Nature of light scalars through photon-photon collisions

The surprising thing is that arising almost 50 years ago from the linear sigma model(LSM)with spontaneously broken chiral symmetry,the light scalar meson problem has become central in the nonperturbative quantum chromodynamics(QCD)for it has been made clear that LSM could be the low energy realization of QCD.First we review briefly signs of four-quark nature of light scalars.Then we show that the light scalars are produced in the two photon collisions via four-quark transitions in contrast to the classic P wave tensor q(q)mesons that are produced via two-quark transitions γγ→q(q).Thus we get new evidence of the four-quark nature of these states.     

Four-quark binding energies from SU(2) lattice Monte Carlo

Energies of four-quark systems have been extracted in a static quenched SU(2) lattice Monte Carlo calculation for six different geometries, both planar and nonplanar, with =2.4 and lattice size 16³×32. In all cases, it is found that the binding energy is greatly enhanced when the four quarks can be partitioned in two ways with comparable energies. Also it is shown that the energies of the four-quark states cannot be understood simply in terms of two-quark potentials.     

SU(3) × SU(3) symmetry breaking in a simple model

A field-theoretical model, due to Lévy, is studied. It contains a triplet of quarks and a pseudoscalar and a scalar meson nonet. The original SU(3) × SU(3) symmetry is broken by terms linear in the scalar meson fields. A renormalization and regularization procedure is defined in order to remove the ultra-violet divergences. The possibility of a spontaneous breakdown of the symmetry is described and the Goldstone theorem is verified in the one-loop approximation.     

Vector and Spinor Decomposition of SU（2） Gauge Potential, Their Equivalence, and Knot Structure in SU（2） Chern-Simons Theory

In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.     

QQqq Four-Quark Bound States in Chiral SU(3) Quark Model

The possibility of QQqq heavy-light four-quark bound states has been analyzed by means of the chiral SU(3) quark model, where Q is the heavy quark (c or b) and q is the light quark (u, d, or s). We obtain a bound state for the bbnn configuration with quantum number J^P=1⁺,I=0 and for the ccnn (J^P=1⁺,I=0) configuration, which is not bound but slightly above the D^*D^* threshold (n is u or d quark). Meanwhile, we also conclude that a weakly bound state in bbnn system can also be found without considering the chiral quark interactions between the two light quarks, yet its binding energy is weaker than that with the chiral quark interactions.     

A silicon bag model with SU(2) × SU(2) chiral dynamics

We describe a soliton bag model which incorporates explicitly SU(2) × SU(2) chiral dynamics, including the conservation of the polar vector current, the partial conservation of the axial vector current, and the SU(2) × SU(2) current algebra. This model appears to be renormalizable so that higher order effects may be treated systematically.     

Variational Cumulant Expansion on SU(2)⊗ SU(2) Chiral Model

The phase transition of the two-dimensional SU(2)⊗ SU(2) lattice chiral model has been studied by a variational cumulant expansion method. The internal energy and the specific heat are calculated to the 4th order correction and they are in good agreement with the Monte Carlo (MC) resdits. Except the behavior of the crossover region, similarities between this model and the four-dimensional SU(2) lattice gauge model are also discussed.     

Mixing of meson isosinglets in SU(5) and an extension to SU(N)

The mixing angles of meson isosinglets belonging to the 24-dimensional and singlet representations of SU(5) are calculated under specific assumptions in the non-relativistic quark model. The procedure to extend the scheme to SU(N) has been outlined. The results have been compared with other earlier estimates.     

Cranking an SU(3)-symmetric chiral soliton

The chiral quark—meson model based on a linear σ model is extended to three flavours of quarks. For an SU(3)-symmetric version of the model we use a lowest-order cranking approach to calculate the splittings between the baryon multiplets. The isospin cranking which governs the octet—decuplet splitting is identical to that in the SU(2) model. The moment of inertia for “strange” rotations gives the energies of states which must involve mesonic excitations. It is found to be small, indicating that such states, if they exist, lie well above the nucleon.     

The vacuum of supersymmetric SU(3) × SU(2) × U(1)

We show that in supersymmetric SU(3) × SU(2) × U(1) it is possible to break SU(2) with an Higgs singlet and at the same time to avoid vacuum expectation values for s-fermions. With rather simple constraints we obtain important restrictions on the values of the model parameters.     

Nuclear Matter in a Chiral SU(3) Quark Mean-Field Model

A quark meson coupling model based on SU(3)_L×SU(3)_R symmetry and scale invariance is proposed. The quarks and mesons get masses through symmetry broken. We apply this SU(3) chiral constituent quark model to investigating the nuclear matter at finite temperature and density. The effective baryon masses, compression modulus and hyperon potentials are all reasonable. The critical temperature of liquid-gas phase transition is also calculated in this model.     

