Four-quark states and nucleon-antinucleon annihilation within the quark model with QCD vacuum-induced interaction

The spectrum of , J^p=0⁺, 2⁺ mesons is discussed. We have shown that due to instanton-induced forces the physical states are strong mixtures of theSU _f (3) group basis states. The cross-sections for annihilation of the system into mesons are obtained. Thea ₀(980) meson is considered as meson consisting of 9 _f and 36 _f plets. The branchings are also predicted for the cross-sections for production of thea ₀(980) and tensor mesons in annihilation.     

Coordinates of the quantum plane as q-tensor operators in (\mathfrak{s}\mathfrak{u}(2)*\mathfrak{s}\mathfrak{u}(2))

The relation between the set of transformations of the quantum plane and the quantum universal enveloping algebra U _q (u(2)) is investigated by constructing representations of the factor algebra U _q (u(2))* . The noncommuting coordinates of , on which U _q (2) * U _q (2) acts, are realized as q-spinors with respect to each U _q (u(2)) algebra. The representation matrices of U _q (2) are constructed as polynomials in these spinor components. This construction allows a derivation of the commutation relations of the noncommuting coordinates of directly from properties of U _q (u(2)). The generalization of these results to U _q (u(n)) and is also discussed.     

Effects of heating on the Raman spectra of YBa2Cu3O7−δ

We report effects of heating to the intensities of Raman modes in the spectra of single-crystals embedded in ceramic YBa₂Cu₃O_7– pellets, and compare the results with those from YBa₂Cu₃O_7– thin-films. Heating was done by either increasing the laser-beam power or resistively heating in a heating cell. From the measurements on a single-crystal in z(xx) polarization, we find that the relative intensity of the B_1g mode of the plane oxygens to that of the A_1g mode of apical oxygens decreases strongly as the samples are heated. For a crystal in near x(zz) polarization, the relative intensity of the two modes increases up to certain value. In thin-films, however, no such change was observed even when heated to higher temperatures than the crystals were. Therefore, we interpret that the change in the relative intensity of the two modes of single-crystals is not due to electronic or structural changes nor thermal decomposition in the heated samples. We propose that a single-crystal, when heated, is fractured into many micro-crystals and these micro-crystals thermally fluctuate in orientations. For thin-films, such fluctuation in orientations might be hindered because there are only a few layers of micro-crystals on top of the substrate. Scanning electron micrographs (SEM) of the heated part of the samples seem to provide the evidence of the micro-crystals.     

Three-hadron form factor via quark-triangle loop

An explicit construction in a manifestly Lorentz-invariant and cyclically symmetric form is given for a three-hadron (H) coupling through their respective (q ) constituents interacting via a quark triangle loop under the most general conditions of unequal mass kinematics atboth the elementary quark and composite-hadron levels. The only ansatz employed is that theHq vertex function _H at each vertexi is a function of _i , the relative momentumtransverse to the corresponding hadron momentumP _i, an assumption which can be justified from several independent angles. The resulting structure , withD( ) being a model-independent function, has proved crucial for an explicit integration over the time-like component of the loop momentum, and thus provided an analytical, cyclically symmetric structure free of overlapping pole singularities. The applicational potential of this quantity is outlined.     

Masses ofq 2 \bar q 2 states in a Bethe-Salpeter model

Ground-state masses ofq ^{2 –2} states (true and mock baryonium) are investigated in the framework of a Bethe-Salpeter formalism motivated from QCD. The four-particle system is described by pairwise interactions betweenqq orq pairs with a spectator approximation for the non-interacting pair. The quark-quark interactions are Coulomb plus harmonic interactions; the harmonic terms have been modified to produce linear confinement for heavier quarks, in agreement with experimental spectra. The confining interaction is proportional to the strong coupling constant _s. Apart from the quark masses, the confining interaction is characterized by three basic parameters: (i) a universal spring constant ₀; (ii) a constantC ₀/ ₀ ² , which defines the vacuum structure; (iii) a constantA ₀, which provides a smooth transition from quadratic to linear confinement as one goes from light to heavy quark systems. These three constants [ ₀ = 0.158 GeV;C ₀=0.296;A ₀=0.0283] have been shown to produce excellent fits to all quarkonia states [q ,q ,Q ] as well as baryon spectra (qqq); thus our predictions forq ^{2 2} states contain no free parameters. In this model, theL=0 ground states occur in the range 1.8–2 GeV, 2.15–2.3 GeV and 6.72–6.75 GeV foru ^{2 2},s ^{2 2} andc ^{2 2} states, respectively. We discuss the prospects for these states to be seen experimentally. In the case of thes ^{2 2} state, this is likely to have a rather narrow width, and may correspond to theX(2.22 GeV) meson observed in radiative decays of theJ/ meson. Thec ^{2 2} state might also be visible as a resonance with an appreciable width.Research supported in part by the National Science Foundation under grant NSF-PHY 86-06364Research supported in part by the U.S. Department of Energy     

SU q (2) covariant\hat R-matrices for reducible representations

We consider SU _q (2) covariant -matrices for the reducible3 1 representation. There are three solutions to the Yang-Baxter equation. They coincide with the previously known -matrices for SO _q (3) and SO _q (3, 1). Also, they are the three -matrices which can be constructed by using four different SU _q (2) doublets. Only two of the three -matrices allow a differential structure on the reducible four-dimensional quantum space.     

