Chiral Soliton Model Research Articles

On the Width of Collective Excitations in Chiral Soliton Models

In chiral soliton models for baryons the computation of hadronic decay widths of baryon resonances is a long standing problem. For the three flavor Skyrme model I present a solution to this problem that satisfies large--$N_C$ consistency conditions. As an application I focus on the hadronic decay of the $\Theta$ and $\Theta^*$ pentaquarks.

Nuclear matter in the chiral quark soliton model with vector mesons(Fundamental Problems and Applications of Quantum Field Theory-Topological Aspects of Quantum Field Theory-)

Nuclear matter in the chiral quark soliton model with vector mesons(Fundamental Problems and Applications of Quantum Field Theory-Topological Aspects of Quantum Field Theory-)

Generalized form factors, generalized parton distributions, and the spin contents of the nucleon

With a special intention of clarifying the underlying spin contents of the nucleon, we investigate the generalized form factors of the nucleon, which are defined as the $n$th $x$ moments of the generalized parton distribution functions, within the framework of the chiral quark soliton model. A particular emphasis is put on the pion mass dependence of final predictions, which we shall compare with the predictions of lattice QCD simulations carried out in the so-called heavy pion region around ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}(700--900)\text{ }\text{ }\mathrm{MeV}$. We find that some observables are very sensitive to the variation of the pion mass. It will be argued that the negligible importance of the quark orbital angular momentum indicated by the LHPC and QCDSF lattice collaborations might be true in the unrealistic heavy pion world, but it is not necessarily the case in our real world close to the chiral limit.

Pentaquarks in chiral soliton models

The spectra of pentaquarks, some of them observed recently, are discussed within the topological soliton model and compared with the simplified quark picture. The results obtained within the chiral soliton model depend to some extent on the quantization scheme: rigid rotator, soft rotator, or bound state model. The similarity of the spectra of baryon resonances obtained within the quark model and the chiral soliton model is pointed out, although certain differences take place as well, which require careful interpretation. In particular, considerable variation of the strange antiquark mass in different SU(3) multiplets of pentaquarks is required to fit their spectra obtained from chiral solitons. Certain difference in the masses of “good” and “bad” diquarks is required as well, in qualitative agreement with previously made estimates. The partners of exotic states with different values of spin which belong to higher SU(3) multiplets have energy considerably higher than the states with the lowest spin, and this could be a point where the difference from simple quark models is striking. The antiflavor excitation energies for multibaryons are estimated as well, and the binding energies of gJ-hypernuclei and anticharm (antibeauty) hypernuclei are presented for several baryon numbers. Some deficiencies are pointed out in the arguments in the literature against the validity of the chiral soliton approach and/or the SU(3) quantization models.

Baryon spectrum in largeNcchiral soliton and in quark models

Strangeness contents of baryons are calculated within rigid rotator model for arbitrary number of colors $N_c$. The problem of extrapolation to realistic value $N_c=3$ is noted, based on explicit calculations and comparison of rigid rotator and rigid oscillator variants of the model. Some features of exotic baryon spectra ($\{\bar{10}\}, \{27\}$-and $\{35\}$-plets of baryons) obtained in the chiral soliton approach can be understood in terms of simplified quark $(4q\bar{q})$ wave functions. The effective mass of strange antiquark in different SU(3) multiplets of pentaquarks should depend on the particular multiplet, to link the predictions of soliton and quark models. The estimate of the $6_F$ and $\bar{3}_F$ diquarks mass difference can be made from comparison with chiral soliton model results for masses of exotic baryons from different SU(3)-multiplets. The masses of baryons partners with different values of spin $J$ are also estimated.

Mathematical Analysis of a Generalized Chiral Quark Soliton Model

A generalized version of the so-called chiral quark soliton model (CQSM) in nuclear physics is introduced. The Hamiltonian of the generalized CQSM is given by a Dirac type operator with a mass term being an operator-valued function. Some mathematically rigorous results on the model are reported. The subjects included are: (i) supersymmetric structure; (ii) spectral properties; (iii) symmetry reduction; (iv) a unitarily equivalent model.

