Charmed baryon resonances with heavy-quark symmetry

We study charmed baryon resonances that are generated dynamically from a coupled-channel unitary approach that implements heavy-quark symmetry. Some states can already be identified with exper-imental observations, such as Λ_c(2595), Λ_c(2660), Σ_c(2902) or Λ_c(2941), while others need a compilation of more experimental data as well as an extension of the model to include higher order contributions. We also compare our model to previous SU(4) schemes.     

The flavour liquid state and Hund‘s rule effects in spin systems with orbital degeneracy

In order to understand the properties of the spin system with orbital degeneracy, we first generalize the linearized semiclassical spin wave method for the SU(2) generators into the SU(4) case, and then investigate the elementary excitations of the orbital-spin systems in the SU(4) limit. The results show that, due to the reduction of the dimensionality of the excitations, the ordered state of the SU(4) spin-orbital model is unstable. Secondly, we study the effects of the Hund interaction on the flavour liquid state of the system. Our mean-field results suggest that, for a small Hund interaction, the flavour liquid state is still stable against the generalized spin-density wave state, but with sufficient deviation from the SU(4) limit, the long-range order may be attained in two-dimensional systems. Finally, the implications for the experimental observations on the material LiNiO₂ are discussed.     

On light supernuclei

The possible existence of charmed analogues of the YN and light hypernuclear systems are investigated using phenomenological one-boson-exchange potential and the SU(4) symmetry. Bound light supernuclei such as C₁N (I=3/2, J=0) and C₁NN(I=2, J=1/2) C₀NN (I=1, J=1/2, and I=0, J=1/2 or 3/2) are predicted with reasonable binding energies using Faddeev formalism for the three body systems.     

Degenerate Integrability of the Spin Calogero–Moser Systems and the Duality with the Spin Ruijsenaars Systems

It is shown that spin Calogero–Moser systems are completely integrable in a sense of degenerate integrability. Their Liouville tori have dimension less than half of the dimension of the phase space. It is also shown that rational spin Ruijsenaars systems are degenerately integrable and dual to spin Calogero–Moser systems in a sense that action-angle variables of one are angle-action variables of the other.     

Magnetic moments of baryons in broken SU(4)

Assuming that the anomalous magnetic moment interaction has the formaT ₁ ¹ +bT ₂ ² +cT ₄ ⁴ +sT _α ^α in SU(4), which may arise due to symmetry breaking or some other dynamical effects, we have obtained the magnetic moments and the transition moments of the ordinary and charmed baryons.     

Ground State and Spin-Glass Phase of the Large-N Infinite-Range Spin Glass via Supersymmetry

The large-N infinite-range spin glass is considered, in particular, the number of spin components k needed to form the ground state and the sample-to-sample fluctuations in the Lagrange multiplier field on each site. The physical significance of k for the correlation functions is discussed. The difference between the large-N and spherical spin glass is emphasized; a slight difference between the average Lagrange multiplier of the large-N and spherical spin glasses is derived, leading to a slight increase in the energy of the ground state compared to the naive expectation. Further, there is a change in the low-energy density of excitations in the large-N system. A form of level repulsion, similar to that found in random matrix theory, is found to exist in this system, surviving interactions. Even though the system is an interacting one, a supersymmetric formalism is developed to deal with the problem of averaging over disorder.     

Spin symmetric solutions of Dirac equation with PSschl-Teller potential

The approximate analytical solutions of the Dirac equation with the Poeschl-Teller potential is presented for arbitrary spin-orbit quantum number κ within the framework of the spin symmetry concept. The energy eigenvalues and the corresponding two Dirac spinors are obtained approximately in closed forms. The limiting cases of the energy eigenvalues and the two Dirac spinors are briefly discussed.     

Chiral SU(4) × SU(4) breaking: masses and decay constants of charmed hadrons

The (4, 4*) ⊕ (4*, 4) model of broken chiral SU (4) × SU (4) symmetry has been used to calculate the third-order coupling constants involving charmed and ordinary pseudoscalar mesons. These coupling constants are exploited to derive some interesting new relations among the masses and decay constants of these charmed particles. Using the known masses and decay constants as inputs, we exploit these relations to predict:F _D = −1·41F _π ,F _F = −1·13F _π ,F _D/F_F = 1·25,m(D _s) = 1·43 GeV,m(F _s) = 1·39 GeV andm(K _s) = 1·02 GeV.     

对称性对总自旋为1/2的三费米体系结构的影响

揭示了量子力学对称性对总自旋s为1/2的三费米子体系结构的决定性影响.     

