Anharmonic corrections in constant-cutoff soliton model

We suggest a quantum stabilization method for theSU(2) -model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then derive the results for anharmonic corrections to the hyperon energy in the bound-state approach to theSU(3)-soliton model for the hyperons, withSU(3)-symmetry breaking. Thus we show that the anharmonic corrections give, as in the case of the complete Skyrme model, negative contributions to the hyperon energies and that they are of the same order of magnitude as those obtained using the complete Skyrme model for bound heavy-flavor two-meson systems in the case of cascade hyperons.     

Constant-cutoff approach to radiative decays of hyperons: E2/M1 transition ratios

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then study the radiative decays ofJ ^π=3/2⁺ baryons using the constant-cutoff approach to theSU(3) collective treatment of the Skyrme model for hyperons. Thus we evaluate the widths and E2/M1 ratios, showing that there is a general qualitative agreement with the results obtained using the complete Skyrme model, as well as the nonrelativistic quark model and quenched lattice model, for the total widths.     

Constant-cutoff approach to Λ (1405) resonance in the bound-state soliton model

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB = 1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then study strong and electromagnetic properties of the Λ(1405) hyperon in the bound-state approach to theSU(3)-soliton model for the hyperons, withSU(3)-symmetry breaking. We calculate the strong coupling constantg _Λ*NK; , the magnetic moment of Λ*, the mean square radii, and the radiative decay amplitudes. Finally we compare the present results with those obtained using other models and with the available empirical data. We show that there is a general qualitative agreement between our results and the results of other models and available empirical data, except for the Λ*πΣ coupling, which, as in the case of the complete Skyrme model, vanishes in the second-order approximation of the kaon fluctuations used in this work.     

Constant-cutoff approach to electric seagull terms in the soliton Hamiltonian

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. Using the constant-cutoff approach, we then study theSU(2) soliton Hamiltonian, which does not contain the electric seagull terms, and show that if the fields are restricted to the collective subspace, the electric seagull terms are induced in the effective Hamiltonian similarly to the case of the complete Skyrme model. These terms are consistent with gauge invariance and leading-term predictions of the chiral perturbation calculation of the electric polarizability.     

Constant-cutoff approach toSU(3)-symmetry breaking for strange dibaryon states

We suggest a quantum stabilization method for theSU(2)-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB = 1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then show that the approach toSU(3)-symmetry breaking for strange dibaryon states proposed by Kopeliovichet al. can be simplified by omitting the Skyrme stabilizing term and using the constant-cutoff stabilization method. We derive the results for spectra of some strange and nonstrange dibaryon states and obtain the numerical results for the absolute masses of these states, in reasonable agreement with the values obtained, using the complete Skyrme model, by Kopeliovichet al.     

Constant-cutoff approach to meson-hyperon couplings

The kaon coupling constants at hyperon-nucleon vertices and the pion coupling constants at hyperon-hyperon vertices are calculated in the framework of the constant-cutoff approach to the CHK bound-state model of hyperons, where the postive-parity hyperons such as Λ, Σ, and ∑^*=∑(1385) are theP-wave bound states of an antikaon and theSU(2) Skyrme soliton, while Λ^* is theS-wave bound state. Meson coupling constants are defined as matrix elements of the meson-source terms between two single-baryon states following the method developed for resolving the Yukawa coupling problem in theSU(2) Skyrme soliton model. The magnitudes of the meson coupling constants are found to be close to those obtained using the complete Skyrme model and the phenomenological values.     

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.     

Semiclassical quantization of SU(3) skyrmions

Semiclassical quantization of the SU(3)-skyrmion zero modes is performed by means of the collective coordinate method. The quantization condition known for SU(2) solitons quantized with SU(3) collective coordinates is generalized for SU(3) skyrmions with strangeness content different from zero. The quantization of the dipole-type configuration with large strangeness content found recently is considered as an example and the spectrum and the mass splittings of the quantized states are estimated. The energy and baryon number density of SU(3) skyrmions are presented in a form emphasizing their symmetry in different SU(2) subgroups of SU(3), and a lower bound for the static energy of SU(3) skyrmions is derived. Zh. éksp. Teor. Fiz. 112, 1941–1958 (December 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Constant-cutoff approach to magnetic moments of hyperons

We calculate the magnetic moments of hyperons in the simplified CHK model, with the stabilizing term proportional toe ^–2 omitted, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishna, Sanyuk, Schechter, and Subbaraman, which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. Thus we show that there is qualitative agreement with the experimental values and the accuracy is similar to that obtained with the complete CHK model.     

