Resonances in at rest

Data on at rest show two resonant processes: (a) f₀(1370)η,f₀(1370)→σσ and ρρ, (b) η(1440)σ, η(1440)→ηπ⁺π⁻. The branching ratio BR[f₀(1370)→ρρ]/BR[f₀(1370)→σσ]=0.98±0.25 in the mass range available here. Using data on , the ratio Γ_4π/Γ_2π5 for f₀(1370). The effects of the strongly s-dependent width of f₀(1370) are discussed in some detail.The η(1440) is observed decaying to ησ and a₀(980)π, with strong destructive interference between them. In its decay to a₀(980)π, a narrow peak appears in the ηπ mass spectrum, but 30–50 MeV above that usually attributed to a₀(980) and significantly above the KK threshold. This effect is explained naturally by a two-step process: η(1440)→K^*(890)K followed by rescattering of the two kaons through a₀(980) to ηπ above the KK threshold.     

Study of in flight

An analysis of data on is presented at beam momenta 600 to 1940 MeV/c. There is evidence for an I=1, J^PC=2⁻⁺ resonance in ηηπ⁰ with mass M=1880±20 MeV and width 255±45 MeV, decaying strongly to a₂(1320)η; it is too strong to be explained as the high mass tail of π₂(1670)→a₂(1320)η. There is tentative evidence also for weak decays to f₀(1500)π. It makes a natural partner to the η₂(1860).     

Principal Fibrations from Noncommutative Spheres

We construct noncommutative principal fibrations S_θ⁷→S_θ⁴ which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. “The algebra inclusion is an example of a not-trivial quantum principal bundle.”     

Observation of the π(1800) and (1880) mesons in decay

A partial-wave analysis of the reaction π⁻p→ηηπ⁻p at 18 GeV/c has been performed on a data sample of approximately 4000 events obtained by Brookhaven experiment E852. The J^PC=0⁻⁺π(1800) state is observed in the a₀(980)η and f₀(1500)π decay modes. It has a mass of 1876±18±16 MeV/c² and a width of 221±26±38 MeV/c². The J^PC=2⁻⁺π₂(1880) meson is observed decaying through a₂(1320)η. It has a mass of 1929±24±18 MeV/c² and a width of 323±87±43 MeV/c². Both states are potential candidates for non-exotic hybrid mesons.     

Families of commuting transfer matrices and integrable models with disorder

A family of commuting transfer matrices is shown to be associated to each symmetry transformation of a given Yang-Baxter algebra. This applies in lattices models and field theory.The Yang-Baxter algebra remains unchanged when an arbitrary parameter μ_l is associated to each lattice site. We generate in this way integrable one-dimensional hamiltonians with long-range couplings and disorder given by the <{;μ₁<};. These operators are lattice versions of the non-local charges in sigma models. As a simple example we get a Dzialozhinski-Moriya interaction with an arbitrary coupling per site from the six-vertex model. A similar model with a disordered magnetic field follows too. Their exact solution by an algebraic Bethe ansatz is presented. We derive the excitations spectrum in terms of the density of parameters (μ).As another application, the total spin S² is computed for a XXZ Heisenberg chain (μ_l ≡ 0) as a function of the anisotropy Δ (− ∞ < Δ < + ∞).     

Elastic double diffractive production of axial-vector mesons and the Landau–Yang theorem

We discuss exclusive elastic double diffractive axial-vector χ_c(1⁺) meson production in proton–antiproton collisions at the Tevatron. The amplitude for the process is derived within the k_t-factorization approach with unintegrated gluon distribution functions (UGDFs). We show that the famous Landau–Yang theorem is not applicable in the case of off-shell gluons. Differential cross sections for different UGDFs are calculated. We compare exclusive production of χ_c(1⁺) and χ_c(0⁺). The contribution of χ_c(1⁺) to the J/Ψ+γ channel is smaller than that of the χ_c(0⁺) decay, but not negligible and can be measured. The numerical value of the ratio of the both contributions is much less dependent on the UGDFs modeling than the cross sections themselves.     

Functional differential equation approach to the large N expansion and mean field perturbation theory

An apparent difference between formulating mean field perturbation theory for λφ⁴ field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)λφ⁴ field theory. A simple method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action Γ(φ, χ) is obtained by directly integrating the functional differential equations for the fields φ and χ ( ) in the presence of two external sources j = −δΓ/δφ, S = −δΓ/δχ.     

