without assuming SU(3) invariance. The most reliable conclusion is that the singlet axial-vector current matrix element is rather small. We calculate this matrix element in a variety of chiral-soliton models in which the axial anomaly equation is satisfied. There are a number of subtleties which we explore. It turns out that reasonable chiral models including only pseudoscalar fields give a zero matrix element. Taking "short-distance" effects consistently into account via the inclusion of vector mesons or explicit quarks does give a small nonzero result. The situation is closely analogous to the prediction of a nonzero result for the nonelectromagnetic part of the neutron-proton mass difference in these chiral models.

A Chiral Quark Soliton Model for the Baryon Embedded in Nuclear Medium11The project supported in part by the National Natural Science Foundation of China.

A chiral quark soliton model for the baryon embedded in nuclear medium is proposed. The effective vacuum expectation value of the scalar field felt up by a quark of the baryon in nuclear medium is estimated. The model is solved for the hedgehog baryon state in the semiclassical approximation and self–consistent approach. Some static properties of the baryon embedded in nuclear medium are calculated. An increment in radius of the baryon is obtained. The numerical results can be used to explain the -dependence of EMC effect and vacuum pressure constants in nuclear medium.

Electromagnetic self-energy of proton and neutron in a chiral soliton model with vector mesons

We calculate the electromagnetic self-energy of the nucleons to lowest-order perturbation theory (one-photon exchange) in a chiral soliton model with vector mesons, including a sum over intermediate states. The matrix elements can be evaluated using wave functions for the baryons given explicitly in terms of collective coordinates. The dependence of the resulting electromagnetic mass splitting between proton and neutron on the values of the input parameters (in our case the pion decay constant f π and the ω coupling constant g ω ) as well as on the definition of the electromagnetic current (Noether method versus current field identity) is exhibited.