Strange solitons in a chiral quark-meson model

We consider aSU(3) quark soliton model based on chiral invariant quark-meson coupling. We find soliton solutions with nonzero strangeness andB=1 in the model with nontrivial kaonic fields, for values of the coupling constant greater than the phenomenologically acceptable number. Hence they do not correspond to known strange baryons.     

THE COMPOSITE SOLITON SOLUTION WITH BARYON NUMBER B=0 BUT HOPF INDEX H=1 IN THE SKYRME MODEL

In the SU(2)×SU(2) Skyrme model,one can treat the topological soliton-Skyrmion having baryon number B=1 as baryon.In this paper,we have used Skyrmion and anti-Skyrmion to construct a kind of composite soliton solution having baryon number B=0 but Hopf index H=1 and have found its mass depends on a dimensionless parameter p(0<p≤1).In addition,we have also discussed the quantization of the soliton and the probability of treating the quantized soliton as baryonium.     

How much can one break chiral symmetry in the linear sigma model?

We show that the hedgehog soliton solution describing the nucleon in theSU(3) ×SU(3) linear sigma model breaks down when the pion mass becomes too large.On leave of absence from the Laboratoire de Physique Théorique, Université de Nice, parc Valrose, F-06034 Nice Cedex, France     

Constant-Cutoff Approach to Strangeness Dependence in Radiative Decays of Hyperons

We suggest a quantum stabilization method forthe SU(2) -model, based on the constant-cutofflimit of the cutoff quantization method developed byBalakrishna et al., which avoids the difficulties with the usual soliton boundary conditions pointedout by Iwasaki and Ohyama. We investigate the baryonnumber B = 1 sector of the model and show that after thecollective-coordinate quantization it admits a stable soliton solution which depends on asingle dimensional arbitrary constant. We then study theradiative decays of J = 3+/2 baryonsusing the constant-cutoff approach to the SU(3)collective treatment of the Skyrme model for hyperons. Thus weinvestigate the radiative hyperon decays and thevariation of the decay widths with strangeness, showingthat the present results are in qualitative agreementwith the results obtained using the complete Skyrmemodel.     

Quantization of the PoissonSU(2) and its Poisson homogeneous space — The 2-sphere

We show that deformation quantizations of the Poisson structures on the Poisson Lie groupSU(2) and its homogeneous space, the 2-sphere, are compatible with Woronowicz's deformation quantization ofSU(2)'s group structure and Podles' deformation quantization of 2-sphere's homogeneous structure, respectively. So in a certain sense the multiplicativity of the Lie Poisson structure onSU(2) at the classical level is preserved under quantization.With an Appendix by Jiang-Hua Lu and Alan Weinstein Department of Mathematics, University of California, Berkely, CA 94720 USAPartially supported by NSF-Grant DMS-8505550     

Extended double soliton solution families for the statically axisymmetric self-dualSU(2) gauge field equations

By using the extended double complex function method, the statically axisymmetric self-dualSU(2) gauge field equations and, in turn, the Belinsky-Zakharov solution-generating technique are generalized to extended double forms. The restriction on “soliton index” in the original solution-generating technique is eliminated so that for each positive integer, we can obtainphysical soliton solutions of the statically axisymmetric self-dualSU(2) gauge field equations in pairs. Some sufficient conditions are given for seed solutions with which the corresponding scattering wave function can be written out directly. As examples, some soliton solution families are given, most solutions of which are new.     