The electrical performance of thinn +-window layers ina-Si: H solar cells

The electrical properties ofn ⁺-window layers inp-i-n a-Si:H solar cells were characterised as a function ofn ⁺-layer thickness, , by measuring firstly the activation energyE _a of the dark conductivity and secondly the built-in potentialV _bi of the cells.E _a was found to increase with decreasing attaining values as high as 0.8 eV for 5nm; bulk values, e.g.E _a . 2eV in the amorphous andE _a<0.01 eV in the microcrystalline case, were only observed for >20nm and for >200nm, respectively. In contrast,V _bi did not depend on at all and was further found to be consistent with expectations based on the Fermi level positions in bulkn ⁺ andp ⁺-material. As a consequenceE _a in very thin films can no longer be considered as a measure of (E _C –E _F), the distance of the Fermi level from the conduction band edge. The apparent inconsistency inherent to theE _a and theV _bi results can be resolved by assuming that the deposition of then ⁺-material proceeds via the growth and coalescence of small islands.     

Ensemble and trajectory statistics in a nonlinear partial differential equation

We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean and variance are well-characterized functions of the noise statistics, and and depend on . When noise is continuously present along the trajectory, and are independent of the noise statistics and . However, in their evolution toward and , both _u (t, x) and _u ² (t, x) depend on the noise and.     

O $$(\bar \Lambda /m_c )$$ effects in tests of factorization hypothesis for heavy-hadron nonleptonic decays

In the framework of the heavy-quark effective theory, theO ( O(_QCD)) corrections are estimated in the test of factorization hypothesis forB-meson nonleptonic decays proposed by Bjorken. Similar calculations are also carried out for _b nonleptonic decays. The effects of these corrections on the estimate of theD _s -meson decay constant are discussed.     

Isospectral hamiltonian flows in finite and infinite dimensions

A moment map is constructed from the Poisson manifold _A of rank-r perturbations of a fixedN×N matrixA to the dual of the positive part of the formal loop algebra =gl(r)[[, ^–1]]. The Adler-Kostant-Symes theorem is used to give hamiltonians which generate commutative isospectral flows on . The pull-back of these hamiltonians by the moment map gives rise to commutative isospectral hamiltonian flows in _A. The latter may be identified with flows on finite dimensional coadjoint orbits in and linearized on the Jacobi variety of an invariant spectral curveX _r which, generically, is anr-sheeted Riemann surface. Reductions of _A are derived, corresponding to subalgebras ofgl(r, ) andsl(r, ), determined as the fixed point set of automorphism groupes generated by involutions (i.e., all the classical algebras), as well as reductions to twisted subalgebras of . The theory is illustrated by a number of examples of finite dimensional isospectral flows defining integrable hamiltonian systems and their embeddings as finite gap solutions to integrable systems of PDE's.This research was partially supported by NSF grants MCS-8108814 (A03), DMS-8604189, and DMS-8601995     

Global conformal invariance in quantum field theory

Suppose that there is given a Wightman quantum field theory (QFT) whose Euclidean Green functions are invariant under the Euclidean conformal groupSO _e (5,1). We show that its Hilbert space of physical states carries then a unitary representation of the universal (-sheeted) covering group* of the Minkowskian conformal group SO _e (4, 2)₂. The Wightman functions can be analytically continued to a domain of holomorphy which has as a real boundary an -sheeted covering of Minkowski-spaceM ⁴. It is known that* can act on this space and that admits a globally*-invariant causal ordering; is thus the natural space on which a globally*-invariant local QFT could live. We discuss some of the properties of such a theory, in particular the spectrum of the conformal HamiltonianH=1/2(P ⁰+K ⁰).As a tool we use a generalized Hille-Yosida theorem for Lie semigroups. Such a theorem is stated and proven in Appendix C. It enables us to analytically continue contractive representations of a certain maximal subsemigroup of to unitary representations of*.     