SU(2) Yang-Mills theory in (1 + 1) dimensions: A finite-lattice approach

Finite-lattice methods are used to calculate the masses of the lowest-lying baryon and meson states in the two-dimensional SU(2) Yang-Mills theory. No sign of a phase transition is seen at non-zero quark mass m. Both the meson and baryon mass vanish at m = 0: this is presumably a “chiral protection” mechanism.     

A SUPERSYMMETRICAL PREON MODEL WITH SU(2)L × SU(2)R ×U(1)B-L SYMMETRY BROKEN BY COUPLING TO SUPERGRAVITY

A supersymmetrical preon model is proposed. In this model there are Higgs particles which are massless at the scale of confinement of hypercolor due to the supersymmetry and a discrete R symmetry. We show that in this model the low energy gauge symmetry SU(2)_L×SU(2)_R×U(1)_B-L can be broken to U(1)_Q at the scale of supersymmetry breaking by coupling to supergravity.     

Asymptotically free SU(2) × SU(2) × SU(4) model of unified interaction

An asymptotically free SU(2) × SU(2) × SU(4) model of unified interaction is constructed. The gauge coupling constants are taken equal (in the order of magnitude) to the electromagnetic one. The strong interaction and the quark confinement is provided for by a gluonic mechanism. Some physical consequence of the model are briefly discussed.     

BRST symmetries in SU(3) linear sigma model

We study the BRST symmetries in the SU(3) linear sigma model which is constructed through the introduction of a novel matrix for the Goldstone boson fields satisfying geometrical constraints embedded in a SU(2) subgroup. To treat these constraints we exploit the improved Dirac quantization scheme. We also discuss phenomenological aspects in the mean field approach to this model. Received: 16 November 2001 / Revised version: 23 February 2002 / Published online: 26 July 2002     

Chiral SU（3） Quark Model Study of Tetraquark States： cnn^-s^-/css^-s^-

The new members of the charm-strange family Dsj^＊（2317）, Dsj（2460）, and Ds（2632）, which have the surprising properties, are challenging the present models. Many theoretical interpretations have been devoted to this issue. Most authors suggest that they are not the conventional cs^- quark model states, but possibly are four-quark states, molecule states, or mixtures of a P-wave cs^- and a four-quark state. In this work, we follow the four-quark-state picture, and study the masses of cnn^-s^-/css^-s^- states （n is u or d quark） in the chiral SU（3） quark model. The numerical results show that the mass of the mixed four-quark state （cnn^-s^-/css^-s^-） with spin parity j^P ： 0^＋ might not be Ds （2632）. At the same time, we also conclude that Dsj^＊（2317） and Dsj（2460） cannot be explained as the pure four-quark state.     

An Extended Chiral SU(3) Quark Model

The chiral SU(3) quark model is extended by including the vector meson exchanges to describe the short range interactions. The phase shifts of NN scattering are studied in this model. Compared with the results of the chiral SU(3) quark model in which only the pseudo-scalar and scalar chiralfields are considered, the phase shifts of 1 So wave are obviously improved.     

Triplication of SU(5) Monopoles

We investigate all spherically symmetric fundamental monopole solutions with fixed topological charge in the SU(5)-->[SU(3) x SU(2) x U(1)]/Z(3) x Z(2) symmetry breaking. We find that there are three solutions that are gauge equivalent but, as we argue, would correspond to physically distinct degrees of freedom in the dualized version of the model. The triplication of monopoles could help us understand the observed family structure of standard model particles.     

Meson-Nucleon Scatterings in an SU(3) × SU(3) σ Model

Meson-nucleon scatterings are investigated in an SU(3) x SU(3) a model with scalar, vector, pseudoscalar and pseudovector couplings between mesons and baryons. from the calculation of effective coupling constants, sigma terms and s-wave scattering lengths for πN and K⁺N scatterings in the tree approximation, we find that the pseudoscalar coupling dominates s- and u-channel baryon Born terms, and the cancellation between the scalar and vector interactions leads to reasonable meson-nucleon scattering properties.     

Mixing of leptonic number in a general SU(2)L ⊗ U(1) ⊗ SU(2)R model

We discuss a general leptonic model based on the SU(2)_L ? U(1) ? SU(2)_R gauge group and we present general results for the ? → ?′ γ and ν? → ν?′γ processes, which can be used for any model based on the SU(2)_L ? U(1) ? SU(2)_R gauge group or on any of its subgroups. The predictions of the μ → eγ branching ratio and of the neutrino lifetime for various models discussed in the literature are reviewed. The main results are summarized in tables.