Bound-state Approach Research Articles

The role of a massive strange quark in the Large- N Skyrme model

We analyze the rigid rotator treatment of the three-flavor Skyrme model in the limit of a large number of colors. This is an approximation to the bound state approach to strangeness. The dynamical picture of baryons that emerges is similar to that of the non-relativistic quark model. In particular, we find a collective excitation of the qq background with all the properties of a constituent strange quark. We calculate the nucleon mass and the matrix element 〈N| ss |N〉 as functions of the mass of the strange quark.

Electromagnetic properties of hyperons in the bound-state approach to the Skyrme model.

We construct the electromagnetic current in the bound-state approach to the Skyrme model using the Callan-Klebanov ansatz. The current is used to calculate magnetic moments and charge radii of the baryons. We consider both massless and massive pions.

The strangeness problem: An SU(3) skyrmion with vector mesons

We study a model for strange baryons (both spin- 1 2 and spin- 3 2 ) in the bound-state approach to strangeness in which the nonet of vector mesons are explicitly incorporated. A special focus is put on the intricate way the strangeness flavor manifests itself in the baryon structure. The model is shown to be consistent with low-energy theorems, including one for five-pseudoscalar vertices. Both binding energy and hyperfine splittings are calculated in an almost parameter-free manner. A very satisfactory agreement with the experimental hyperon masses is found.

Magnetic moments of hyperons in the bound state approach to the skyrme model

We construct the electromagnetic current in the bound state approach to the Skyrme model using the Callan-Klebanov ansatz. The current is used to calculate the magnetic moments of the baryons for the case of massless pions. The agreement of the magnetic moments in the bound state approach with the experimental magnetic moments is qualitatively satisfying. We disagree with previous work by Nyman and Riska.

Effects of Dissipative Perturbation on Bound-State Solitons of Nonlinear Schrödinger Equation

The perturbation theory and numerical simulations show that the period of a bound state of two solitons of the nonlinear Schrödinger equation increases at each collision due to a dissipative perturbation. After some collisions, the bound state approaches to a double-pole state and practically splits into two single solitons of equal amplitude.

Strange dibaryons in the skyrme model

The bound state approach to strange dibaryons in the Skyrme model is extended to baryon number n > 1. Kaon bound states are obtained in a (variational) axially symmetric SU(2) Skyrmion background field. Collective quantization of isospin and spatial zero modes leads to dibaryon quantum states. These are classified in flavor multiplets.

Meson-hyperon coupling constants in the bound-state approach to strangeness

Abstract Meson-hyperon coupling constants are calculated using the bound-state approach to strangeness of Callan and Klebanov. In this model K and π mesons are treated in entirely different ways, and it thus lacks SU(3) symmetry. It is shown that the coupling constants of the model nevertheless approximately obey the SU(3) symmetry, with an approximate D - F mixing close to the quark-model value. The predicted coupling constants agree with experiments to the usual ±30% accuracy expected of the Skyrme model.

Hyperons as bound states in the skyrme model

We show that the bound-state approach to the hyperons in the Skyrme model developed by Callan, Klebanov and Hornbostel can be formulated in a way that avoids the square root of the SU(2) soliton. While the results for the single hyperons remain unchanged, the present version simplifies the extension of the model to the case of hypernuclei, which requires approximate forms for the SU(2)-soliton field operator. The effect of the pion mass term is shown to be small for the ground-state hyperons, but it introduces an additional bound D-state.

Bound state approach for strange dibaryons in the skyrme model

The bound state approach to strange dibaryons in the Skyrme model is extended to baryon number n > 1. Kaon bound states are obtained in a (variational) axially symmetric SU (2) skyrmion background field. Collective quantization of isospin and spatial zero modes leads to dibaryon quantum states. These are classified in flavor multiplets.

A new approach to the SU(3) Skyrme model: Exact treatment of the SU(3) symmetry breaking

On the basis of the collective coordinate quantization method, a new method to exactly treat the SU(3) symmetry breaking in the SU(3) Skyrme model is proposed. The masses of the baryons belonging to the lower multiplets are calculated by this method. Good agreement with experimental values is obtained when the vacuum-like energy correction is made and when somewhat stronger symmetry breaking is adopted. The strong symmetry breaking limit in our approach is studied and it is found that the mass formula in this limit has a form quite similar with the ones derived by the bound state approach. Comparison with two other methods, i.e. the collective-coordinate method with perturbation and the bound state approach, shows that these methods are two extreme approximations to our exact method.

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

We diagonalize exactly the O( N 0 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.

Bound-state approach to strangeness in the Skyrme model

Abstract 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(Nc0), in the sense of the large-Nc expansion, but at O(1/Nc) 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.