Morse and Melnikov functions for NLS Pde's

The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat linear operator , is developed in sufficient detail for later use in studies of perturbations of the NLS equation. Counting lemmas for the non-selfadjoint operator , are established which control its spectrum and show that all of its eccentricities are finite in number and must reside within a finite discD in the complex eigenvalue plane. The radius of the discD is controlled by theH ¹ norm of the potential . For this integrable NLS Hamiltonian system, unstable tori are identified, and Backlund transformations are then used to construct global representations of their stable and unstable manifolds-whiskered tori for the NLS pde.The Floquet discriminant is used to introduce a natural sequence of NLS constants of motion, [ , where _c ^j denotes thej ^th critical point of the Floquet discriminant ()]. A Taylor series expansion of the constants , with explicit representations of the first and second variations, is then used to study neighborhoods of the whiskered tori. In particular, critical tori with hyperbolic structure are identified through the first and second variations of , which themselves are expressed in terms of quadratic products of eigenfunctions of . The second variation permits identification, within the disc D, of important bifurcations in the spectral configurations of the operator . The constant , as the height of the Floquet discriminant over the critical point _c ^j , admits a natural interpretation as a Morse function for NLS isospectral level sets. This Morse interpretation is studied in some detail. It is valid globally for the infinite tail, , which is associated with critical points outside the discD. Within this disc, the interpretation is only valid locally, with the same obstruction to its global validity as to a global ordering of the spectrum. Nevertheless, this local Morse theory, together with the Backlund representations of the whiskered tori, produces extremely clear pictures of the stratification of NLS invariant sets near these whiskered tori-pictures which are useful in the study of perturbations of NLS. Finally, a natural connection is noted between the constants of the integrable theory and Melnikov functions for the theory of perturbations of the NLS equation. This connection generates a simple, but general, representations of the Melnikov functions.Funded in part by AFOSR-90-0161 and by NSF DMS 8922717 A01     

Algebras of observables with continuous representations of symmetry groups

Concrete C*-algebras, interpreted physically as algebras of observables, are defined for quantum mechanics and local quantum field theory.Aquantum mechanical system is characterized formally by a continuous unitary representation up to a factorU _g of a symmetry group in Hilbert space and a von Neumann algebra on invariant with respect toU _g . The set of all operatorsX such thatU _g X U _g ^–1 , as a function ofg , is continuous with respect to the uniform operator topology, is aC*-algebra called thealgebra of observables. The algebra is shown to be the weak (or strong) closure of .Infield theory, a unitary representation up to a factorU(a, ) of the proper inhomogeneous Lorentz group and local von Neumann algebras _C for finite open space-time regionsC are assumed, with the usual transformation properties of underU(a, ). The collection of allX_C giving uniformly continuous functionsU (a, )X U ^–1 (a, ) on is then a localC*-algebra , called thealgebra of local observables. The algebra is again weakly (or strongly) dense in _c . The norm-closed union of the for allC is calledalgebra of quasilocal observables (or quasilocal algebra).In either case, the group is represented by automorphisms V _g resp. V(a, ) — with V _g X=U _g X U _g ^–1 — of theC*-algebra , and this is astrongly continuous representation of on the Banach space . Conditions for V (a, ) can then be formulated which correspond to the usualspectrum condition forU (a, ) in field theory.Work supported in part by the Deutsche Forschungsgemeinschaft.     

Modified Weyl theory and extended elementary objects

To represent extension of objects in particle physics, a modified Weyl theory is used by gauging the curvature radius of the local fibers in a soldered bundle over space-time possessing a homogeneous space G/H of the (4, 1)-de Sitter group G as fiber. Objects with extension determined by a fundamental length parameter R₀ appear as islands D_(i) in space-time characterized by a geometry of the Cartan-Weyl type (i.e., involving torsion and modified Weyl degrees of freedom). Farther away from the domains D_(i), space-time is identified with the pseudo-Riemannian space of general relativity. Extension and symmetry breaking are described by a set of additional fields ( , given as a section on an associated bundle over space-time B with structural group = G D(1), where D(1) is the dilation group. Field equations for the quantities defining the underlying bundle geometry and for the fields are established involving matter source currents derived from a generalized spinor wave function. Einstein's equations for the metric are regarded as the part of the -gauge theory related to the Lorentz subgroup H of G exhibiting thereby the broken nature of the -symmetry for regions outside the domains D_(i).Talk presented at the International Conference on Field Theory and General Relativity held at Utah State University, Logan, Utah, June 26–July 2, 1988.     