Pion mass dependence of the nucleon mass in the chiral quark soliton model

The dependence of the nucleon mass on the mass of the pion is studied in the framework of the chiral quark-soliton model. A remarkable agreement is observed with lattice data from recent full dynamical simulations. The possibility and limitations to use the results from the chiral quark soliton model as a guideline for the chiral extrapolation of lattice data are discussed.

Mass splittings of nuclear isotopes in chiral solition approach

The differences in the masses of isotopes with atomic numbers between ∼10 and ∼30 can be described within the chiral soliton model in satisfactory agreement with data. The rescaling of the model is necessary for this purpose—a decrease in the Skyrme constant by ∼30%, providing the “nuclear variant” of the model. The asymmetric term in the Weizsäcker-Bethe-Bacher mass formula for nuclei can be obtained as the isospin-dependent quantum correction to the nucleus energy. Some predictions of the binding energies of neutron-rich isotopes are made in this way from, e.g., 16Be, 19B to 31Ne or 32Na. The neutron-rich nuclides with high values of isospin are unstable relative to decay owing to strong interactions. The SK4 (Skyrme) variant of the model, as well as the SK6 variant (sixth-order term in the derivatives of the chiral field in the Lagrangian as soliton stabilizer), is considered; the rational-map approximation is used to describe multi-Skyrmions.

Nuclear matter in the chiral quark soliton model with vector mesons(Fundamental Problems and Applications of Quantum Field Theory)

Nuclear matter in the chiral quark soliton model with vector mesons(Fundamental Problems and Applications of Quantum Field Theory)

Bound-state versus collective-coordinate approaches in chiral soliton models and the width of the Θpentaquark

We thoroughly compare the bound state and rigid rotator approaches to three--flavored chiral solitons. We establish that these two approaches yield identical results for the baryon spectrum and kaon--nucleon $S$--matrix in the limit that the number of colors ($N_C$) tends to infinity. After proper subtraction of the background phase shift the bound state approach indeed exhibits a clear resonance behavior in the strangeness $S=+1$ channel. We present a first dynamical calculation of the widths of the $\Theta^+$ and $\Theta^*$ pentaquarks for finite $N_C$ in a chiral soliton model.

Quantization of the chiral soliton in medium

Chiral solitons coupled with quarks in medium are studied based on the Wigner–Seitz approximation. The chiral quark soliton model is used to obtain the classical soliton solutions. To investigate nucleon and Δ in matter, the semi-classical quantization is performed by the cranking method. The saturation for nucleon matter and Δ matter are observed.

Structure and reactions of pentaquark baryons

We review the current status of the exotic pentaquark baryons. After a brief look at experiments of both positive and negative results, we discuss theoretical methods to study the structure and reactions for the pentaquarks. First we introduce the quark model and the chiral soliton model, where we discuss the relation of mass spectrum and parity with some emphasis on the role of chiral symmetry. It is always useful to picture the structure of the pentaquarks in terms of quarks. As for other methods, we discuss a model independent method, and briefly mention the results from the lattice and QCD sum rule. Decay properties are then studied in some detail, which is one of the important properties of Theta+. We investigate the relation between the decay width and the quark structure having certain spin-parity quantum numbers. Through these analyses, we consider as plausible quantum numbers of Theta+, JP = 3/2-. In the last part of this note, we discuss production reactions of Theta+ which provide links between the theoretical models and experimental information. We discuss photoproductions and hadron-induced reactions which are useful to explore the nature of Theta+

Chiral-odd twist-3 e( x) of the nucleon

We clarify the nonperturbative origin of the δ -function singularity at x = 0 in the chiral-odd twist-3 distribution function e ( x ) of the nucleon. We also compare a theoretical prediction for e ( x ) based on the chiral quark soliton model with the empirical information extracted from the CLAS semi-inclusive DIS measurement.

Chiral soliton model vs. pentaquark structure for Θ(1540)

The exotic baryon $\Theta^+$ (1540 MeV)$ is visualised as an expected (iso) rotational excitation in the Chiral Soliton Model. It is also argued as a Pentaquark baryon state in a constituent quark model with strong diquark correlations. I contrast the two points of view; the similarities and differences between the two pictures. Collective excitation, characteristic of Chiral Soliton Model points toward small mixing of representations in the wake of SU(3) breaking. In contrast, Constituent quark Models prefer near ``ideal'' mixing, similar to $\omega - \phi$ mixing.

