Flavored exotic multibaryons and hypernuclei in topological soliton models

The energies of baryon states with positive strangeness, or anticharm (antibeauty), are estimated in the chiral soliton approach, in the “rigid oscillator” version of the bound-state soliton model proposed by Klebanov and Westerberg. Positive strangeness states can appear as relatively narrow nuclear levels (Θ-hypernuclei), and the states with heavy antiflavors can be bound with respect to strong interactions in the original Skyrme variant of the model (SK4 variant). The binding energies of antiflavored states are also estimated in the variant of the model with a sixth-order term in chiral derivatives added to the Lagrangian to stabilize solitons (SK6 variant). This variant is less attractive, and nuclear states with anticharm and antibeauty can be unstable relative to strong interactions. The chances of obtaining bound hypernuclei with heavy antiflavors increase within the “nuclear variant” of the model with a rescaled model parameter (the Skyrme constant e or e′ decreased by a out 30%), which is expected to be valid for baryon numbers greater than B ～ 10. The rational map approximation is used to describe multiskyrmions with a baryon number of up to about 30 and to calculate the quantities necessary for their quantization (moments of inertia, sigma term, etc.).     

Characteristic predictions of topological soliton models

Characteristic predictions of the chiral soliton models (the Skyrme model and its extensions) are discussed. The chiral soliton model predictions of low-lying dibaryon states qualitatively agree with recent evidence for the existence of narrow dibaryons in reactions of the inelastic proton scattering on deuterons and the double photon radiation pp→ppγγ. The connection between magnetic moment operators and inertia tensors valid for arbitrary SU(2) skyrmion configurations allows us to estimate the electromagnetic decay width of some states of interest. Predictions of a different type are multibaryons with a nontrivial flavor (strangeness, charm, or bottom), which can be found, in particular, in high-energy heavy ion collisions. It is shown that the large-B multiskyrmions given by the rational map ansatz can be described within the domain-wall approximation or as a spherical bag with the energy and the baryon number density concentrated at the boundary.     

Baryon masses in the bound state approach to strangeness in the skyrme model

We diagonalize exactly the O(N⁰_c) hamiltonian relevant to the bound state approach to strangeness in the Skyrme model. The hyperfine splitting of strange baryons computed within this framework agree well with the experimental values.     

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.     

Strangeness −2 two-baryon systems

We derive strangeness −2 baryon–baryon interactions from a chiral constituent quark model including the full set of scalar mesons. The model has been tuned in the strangeness 0 and −1 two-baryon systems, providing parameter free predictions for the strangeness −2 case. We calculate elastic and inelastic NΞ and ΛΛ cross sections which are consistent with the existing experimental data. We also calculate the two-body scattering lengths for the different spin–isospin channels.     

SU(3) symmetry breaking for masses, magnetic moments and sizes of baryons

We use the SU(3) Skyrme model to investigate the effects of symmetry breaking imposed by different pseudoscalar meson masses on the structure of baryons. Specifically, we calculate their mass splittings, magnetic moments, charge radii, semileptonic decays as well as different strangeness contents of the proton. Since the Skyrme soliton is allowed to deform under the pressure of the symmetry breaking we find significant variations in baryon sizes with respect to strangeness.     

Stabilization of skyrmions via ϱ-mesons

It is shown that a skyrion can be stabilized by introducing ?-mesons into the chiral SU(2)_L × SU(2)_R lagrangian without higher-derivative terms like the Skyrme term. The ?-mesons are considered as dynamical gauge bosons associated with a hidden local symmetry of the non-linear sigma model. The lagrangian reduces to the Skyrme model in a limit of parameters. The Skyrmion mass M is found to be M = 1058 MeV when the parameters are fixed so as to satisfy the KSRF relation. It is also shown that a solition solution in a model with Ω-meson coupled with the baryonic current is a saddle-point solution.     

The SU(3) dibaryons in the chiral quark soliton model

In this Letter we investigate an SU(3) extension of the axially symmetric B=2 chiral quark soliton model. The classical soliton is extended to the SU(3) by trivial embedding. We expand the quark determinant in terms of the collective angular velocity up to the second order and the quark mass difference of the first order. The mass spectrum and the binding energy of the baryon–baryon channels down to strangeness S=−6 are then obtained.     

Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyrme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in arXiv:0910.4979 by Gebremariam et al. to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N²LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A link to a downloadable Mathematica notebook containing the novel density-dependent couplings is provided.     

Strong-symmetry-breaking limit of SU(3) Skyrme model and bound-kaon approach to strangeness

The semi-leptonic weak decays of hyperons are investigated in the Skyrme model. The vector currents for strangeness-changing processes are shown to have a very similar structure in the strong-symmetry-breaking limit in the SU(3) collective-coordinate method, proposed by Yabu and Ando, with those in the bound-kaon approach to strangeness by Callan and Klebanov. It is also shown that the quite differentN _c dependence between them becomes also to coincide with each other in the limit.Dedicated to Prof. Erich Schmid on the occasion of his 60th birthday     

Strange-quark matter within the Nambu-Jona-Lasinio model

The equation of state of baryon-rich quark matter is studied within the SU(3) Nambu-Jona-Lasinio model with flavor-mixing interaction. Possible bound states (strangelets) and chiral phase transitions in this matter are investigated at various values of the strangeness fraction r _s. Model predictions are very sensitive to the ratio of the vector and scalar coupling constants, ξ=G _V/G _S. At ξ=0.5 and zero temperature, the binding energy takes a maximum value of about 15 MeV per baryon at r _s?0.4. Such strangelets are negatively charged and have typical lifetimes of about 10^?7s. Calculations are performed at finite temperatures as well. According to these calculations, bound states exist up to temperatures of about 15 MeV. The model predicts a first-order chiral phase transition at finite baryon densities. The parameters of this phase transition are calculated as functions of r _s.     

SU(2) Skyrme vortices

A regular method for constructing vortexlike solutions with cylindrical symmetry to the equations of the SU(2) Skyrme chiral model is proposed. A numerical estimate for the length density of mass is given.     

On the lifetime of the kappa meson

The lifetime of a hypotheticalκ meson with low mass, introduced byGlashow andWeinberg in a model for simultaneous breaking ofSU(3) and chiral symmetry, is calculated. The coupling constant of theκ toKπ is obtained by assuming that the divergence of the strangeness changing vector current is dominated by theκ pole.     

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.     

Bound-state approach to strangeness in the Skyrme model

We show that baryons carrying heavy flavors, such as strangeness and charm, can be described by bound states of the corresponding heavy mesons in the background field of the basic SU(2) skyrmion. This method is quantitatively successful to O(N_c⁰), in the sense of the large-N_c expansion, but at O(1/N_c) it experiences problems associated with our lack of knowledge of higher-derivative terms in the Skyrme action. We derive a model-independent mass relation for strange baryons which is in excellent agreement with experiment.     

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.