Properties of multi-Skyrmions and their quantization within a generalized chiral soliton model

A semiclassical quantization of the Skyrme model featuring a sixth-order term in the derivatives of the chiral field in the Lagrangian is performed. The orbital, isotopic, interference, and flavor tensors of inertia are calculated. For this version of the model, numerical calculations are performed for the excitation energies of flavors in baryon systems.     

Baby Skyrmions stabilized by canonical quantization

We analyse the effect of the canonical quantization of the rotational mode of the O(3)$O(3)$σ  -model which includes the Skyrme term. Numerical evidence is presented that the quantum correction to the mass of the rotationally-invariant charge n=1,2$n=1,2$ configurations may stabilize the solution even in the limit of vanishing potential. The corresponding range of values of the parameters is discussed.     

Axially symmetric multi-baryon solutions and their quantization in the chiral quark soliton model

We study axially symmetric solutions with B=2-5 in the chiral quark soliton model. In the background of axially symmetric chiral fields, the quark eigenstates and profile functions of the chiral fields are computed self-consistently. The resultant quark bound spectrum are doubly degenerate due to the symmetry of the chiral field. Upon quantization, various observable spectra of the chiral solitons are obtained. Taking account of the Finkelstein-Rubinstein constraints, we show that the quantum numbers of our solitons coincide with the physical observations for B=2 and 4 while B=3 and 5 do not.     

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. Based partly on the talks presented at the International Seminar on High Energy Physics Quarks-2004, Pushkinogorie, Russia, May 24–30, 2004; International Workshop on Quantum Field Theory and High Energy Physics QFTHEP-04, Saint-Petersburg, Russia, June 17–23, 2004, and Symposium of London Mathematical Society “Topological Solitons and their Applications,” Durham, UK, August 2–12, 2004. A slightly reduced version of this paper is available as E-print HEP-PH/0507028. The text was submitted by the author in English.     

Derivation of soliton quantization in two gauge models

Feynman rules are derived by a path-integral method for gauge theory solitons using as particular examples the Nielsen-Olesen vortex and the 't Hooft-Polyakov-Julia-Zee monopole-dyon. The masses of these solitons are proven to be manifestly renormalizable to one-loop order in the absence of knowledge of exact solitary solutions. This is done using a technique similar to 't Hooft's “background field method”.     

Cancellation of the zero-mode singularities in soliton quantization theory

We give a proof of an exact cancellation of the zero-mode singularities in each order of the loop expansion determining the quantum corrections to soliton (particle-like) solutions of classical field equations. The cancellation restores an underlying symmetry broken by a specific classical solution, and is owing to the stability of the soliton with respect to small perturbation generated by the symmetry group transformations.     

The soliton of the effective chiral action

The baryon-number-1 soliton solution of the effective chiral meson action of QCD is found numerically. For this purpose the underlying fermion determinant (quark loop) is calculated in a non-perturbative way by diagonalizing the corresponding Dirac hamiltonian. The vacuum energy is defined within a static version of the proper-time regularization. Topological soliton solutions are found for cut-offs below some critical value, above which only topologically trivial solutions exist.     

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.     

Neutron-rich hypernuclei in the chiral soliton model

The binding energies of neutron-rich strangeness S = ?1 hypernuclei are estimated in the chiral soliton approach using the bound state rigid oscillator version of the SU(3) quantization model. Additional binding of strange hypernuclei in comparison with nonstrange neutron-rich nuclei takes place at not large values of atomic (baryon) numbers, A = B ?? ??10. This effect becomes stronger with increasing isospin of nuclides, and for the ??nuclear variant?? of the model with rescaled Skyrme constant e. Binding energies of _?? ⁸ He and recently discovered _?? ⁶ H satisfactorily agree with data. Hypernuclei _?? ⁷ H, _?? ⁹ He are predicted to be bound stronger in comparison with their nonstrange analogues ⁷H, ⁹He; hypernuclei _?? ¹⁰ Li, _?? ¹¹ LI, _?? ¹² Be, _?? ¹³ Be, etc. are bound stronger in the nuclear variant of the model.     

Mean-field approximation for the chiral soliton in a chiral phase transition

Using the mean-field approximation, we study the chiral soliton within the linear sigma model in a thermal vacuum. The chiral soliton equations with different boundary conditions are solved at finite temperatures and densities. The solitons are discussed before and after chiral restoration. We find that the system has soliton solutions even after chiral restoration, and that they are very different from those before chiral restoration, which indicates that the quarks are still bound after chiral restoration.     

Batalin-Tyutin quantization of the chiral Schwinger model

We quantize the chiral Schwinger model by using the Batalin-Tyutin formalism. We show that one can systematically construct the first-class constraints and the desired involutive Hamiltonian, which naturally generates all secondary constraints. Fora>1, this Hamiltonian gives the gauge invariant Lagrangian including the well-known Wess-Zumino terms, while fora=1 the corresponding Lagrangian has the additional new type of the Wess-Zumino terms, which are irrelevant to the gauge symmetry.     

On the BRST quantization of chiral bosons

The Siegel action for two right-moving chiral bosons can be BRST quantized. In the case in which their kinetic terms have opposite signs the momenta in the left-moving sector must be constrained to be zero. In this case the two chiral bosons can be described also by a quadratic action. There is no analogous BRST quantization for a single chiral boson.     

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.     

Baryons as rotating excitations of the chiral soliton

We show that the usual ansatz used for quantizing the collective coordinates corresponding to a rotation of chiral soliton does not satisfy the equations of motion. We suggest a more general ansatz that admits the separation of rotational degrees of freedom and does not contradict the equations of motion.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.