Charged nontopological soliton of the <Emphasis Type="Italic">SU</Emphasis>(2) × <Emphasis Type="Italic">U</Emphasis>(1) gauge model

The SU(2) × U(1) gauge model that is the bosonic sector of the Standard Model of electroweak interactions is considered. The existence of electrically charged nontopological solitons is shown to be possible in this model. Some properties of a charged nontopological soliton are investigated. Asymptotic expressions are derived for the soliton radius, energy, and phase frequency in the thin-wall regime by the method of trial functions. Numerical solutions of the model field equations corresponding to electrically charged non-topological solitions have been obtained. The dependences of the soliton energy and charge on phase frequency are given for several model parameters. It follows from the data obtained that there exists a domain of parameters in which a charged nontopological soliton is stable to the transition to a plane-wave field configuration.     

Chiral hyperbags

We construct and studySU (3) chiral bags (called chiral hyperbags) in the scheme of collective-coordinate quantization with chiral symmetry breaking treated as perturbation. We show how the Wess-Zumino constraint arises from the quark-bag sector, complementing the soliton sector, in a manner analogous to what happens in (1+1) dimensional chiral bags. Due to the Wess-Zumino term, all the quantum numbers — baryon charge, isopin, angular momentum, hypercharge etc. are fractionized in a prescribed manner. One notable aspect of the fractionization is that for all ranges of bag radius, there is alwaysmore angular momentum lodged in the soliton sector than in the quark sector. It is shown thatwithin the scheme we have adopted, the symmetry breaking termobstructs the Cheshire Cat principle and that consequently when strange quarks are present, the baryons (i.e. hyperons) favor a bigger bag (say R ? 1 fm) than non-strange baryons; this confirms a phenomenological argument put forward some time ago by Brown, Klimpt, Rho and Weise (at least in the collective-coordinate scheme). Our approach allows us to calculate the strangeness content of the proton — a highly topical issue — and we find that while a perturbative treatment of the symmetry breaking term can be made to work (for a big bag) for hyperon spectroscopy, the strangeness content of the proton is insensitive to the bag radius; for relevant ranges of bag radius, the ¯ss admixture stays significant, say, ?19%. This result is in stark contrast to the Callan-Klebanov Skyrmion — a remarkably successful model for hyperons — which predicts only about 3%. A subtle role of the Wess-Zumino term is suggested.     

Strange and singlet form factors of the nucleon: Predictions for G0, A4, and HAPPEX II experiments

We investigate the strange and flavor-singlet electric and magnetic form factors of the nucleon within the framework of the SU(3) chiral quark-soliton model. Isospin symmetry is assumed and the symmetry-conserving SU(3) quantization is employed, rotational and strange-quark mass corrections being included. For the experiments G0, A4, and HAPPEX II we predict the quantities G⁰_E + G⁰_M and G^s_E + G^s_M. The dependence of the results on the parameters of the model and the treatment of the Yukawa asymptotic behavior of the soliton are investigated.     

Kaon properties in (proto-)neutron star matter

The modification of kaon and antikaon properties in the interior of (proto-)neutron stars is investigated using a chiral SU(3) model. The parameters of the model are fitted to nuclear-matter saturation properties, baryon octet vacuum masses, hyperon optical potentials and low-energy kaon-nucleon scattering lengths. We study the kaon/antikaon medium modification and explore the possibility of antikaon condensation in (proto-)neutron star matter at zero as well as finite temperature/entropy and neutrino content. The effect of hyperons on kaon and antikaon optical potentials is also investigated at different stages of the neutron star evolution.     

Spin Chain Models with Spectral Curves from M Theory

We construct the integrable model corresponding to the ?= 2 supersymmetric SU(N) gauge theory with matter in the antisymmetric representation, using the spectral curve found by Landsteiner and Lopez through M Theory. The model turns out to be the Hamiltonian reduction of a N+2 periodic spin chain model, which is Hamiltonian with respect to the universal symplectic form we had constructed earlier for general soliton equations in the Lax or Zakharov–Shabat representation. Received: 22 December 1999 / Accepted: 3 March 2000