Spectral properties of a Dirac operator in the chiral quark soliton model

We consider a Dirac operator H acting in the Hilbert space L2(R3;C4)⊗C2, which describes a Hamiltonian of the chiral quark soliton model in nuclear physics. The mass term of H is a matrix-valued function formed out of a function F:R3→R, called a profile function, and a vector field n on R3, which fixes pointwise a direction in the isospin space of the pion. We first show that, under suitable conditions, H may be regarded as a generator of a supersymmetry. In this case, the spectra of H are symmetric with respect to the origin of R. We then identify the essential spectrum of H under some condition for F. For a class of profile functions F, we derive an upper bound for the number of discrete eigenvalues of H. Under suitable conditions, we show the existence of a positive energy ground state or a negative energy ground state for a family of scaled deformations of H. A symmetry reduction of H is also discussed. Finally a unitary transformation of H is given, which may have a physical interpretation.

HADRON SPECTROSCOPY WITHOUT CONSTITUENT GLUE

Glueballs and hybrids are predicted to exist but searches for them have failed to provide conclusive evidence. One–gluon exchange is not an important part of strong interactions in this energy regime. Instead, quarks seem to interact indirectly, via changes of the QCD vacuum. Strong interactions seem to be governed by instanton–induced interactions; the chiral soliton model gives a more suitable interpretation of the Θ+(1540) than models based on the dynamics of four quarks and one antiquark.

Generalized parton distribution functions and the nucleon spin sum rules in the chiral quark soliton model

The theoretical predictions are given for the forward limit of the unpolarized spin-flip isovector generalized parton distribution function $(E^u - E^d)(x, \xi, t)$ within the framework of the chiral quark soliton model, with full inclusion of the polarization of Dirac sea quarks. We observe that $[(H^u - H^d) + (E^u - E^d)](x,0,0)$ has a sharp peak around $x=0$, which we interpret as a signal of the importance of the pionic $q \bar{q}$ excitation with large spatial extension in the transverse direction. Another interesting indication given by the predicted distribution in combination with Ji's angular momentum sum rule is that the $\bar{d}$-quark carries more angular momentum than the $\bar{u}$-quark in the proton, which may have some relation with the physics of the violation of the Gottfried sum rule.

On the NuTeV anomaly and the asymmetry of the strange sea in the nucleon

Our recent theoretical analysis based on the flavor SU(3) chiral quark soliton model predicts fairly large particle-antiparticle asymmetry of the strange sea in the nucleon. We point out that the predicted magnitude of asymmetry is large enough to solely resolve the so-called NuTeV anomaly on the fundamental parameter $\sin^2 \theta_W$ in the standard model.

The Experimental Search for Pentaquark

The existence of an anti-decuplet of pentaquark particles has been predicted some year ago within the chiral soliton model. In the last year, several experimental groups have reported evidence for a S=+1 baryon resonance, with mass ranging from 1.52 and 1.55 GeV and width less than 25 MeV, by looking at the invariant mass of the $K N$ system. This resonance, has been identified with the lowest mass of the anti-decuplet, the $\Theta^+$. At the same time, there are a number of experiment, mostly at high energies, that report null results. An overview of the experimental results so far obtained will be given here together with a review of the second generation experiments currently ongoing and planned at Jefferson Lab Hall B.

Today’s view on strangeness

There are several different experimental indications, such as the pion-nucleon sigma term and polarized deep-inelastic scattering, which suggest that the nucleon wave function contains a hidden s bar s component. This is expected in chiral soliton models, which also predicted the existence of new exotic baryons that may recently have been observed. Another hint of hidden strangeness in the nucleon is provided by copious phi production in various N bar N annihilation channels, which may be due to evasions of the Okubo-Zweig-Iizuka rule. One way to probe the possible polarization of hidden s bar s pairs in the nucleon may be via Lambda polarization in deep-inelastic scattering.