Superconformal current algebras and their unitary representations

A natural supersymmetric extension is defined of the current (= affine Kac-Moody Lie) algebra ; it corresponds to a superconformal and chiral invariant 2-dimensional quantum field theory (QFT), and hence appears as an ingredient in superstring models. All unitary irreducible positive energy representations of are constructed. They extend to unitary representations of the semidirect sumS (G) of with the superconformal algebra of Neveu-Schwarz, for , or of Ramond, for =0.On leave of absence from the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences, BG-1184 Sofia, Bulgaria     

Isospectral Hamiltonian flows in finite and infinite dimensions

The approach to isospectral Hamiltonian flow introduced in part I is further developed to include integration of flows with singular spectral curves. The flow on finite dimensional Ad^*-invariant Poisson submanifolds of the dual of the positive part of the loop algebra is obtained through a generalization of the standard method of linearization on the Jacobi variety of the invariant spectral curveS. These curves are embedded in the total space of a line bundleTP ₁(C), allowing an explicit analysis of singularities arising from the structure of the image of a moment map from the space of rank-r deformations of a fixedN×N matrixA. It is shown how the linear flow of line bundles over a suitably desingularized curve may be used to determine both the flow of matricial polynomialsL() and the Hamiltonian flow in the spaceM _N,r×M_N,r in terms of -functions. The resulting flows are proved to be completely integrable. The reductions to subalgebras developed in part I are shown to correspond to invariance of the spectral curves and line bundles under certain linear or anti-linear involutions. The integration of two examples from part I is given to illustrate the method: the Rosochatius system, and the CNLS (coupled non-linear Schrödinger) equation.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and by U.S. Army grant DAA L03-87-K-0110     

Measurement ofR and determination of the charged-particle multiplicity ine+e? annihilation at 13-113-113-1around 10 GeV

We have measured theR value in non-resonante ⁺ e ^– annihilation using the ARGUS detector at the storage ring DORIS II. At a centre-of-mass energy GeV the ratio of the hadronic cross-section to the -pair cross section in lowest order QED has been determined to beR=3.46±0.03±0.13. In addition, we have measured the charged-particle multiplicities in non-resonant hadron production at GeV just below theB threshold and in (4S) resonance decays. For the average charged-particle multiplicities in continuum events and (4S)B decays we obtain n>_cont=8.35±0.02±0.20 and n>_(4s)=10.81±0.05±0.23.Supported by the German Bundesministerium für Forschung und Technologie, Contract no. 054DO51P     

N=2 structures on solvable Lie algebras: Thec=9 classification

Let be a finite-dimensional Lie algebra (not necessarily semisimple). It is known that if is self-dual (that is, if it possesses an invariant metric) then it admits anN=1 (affine) Sugawara construction. Under certain additional hypotheses, thisN=1 structure admits anN=2 extension. If this is the case, is said to possess anN=2 structure. It is also known that anN=2 structure on a self-dual Lie algebra is equivalent to a vector space decomposition , where are isotropic Lie subalgebras. In other words,N=2 structures on in one-to-one correspondence with Manin triples . In this paper we exploit this correspondence to obtain a classification of thec=9N=2 structures on solvable Lie algebras. In the process we also give some simple proofs for a variety of Lie algebras. In the process we also give some simple proofs for a variety of Lie algebraic results concerning self-dual Lie algebras admitting symplectic or Kähler structures.     

From the deuteron to deusons,an analysis of deuteronlike meson-meson bound states

A systematic study of possible deuteronlike twomeson bound states,deusons, is presented. Previous arguments that many such bound states may exist are elaborated with detailed arguments and numerical calculations including, in particular, the tensor potential. This tensor potential which is crucial for the deuteron binding is shown to be very important also in the mesonic case. Especially, in the pseudoscalar³ P ₀ pseudoscalar-vector and vector-vector channels the important observation is made that the centrifugal barrier from theP-wave can be overcome by the 1/r ² and 1/r ³ terms of the tensor potential. In the heavy meson sector one-pion exchange alone is strong enough to form at least deuteronlike and composites bound by approximately 50 MeV. Composites of and states bound by pion exchange alone are expected near the thresholds, while in the light meson sector one generally needs some additional short range attraction to form bound states. The quantum numbers of these states areI=0, andJ ^PC=0^–+, 1⁺⁺ for the states andI=0,J ^PC=0⁺⁺, O^–+, 1^+– and 2⁺⁺ for the composites. In the states: ^b (10545), _b1(10562) are predicted and in , one finds the states: ^b (10590), _bQ (10582),h _b(10608), _b2(10602). Near the threshold the states: ^c (3870), _c0(3870) are predicted, and near the threshold one finds the states: _b0(4015), ^c (4015),h _c(4015), _c2(4015). Within the light meson sector pion exchange gives strong attraction for and systems with quantum numbers where the best non- candidates exist, although pion exchange alone is not strong enough to support such bound states. Thus, although one cannot conclude with certainty it to be the case, this fact does favour the picture that the (1440) and thef ₁ (1420) are mainly composites and thef ₀(1710) mainly a bound state, while thef ₀(1515) andf ₂(1520) could be predominantly composites. If the predicted and states are found, these would support this interpretation of the light states. In channels with exotic flavour orCP quantum numbers pion exchange is generally repulsive or quite weak. Therefore one does not expect that such deuteronlike bound states exist, althoughB*B* may be an exception.