Constant-cutoff approach to hyperon polarizabilities 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 apply this approach to the calculation of electric and magnetic static polarizabilities of octet hyperons in the bound-stateSU(3)-soliton model for hyperons, withSU(3)-symmetry breaking. The results, with both seagull and dispersive contributions included, are compared with the predictions obtained using the complete Skyrme model.     

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 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 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.     

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 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 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.     

The energy levels of the heavy flavour baryons in the topological soliton model

The energy levels of the charm and bottom as well as the mixed flavour hyperons are calculated with the model in which the hyperons are described as bound states of a topologicalSU (2) soliton andK-, D- andB-mesons. The spectra are obtained in a modified version of the Skyrme model where the chiral symmetry breaking term in the Lagrangian density is modified so as to incorporate the different values of the decay constants of the mesons of different flavour. The predicted strange and charmed hyperon spectra are in very good agreement with the empirical values, while the bottom hyperon energies that are more sensitive to the short range dynamics are somewhat below the empirical values. The predicted hyperfine spectra are remarkably close to those obtained with the constituent quark model, more or less independently of the short-distance properties of the effective Lagrangian. We suggest that this feature reflects the presence of an induced nonabelian gauge potential generated by the interplay between “fast” and “slow” degrees of freedom in the meson-soliton system.     

Constant-Cutoff Approach to Axially Symmetric Dibaryons

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 thedibaryon configurations in this approach, using thegeneralized axially symmetric ansatz to determine the soliton background. Thus we calculate therotational contributions to the masses of the axiallysymmetric dibaryons and show that they are inqualitative agreement with the results obtained usingthe complete Skyrme model. We conclude also that,as in the case of the complete Skyrme model, the lowestallowed S = –2 state has the quantum numbers ofthe H-particle. We find that in the present approach, similarly to the case of the complete Skyrmemodel, this particle is bound, even though the neglectedvacuum effects might contribute to the unbinding of theH-particle.     

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.     

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.     

Spin polarizability of hyperons

We review the recent progress of the theoretical understanding of spin polarizabilities of the hyperon in the framework of SU(3) heavy baryon chiral perturbation theory (HBChPT). We present the results of a systematic leading-order calculation of hyperon Compton scattering and extract the forward spin polarizability (γ ₀) of hyperons. The results obtained for γ ₀ in the case of nucleons agree with the known results of SU(2) HBChPT when kaon loops are not considered.     

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     

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.     

Quark model analysis of hyperon semileptonic decays

A study of hyperon semileptonic decays has been made in various quark models and compared with the standard Cabibbo analysis which is found to be in good agreement with experiments. Results obtained in a quasirelativistic constituent quark model are in reasonable agreement with the standard Cabibbo analysis and show no sizeableSU(3) symmetry breaking effects. Results in other quark models which take into account theSU(3) symmetry breaking effects in the dominant form factors are similar to the quasirelativistic constituent quark model.     

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.     

q-Weyl coefficients forU q (3) andq-Racah coefficients forSU q (2)

We show that theq-Weyl coefficients of the quantum algebraSU _q (3) are equal to theq-Racah coefficients of the quantum algebraSU _q (2) (up to a simple phase factor). Using aq-analog of the resummation procedure we obtain also theq-analogues of all known general analytical expressions for the 6j-symbols (or the Racah coefficients) of the quantum algebraSU _q (2) starting from one such formula.Presented at the 4th Colloquium Quantum groups and integrable systems, Prague, 22–24 June 1995.The research described in this publication was supported in part by Grants No. MB1000 and No. NRC000 from International Science Foundation.     

Extraction of the CKM matrix element V<Subscript>us</Subscript> from the hyperon semileptonic decays

The chiral constituent quark model with configuration mixing ( c \chi CQM _config , which is successful in explaining the weak vector and axial-vector form factors for the strangeness-changing as well as strangeness-nonchanging hyperon semileptonic decays at Q ² = 0 , has been extended to determine the CKM matrix element V _us for the strangeness-changing decays. The implications of the effect of the SU(3) symmetry breaking, Q²-dependence and radiative corrections on the form factors and V _us have also been investigated. It is found that the results with SU(3) symmetry breaking show considerable improvement over the SU(3) symmetric results when compared with the existing experimental data. The inclusion of the Q²-dependence and radiative corrections in form factors have only a small effect on the prediction of V _us as is expected from the theory.     

Mass operator in theSU(3)-symmetric strong coupling theory with pseudoscalar mesons

In this paper theSU(3)-symmetric model of a static baryon octet source interacting with pseudoscalar meson octet fields by the coupling of Yukawa type is considered in the strong coupling limit. Using the result derived earlier that the isobaric states form the basis of the unitary irreducible representation of the dynamical group G=T ₂₄ [SU(3) SU(2)], the mass operator is specified by the kinetic part of the Hamiltonian as a particular element of the universal enveloping algebra of the symmetry groupSU(3) SU(2) acting in the space of isobaric states.     

The Interaction Energy of Well-Separated Skyrme Solitons

We prove that the asymptotic field of a Skyrme soliton of any degree has a non-trivial multipole expansion. It follows that every Skyrme soliton has a well-defined leading multipole moment. We derive an expression for the linear interaction energy of well-separated Skyrme solitons in terms of their leading multipole moments. This expression can always be made negative by suitable rotations of one of the Skyrme solitons in space and iso-space. We show that the linear interaction energy dominates for large separation if the orders of the Skyrme solitons multipole moments differ by at most two. In that case there are therefore always attractive forces between the Skyrme solitons.