First and second order hadron mass formulas in internal SU(6)

We use broken SU(6) internal symmetry to derive the mass formulas amongst hadrons (1/2⁺, 3/2⁺, 0⁻, 1⁻) including second order mass contributions from symmetric 405 representation. Some hybrid mass relations are also obtained by relating second order parameters.     

相对论谐振子下的自旋和赝自旋轨道伙伴态劈裂

通过求解具有谐振子势的径向标量势与矢量势的Dirac方程, 分别分析了原子核中赝自旋和自旋双重态的能级劈裂和波函数劈裂随着谐振子的振动频率参数ω和描述谐振子势阱底偏离中心参数r₀的变化关系. 研究发现, 这些参数对于赝自旋和自旋双重态的能级劈裂和波函数劈裂都有着显著的影响. 此外, 也研究了能级劈裂和波函数劈裂随着量子数的变化关系. 由于参数ω与核子数有关, 而参数r₀与形变核有关, 所以以这些参数为变量对于赝自旋劈裂和自旋劈裂的研究是有意义的, 研究的结果至少可以定性地应用到大部分原子核中.     

Spin symmetry in the relativistic modified Rosen-Morse potential with the approximate centrifugal term

By applying a Pekeris-type approximation to the centrifugal term, we study the spin symmetry of a Dirac nucleon subjected to scalar and vector modified Rosen-Morse potentials. A complicated energy equation and associated two-component spinors with arbitrary spin-orbit coupling quantum number k are presented. The positive-energy bound states are checked numerically in the case of spin symmetry. The relativistic modified Rosen-Morse potential cannot trap a Dirac nucleon in the limiting case α→ 0.     

On Decay of Correlations for Unbounded Spin Systems with Arbitrary Boundary Conditions

We propose a method based on cluster expansion to study the truncated correlations of unbounded spin systems uniformly in the boundary condition and in a possible external field. By this method we study the spin–spin truncated correlations of various systems, including the case of infinite range simply integrable interactions, and we show how suitable boundary conditions and/or external fields may improve the decay of the correlations.     

自旋不是轨道角动量的相对论效应——与许方官和高春媛商榷

对《大学物理》2000年第11期上发表的《氢原子的磁矩－对自旋的讨论之一》一提出了不同的看法，认为该错把相对论的流密度当成了非相对论的流密度，前不能在非相对论近似下过滤到后，在相对论情况下，自旋和轨道耦合在一起，不能互相独立，在非相对论情况下自旋独立于轨道运动而存在；因而，自旋不是轨道角动量的相对论效应。     

Parity violating non-leptonic decays of hyperons and of charmed baryons in SU (8)

The parity violating non-leptonic decays of hyperons and of charmed baryons are discussed in the framework of SU (8) symmetry. Several relations in addition to the ones obtained earlier by using SU (4) symmetry and20″-dominance, are obtained. The assumption of20″-dominance at the SU (4) level is no longer required for explaining the non-leptonic decays of 1/2⁺ baryons.     

The Spin Symmetry of Heavy Baryons in the Framework of the Bethe-Salpeter Equation

We study the baryons containing a heavy quark in the framework of Bethe-Salpeter (BS) equation. The most general forms of the BS wavefunctions are given. In the heavy-quark limit we simplify the BS equations and we show clearly that the spin symmetry exists in heavy baryon states.     

Weinberg-Salam model and chiral symmetry of mesons

Weinberg-Salam model is considered in the light of SU(4) × SU(4) chiral symmetry for mesons. The Higgs doublet and the pseudoscalar mesons mix in this framework. Consequences of this mixing for the Higgs decays and the nonleptonic decays of the mesons are explored.     

Spin and Pseudospin Symmetries of Dirac Equation and the Yukawa Potential as the Tensor Interaction

Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.     

Mean Field Behaviour of Spin Systems with Orthogonal Interaction Matrix

For the long-range deterministic spin models with glassy behaviour of Marinari, Parisi and Ritort we prove weighted factorization properties of the correlation functions which represent the natural generalization of the factorization rules valid for the Curie–Weiss case.     

Spin and Pseudospin Symmetries of Dirac Equation and the Yukawa Potential as the Tensor Interaction

Considering of a tensor interaction in Dirac equation removes the degeneracy in spin and pseudospin doublets and consequently leads to results consistent with the experimental data. Here, instead of the commonly used Coulomb or linear terms, we investigate a tensor interaction of Yukawa form. We obtain arbitrary state solutions of Dirac equation under vector, scalar and tensor Yukawa potentials via a physical approximation and the Nikiforov-Uvarov methodology. The solutions are discussed in detail.