Evidence for non-q \bar q mesons

The non-Abelian nature of QCD suggests that particles that have a gluon constituent, such as glueballs or hybrids, should exist. In addition,q q states are also predicted. This paper describes a search for these non-q q mesons performed by experiment WA 76 using the CERN Omega Spectrometer and discusses three candidates which have been observed.Invited talk at HEXAM 89, Bechyn Castle, Czechoslovakia, June 25–30, 1989.     

Slepton and squark production and decay inep collisions at the LHC

We present a detailed study of and and the subsequent decays of , , and at the LHC . We explore the relevant supersymmetry parameter range. We calculate the cross sections as well as the rates for interesting signatures such as the production of one or two leptons on the lepton side.     

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     

Unbounded derivations commuting with compact group actions

Let be a closed * derivation in aC* algebra which commutes with an ergodic action of a compact group on . Then generates aC* dynamics of . Similar results are obtained for non-ergodic actions on abelianC* algebras and on the algebra of compact operators.Research supported by N.S.F.     

Logarithmic Sobolev inequality for lattice gases with mixing conditions

Let denote the grand canonical Gibbs measure of a lattice gas in a cube of sizeL with the chemical potential and a fixed boundary condition. Let be the corresponding canonical measure defined by conditioning on . Consider the lattice gas dynamics for which each particle performs random walk with rates depending on near-by particles. The rates are chosen such that, for everyn andL fixed, is a reversible measure. Suppose that the Dobrushin-Shlosman mixing conditions holds for forall chemical potentials . We prove that for any probability densityf with respect to ; here the constant is independent ofn orL andD denotes the Dirichlet form of the dynamics. The dependence onL is optimal.Research partially supported by U.S. National Science Foundations grant 9403462, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship.     

Entropy functionals of Kolmogorov-Sinai type and their limit theorems

Two functionals and are introduced forC ^*-dynamical systems with invariant states and stationary channels. It is shown that the Kolmogorov-Sinai-type theorems hold for these functionals and . Our functionals and are set within the framework of quantum information theory and generalize a quantum KS entropy by CNT and the mutual entropy by Ohya.     

Recursion method for the density of states and spectral dimension of percolation networks

We use the recursion method to calculate the vibrational density of states of site percolation clusters slightly above the percolation threshold. It is found that is proportional to at long wavelengths. At shorter length scales, is proportional to , with the fraction dimension . The cross-over from phonon to fraction regime is characterized by a rapid rise in in agreement with effective medium calculations.     

Derivations and automorphisms of operator algebras

The theorem that each derivation of aC*-algebra extends to an inner derivation of the weak-operator closure ( )^– of in each faithful representation of is proved in sketch and used to study the automorphism group of in its norm topology. It is proved that the connected component of the identity in this group contains the open ball of radius 2 with centerl and that each automorphism in extends to an inner automorphism of ( )^–.Research conducted with the partial support of the NSF and ONR.     

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.     

On the support of the Ashtekar-Lewandowski measure

We show that the Ashtekar-Isham extension of the configuration space of Yang-Mills theories is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices.These results are then used to prove that is contained in a zero measure subset of with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure on . Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the extended configuration space .     

Total Electron Emission from Metals Due to the Impact of Highly-Charged Xe Ions with Energies Up to MeV

Total electron emission from metals due to the impact of multiply charged ions, , may significantly influence quantitative measurements of ion current in corpuscular diagnostics. The value of (/q) was determined for Xe ions impacting clean polycrystalline copper as a function of ion charge state and of ion kinetic energy, keV/q, i.e. in the energy region up to keV/amu, where there is a lack of such data. For highly charged projectile ions, was found to have a clear minimum as a function of E _i. With decreasing charge state of the projectile ion this minimum shifts to a lower energy and becomes shallower. This observation is in agreement with compiled results of other authors. Limits for values of are estimated and discussed.     

On the purification of factor states

Let be aC*-algebra and be an opposite algebra. Notions of exact andj-positive states of are introduced. It is shown, that any factor state of can be extended to a pure exactj-positive state of . The correspondence generalizes the notion of the purifications map introduced by Powers and Størmer. The factor states ₁ and ₂ are quasi-equivalent if and only if their purifications and are equivalent.     

Ellipsoidal bag model for heavy quark system

The ellipsoidal bag model is used to describe heavy quark systems such asQ ,Q g andQ ² . Instead of two step model, these states are described by an uniform picture. The potential derived from the ellipsoidal bag forQ is almost equivalent to the Cornell potential. For aQ ² system with large quark pair separation, an improvement of 70 MeV is obtained comparing with the spherical bag.     

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.     

Covariance algebras in field theory and statistical mechanics

Starting from aC*-algebra and a locally compact groupT of automorphisms of we construct a covariance algebra with the property that the corresponding *-representations are in one-to-one correspondence with covariant representations of i.e. *-representations of in which the automorphisms are continuously unitarily implemented. We further construct for relativistic field theory an algebra yielding the *-representations of in which the space time translations have their spectrum contained inV. The problem of denumerable occurence of superselection sectors is formulated as a condition on the spectrum of . Finally we consider the covariance algebra built with space translations alone and show its relevance for the discussion of equilibrium states in statistical mechanics, namely we restore in this framework the equivalence of uniqueness of the vacuum, irreducibility and a weak clustering property.On leave of absence from Istituto di Fisica G. Marconi — Roma.     

Comments on “power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas”

A simple argument is presented by which one can show that the critical inverse temperature _c of a two-dimensional Coulomb gas (standard or hard-core) with activityz satisfies , where in the low-activity limit. Previous results yield .     

Conformal field theories,representations and lattice constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted andZ ₂-twisted theories, () and respectively, which may be constructed from a suitable even Euclidean lattice . Similarly, one may construct lattices and by analogous constructions from a doubly-even binary code . In the case when is self-dual, the corresponding lattices are also. Similarly, () and are self-dual if and only if is. We show that has a natural triality structure, which induces an isomorphism and also a triality structure on . For the Golay code, is the Leech lattice, and the triality on is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories () and with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.     

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*.     

Automorphisms that commute with a modular automorphism

For M a factor of type III₁ we can find for every automorphism group _s that commutes with a modular automorphism group _t and another modular automorphism group , an automorphism group that commutes with is connected with _s by an inner cocycle.     

Conformal tensor discontinuities in general relativity

The postulate is made that across a given hypersurfaceN the metric and its first derivatives are continuous. This postulate is used to derive conditions which must be satisfied by discontinuities in the Riemann tensor acrossN. These conditions imply that the conformal tensor jump is uniquely determined by the stress-energy tensor discontinuity ifN is non-null (and to within an additive term of type Null ifN is lightlike). Alternatively, and [R] determine ifN is non-null. These relationships between the conformal tensor and stress-energy tensor jumps are given explicitly in terms of a three-dimensional complex representation of the antisymmetric tensors. Application of these results to perfect-fluid discontinuities is made: is of type D across a fluid-vacuum boundary and across an internal, non-null shock front. is of type I (non-degenerate) in general across fluid interfaces across which no matter flows, except for special cases.The research reported herein was supported in part by the Atomic Energy Commission under contract number AT (11-1)-34, Project Agreement No. 125, while the author was at the University of California at Berkeley, and in part by National Science Foundation Grant GU-1598-University Science Development Program.