The algebra ,η( ) and infinite Hopf family of algebras

New deformed affine algebras, _,η( ), are defined for any simply laced classical Lie algebra g, which are generalizations of the algebra, _,η( ₂), recently proposed by Khoroshkin-Lebedev-Pakuliak (KLP). Unlike the work of KLP, we associate with the new algebras the structure of an infinite Hopf family of algebras in contrast to the one containing only finite number of algebras, introduced by KLP. Bosonic representation for _,η( ) at level 1 is obtained, and it is shown that, by repeated application of Drinfeld-like comultiplications, a realization of _,η( ) at any positive integer level can be obtained. For the special case of g = sl_r+1, (r + 1)-dimensional evaluation representation is given. The corresponding interwining operations are also discussed.     

Changes in electrical properties in α- and γ-exposed PADC track detector

The changes in the dielectric properties and temperature dependence of the d.c. conductivity of α-exposed poly allyl diglycol carbonate (PADC) have been studied. On α-irradiation the dielectric constant (′) as a function of frequency has been found to decrease significantly. The temperature dependence of resistivity in pristine and γ-irradiated samples is of the form ρ(T)=ρ_∝ exp(T₀/T) which can be attributed to conduction of thermally generated carriers. In case of (γ+α) irradiated samples the temperature dependence of resistivity is of the form ρ(T)=ρ_∝ exp(T₀/T)^1/2 which is due to one-dimensional hopping of carriers.     

Observation of χb production in the exclusive reaction ′→γγχb→γγ→γγ(eeorμμ−)

We report on the observation of 1 ³P_J (χ_b) production in the reaction ′→γχ_b→γγ→γγ(e⁺e⁻ or μ⁺μ⁻). The data were recorded with the nonmagnetic CUSB detector at the Cornell Electron Storage Ring, CESR. We observe 124 γγ events with either an electron or muon pair in the final state. In the γγ correlation plot about 40% of the events cluster around (120, 430) MeV.     

Spectrum Invariance for a Particular Class of Optical Fields Propagated in Far Zone

This paper describes invariance of the normalized optical spectrum for a particular class of optical fields propagated in the far zone from a secondary, spatially, partially coherent source. The optical field across the secondary planar source is inhomogeneous to give the complex degree of spectral coherence such that μ = h(αω(ρ₁–ρ₂))exp(iɛω(ρ₁²–ρ₂²)), where α, ɛ are constants, ω is optical frequency, and ρ₁, ρ₂ denote two points in the secondary source. This expression for μ is the same as obtained in the Fresnel zone from a primary, spatially incoherent source. The invariance law does not hold for the spectrum of the light propagated from the primary source.     

On integrability of generalized Veronese curves of distributions

Given a 1-parameter family of 1-forms γ(t) = γ₀+tγ₁+ ···+tⁿψ_n, consider the condition dγ(t)γ(t) = 0 (of integrability for the annihilated by γ(t) distribution w(t)). We prove that in order that this condition is satisfied for any t it is sufficient that it is satisfied for N = n + 3 different values of t (the corresponding implication for N = 2n + 1 is obvious). In fact we give a stronger result dealing with distributions of higher codimension. This result is related to the so-called Veronese webs and can be applied in the theory of bihamiltonian structures.     

Looking for double beta decay of Nd to excited states of Sm by gamma ray spectroscopy

We have measured the gamma ray activity of a sample of 6189 grams of metallic Neodimium with a germanium detector. From the gamma energy spectrum recorded during almost 6500 hours we extract lower limits for the halflife of the inclusive (0ν + 2ν) ββ decay of ¹⁵⁰Nd to the first excited states of ¹⁵⁰Sm : t_1/2(0⁺ → 0₁⁺ > 1.0·10²⁰, t_1/2(O⁺ → 0₂⁺) > 2.0 · 10²⁾, t_1/2(0⁺ → 2₁⁺) > 9.1 · 10¹⁹.     

The set of equivalent classes of invariant star products on (G; β1)

This article, in conjunction with a previous one, proves Drinfeld's theorems about invariant star products, ISPS, on a connected Lie group G endowed with an invariant symplectic structure β₁ ε ²( ). In particular, we prove that every formal 2-cocycle · ² ( ))[[ ]] determines an ISP, , and conversely any ISP, F, determines a formal 2-cocycle fx360-1 such that F is equivalent to . We also prove that two ISPS and are equivalent if and only if the cohomology classes of and coincide. These properties define a bijection between the set of equivalent classes of ISP on (G; β₁) and the set · ²( )[[ ]].     