Analysis of resonances in 8Be using polarized α-particles

The band of resonances in 8Be starting at 20.1 MeV is investigated both from a scattering and a bound-state point of view. The scattering description is appropriate for studying the decay properties and the bound-state approach is best suited to reveal the structure of the states. A model is proposed including α-clustering and polarization of the α-particles as generator coordinates. It is shown that the generator coordinate method is a very versatile tool for making an analysis of the connection between the scattering and structure descriptions. The probability integral and widths of quasibound states are readily calculated. The connection between the scattering wave functions and quasibound and transit states is established. It is shown that the resonances are α + α ∗ configurations and the approximate selection rule causing their long lifetime is identified.

On the possibility of the multiple spin density wave state in the first-kind antiferromagnetic FCC metals

It is shown that the triple-Q spin density wave state with components Qx, Qy and Qz can be stabilised in the first-kind FCC antiferromagnet by the fourth-order term with respect to the transfer integral. Using the interacting virtual bound state approach, this state is found to be more stable than the simple-Q state in the nearly half-filled band region.

Strain Waves in Cr, CrMn and CrV Alloys

The strain waves in pure Cr, CrMn and CrV alloys were studied by means of neutron diffraction. The strain wave amplitude, Δ a / a , due to the spin density wave ordering is (1.1 ±0.1) ×10 -3 for pure Cr. This value is almost the same for CrMn alloys and is smaller for CrV alloys. The ratio of the modulated strain to the uniform lattice expansion, ( Δ a / a )/( Δ L / L ) mag , is about 3 for pure Cr and is smaller for CrMn alloys. These results can be explained either by the two band nesting model or by the virtual bound state approach, qualitatively.

Third Harmonics of Spin Density Wave in Cr and Its Alloys

The third harmonics of the spin density wave in pure Cr, CrMn and CrV alloys were studied by means of neutron diffraction, and the following results were obtained. The phase relation between the third and the primary spin density wave was determined to be “rectangular like” in pure Cr and in CrMn alloy. The ratio of the amplitude of the third harmonics spin density wave to that of the primary spin density wave, | S 3 / S 1 |, increases in CrMn and decreases in CrV alloys compared with that of the pure Cr. These results can be qualitatively explained by both of the theories based on the two band nesting model and the virtual bound state approach to the spin density wave.

Spectral Properties of the Spinor-Spinor Bethe-Salpeter Equation: A Speculation Based on a Simplified Model Equation

Spectral properties of the Beth-Salpeter equation are analyzed for the bound state of a fermion-antifermion system in the ladder approximation of a massless vector particle exchange. The original system of equations is simulated by a single equation. The equation well approximates the original one as the mass of the bound state approaches zero and threshold. On a suitable assumption, it is shown that the discrete part of the spectra (of the coupling constant) is gradually absorbed in the continuous part of the spectra as the energy recedes from the nonrelativistic region and disappears completely at some positive intermediate energy.

TestingQ 2 duality in charmonium potential models

The\(\bar p\) bound-state contributions to electron-positron annihilation into hadrons in the 4–6 GeV range are calculated using a wide class of confining potentials. When suitably averaged over, they satisfy “precocious scaling”, i.e. they closely approximate the quark-parton value forR. This illustrates duality in theQ2 variable between the (almost free) quark-parton approach and the bound-state (vector meson) approach.

Calculation of photoionization cross sections by the absorbing boundary method

A new method for the calculation of quantum state decay rates, the absorbing boundary method (ABM), has recently been developed. In this talk the general form of the ABM will be outlined. The pseudo bound state approach to the calculation of continuum rates such as photoionization cross sections and used by Langhoff and coworkers will be briefly reviewed and shown to lack precision in the absence of information about the line widths and shapes of the pseudo bound states. It will then be noted that the ABM can be used to construct a rigorous new approach to the calculation of photoionization cross sections incorporating the necessary lifetime information for the pseudo bound states while still allowing the computation to be carried out by bound state procedures.

Bound-state-induced phase transition in a two-field thermodynamic system with λS 2 (x)Q 2(x)-coupling

The thermodynamics of a Gaussian version of a Ashkin-Teller model withmS2≪MQ2 is studied by means of field-theoretic methods. This field-theoretical model is equivalent to a model in which two new composite fields, representing respectively a 2S bound state and a 2Q resonant state, interact both with theS- andQ-field. When the temperature is lowered the mass of the 2S bound state approaches the first zero and produces thus a second-order phase transition. The process can also be described consistently by an attractiveS4-coupling theory of which we review the usual objections in the light of our results.