The bending energy levels of C2H2

Absorption spectra of C₂H₂ have been recorded between 50 and 1450 cm⁻¹, with a resolution always better than 0.005 cm⁻¹, using two different Fourier transform spectrometers. Analysis of the data provided two sets of results. First, the bending levels with Σ_t V_t(t = 4, 5) ≤ 2 were characterized by a coherent set of 34 parameters derived from the simultaneous analysis of 15 bands, performed using a matrix Hamiltonian. The following main parameters were obtained (in cm⁻¹): ω₄⁰ = 608.985196(14), ω₅⁰ = 729.157564(10); B₀ = 1.17664632(18), α₄ = −1.353535(86) × 10⁻³, α₅ = −2.232075(40) × 10⁻³; q₄⁰ = 5.24858(12) × 10⁻³, and q₅⁰ = 4.66044(12) × 10⁻³, with the errors (1σ) on the last quoted digit. Second, a more complete set of bending levels with Σ_t V_t ≤ 4, some of which have never previously been reported, and also including V₂ = 1 have been fitted to 80 parameters. This simultaneous fit involved 43 bands and used the same full Hamiltonian matrix. Some perturbations which affect the higher excited levels are discussed.     

On the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper''s operator

Harper's operator is the self-adjoint operator on defined by

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. We first show that the determination of the spectrum of the transition operator on the Cayley graph of the discrete Heisenberg group in its standard presentation, is equivalent to the following upper bond on the norm of H_θ,: H_{θ,≤ 2(1 + √2 + cos(2πθ))}. We then prove this bound by reducing it to a problem on periodic Jacobi matrices, viewing H_θ, as the image of H_θ = U_θ + _θ^* + V_θ + V_θ^* in a suitable representation of the rotation algebra A_θ. We also use powers of H_θ to obtain various upper and lower bounds on H_θ = maxH_θ,. We show that “Fourier coefficients” of H_θ^k in A_θ have a combinatorial interpretation in terms of paths in the square lattice ². This allows us to give some applications to asymptotics of lattice paths combinatorics.     

Effects of superstrings in collisions

Superstring theory in d = 10 dimensions after Calabi—Yau compactification yields a minimum low-energy gauge group SU(3)_C × SU(2)_L × U(1)_Y × U(1)_E. The low-energy theory includes particles with the quantum numbers of 27 representations of E₆, each of which contains an extra neutrino ν^c conventionally called a “right-handed neutrino”. The contributions of ν and ν^c to through Z⁰ and Z_E mixing is calculated. Small contributions are found of the new right-handed neutrino and of the superstring boson Z_E to σ(e⁺e⁻ → γ + nothing).     

Analysis of the 2ν3 band of CD3F at 5.06 μm recorded under high resolution

The 2ν₃(A₁) band of ¹²CD₃F near 5.06 μm has been recorded with a resolution of 20–24 × 10⁻³ cm⁻¹. The value of the parameter (α^B − α^A) for this band was found to be very small and, therefore, the K structure of the R(J) and P(J) manifolds was unresolved for J < 15 and only partially resolved for larger J values. The band was analyzed using standard techniques and values for the following constants determined: ν₀ = 1977.178(3) cm⁻¹, B″ = 0.68216(9) cm⁻¹, D″_J = 1.10(30) × 10⁻⁶ cm⁻¹, α^B = (B″ − B′) = 3.086(7) × 10⁻³ cm⁻¹, and β^J = (D″_J − D′_J) = −3.24(11) × 10⁻⁷ cm⁻¹. A value of α^A = (A″ − A′) = 2.90(5) × 10⁻³ cm⁻¹ has been obtained through band contour simulations of the R(J) and P(J) multiplets.     

Compositionally asymmetrical multiquantum wells: “Pseudo-molecules” for giant optical nonlinearities in the infrared (9–11 μm)

Intersubband transitions in quantum well have extremely large oscillator strengths and induce strong nonlinear effects in structures where inversion symmetry is broken, realized by growing AlGaAs quantum wells with asymmetrical A1 gradients. These compositionally asymmetrical multiquantum wells may thus be viewed as giant “quasimolecules” optimized for optimal nonlinearities in the mid infrared. Optical rectification as well as second harmonic generation have been measured in those structures using a continuous CO₂ laser. At 10.6 μm the nonlinear coefficients are more than 3 orders of magnitude higher in these samples than for bulk GaAs (i.e. χ₀⁽²⁾ = 5.3 × 10⁻⁶m/V, χ_2ω⁽²⁾ = 7.2 × 10⁻⁷ m/V) and are in good agreement with theoretical predictions. We present more complex “pseudo-molecules” involving weakly coupled quantum wells. The optical rectification effects in these devices are so large χ₀⁽²⁾ = 1.6 × 10⁻³ m/V) that application to infrared detection may be envisioned.