Extracting (α/π) Σa,μνGμνGμν from gauge theories on a lattice

The quantity G = (α/π) Σ_a,μνG_μν^aG_μν^a is extracted from Monte Carlo data for SU(2) lattice gauge theory We find G = 0.015 ± 0.002 GeV⁴.     

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.     

Contribution to the Analysis of theA2←XA1“Wulf” Transition of Ozone by High-Resolution Fourier Transform Spectrometry

The analysis of the rotational structure of the high-resolution Fourier transform 0⁰₀absorption spectrum of the³A₂←X¹A₁band system of the “Wulf” transition of the isotopomer¹⁶O₃of ozone is reported for the first time. With a near pure case (b) coupling model for the upper triplet state, we have assigned a significant portion of the spectrum, mainly theF₁(J=N+ 1) andF₂(J=N) spin components, primarily in the lower frequency region of the band. The lines corresponding to theF₃(J=N− 1) component are weak at lower frequencies and heavily congested in the central and higher frequency regions of the spectrum. Perturbations and predissociation phenomena have reduced the effective lifetime of the metastable³A₂state and have also limited the number of transitions included in the least-squares fit of the band. Approximately 100 lines have been assigned in the range from 9100–9550 cm⁻¹. Three rotational, three centrifugal distortion, three spin–rotation, and one spin–spin constant were varied. The geometry of the molecule in the³A₂state, as determined from these constants, isr= 1.345 Å and θ = 98.9°, in good agreement withab initioresults.     

Rotational absorption spectrum of methylene fluoride in the 20–100 cm region

The pure rotational spectrum of CH₂F₂ was recorded in the 20–100 cm⁻¹ spectral range and analyzed to obtain rotation and centrifugal distortion constants. Analysis of the data yielded rotation constants: A = 1.6392173 ± 0.0000015, B = 0.3537342 ± 0.00000033, C = 0.3085387 ± 0.00000027, τ_aaaa = −(7.64 ± 0.46) × 10⁻⁵, τ_bbbb = −(2.076 ± 0.016) × 10⁻⁶, τ_cccc = −(9.29 ± 0.12) × 10⁻⁷, T₁ = (4.89 ± 0.20) × 10⁻⁶, and T₂ = −(1.281 ± 0.016) × 10⁻⁶cm⁻¹.     

Condition for adiabatic passage in the earth’s-field NMR technique

The equation of motion dM/dt=γ M×B(t) is solved for the case B(t)=jB_p(t)+kB_e. The field B_e is a small static field, typically the earth’s field. The field B_p(t) decays exponentially toward zero with time constant T. This decay is produced by an overdamped switching transient that occurs near the end of the rapid cutoff of the coil current used to polarize the sample. It is assumed that B_p is initially large compared to B_e, and that magnetization M is initially along the resultant field B. Exact solutions are obtained numerically for several decay time constants of B_p, and the motion of M is depicted graphically. It is found that for adiabatic passage, the final cone angle β of the precession in field B_e is related to the decay time constant of B_p by β=2e^{−(π/2)ω_eT}. This is confirmed by measurements of the amplitudes of the ensuing free-precession signals for various decay rates of B_p. Near-perfect adiabatic passage (magnetization aligned within 2° of the earth’s field) can be achieved for time constants T2.6/ω_e. For the case of sudden passage, an approximate analytic solution is developed by linearizing the equation of motion in the laboratory frame of reference. For the adiabatic case, an approximate analytic solution is obtained by linearizing the equation of motion in a rotating frame of reference that follows the resultant field B=B_p+B_e.     

Symmetries of WDVV equations

We say that a function F(τ) obeys WDVV equations, if for a given invertible symmetric matrix η^αβ and all , the expressions can be considered as structure constants of commutative associative algebra; the matrix η_αβ inverse to η^αβ determines an invariant scalar product on this algebra. A function x^α(z,τ) obeying is called a calibration of a solution of WDVV equations. We show that there exists an infinite-dimensional group acting on the space of calibrated solutions of WDVV equations (in different form such a group was constructed in [A. Givental, math.AG/0305409]). We describe the action of Lie algebra of this group.     

Contributions to the Gaussian Line Broadening of the Proxyl Spin Probe EPR Spectrum Due to Magnetic-Field Modulation and Unresolved Proton Hyperfine Structure

A simple expression is derived to compute the total Gaussian linewidth of a Voigt line that is broadened by sinusoidal magnetic-field modulation as follows: ΔH^G_pp(H_m)²= ΔH^G_pp(0)²+ κ²H²_m, where ΔH^G_pp(H_m) is the Gaussian linewidth observed with an modulation amplitudeH_m/2 and ΔH^G_pp(0) is the Gaussian linewidth in the limit of zero modulation. The field modulation contributes an additional Gaussian broadening of κH_m, where κ is a constant, which adds in quadrature to ΔH^G_pp(0) to give the total Gaussian linewidth. Denoting the overall linewidth of the Voigt line in the absence of modulation broadening by ΔH⁰_pp(0), it is shown, both by analytical means and by spectral simulation, that the constant κ is equal to 1/2 in the limit ofH_m ΔH⁰_pp(0); however, using values ofH_mas large as ΔH⁰_pp(0) leads to only minor departures from κ = 1/2. The formulation is valid both for Lorentzian and Voigt lines and is tested for 2,2,5,5-tetramethylpyrrolidin-1-oxyl-3-carboxylic acid (3-carboxy proxyl) in CCl₄and in aqueous buffer. This spin probe was studied because the proxyl group is the only major spin-probe moiety whose Gaussian linewidth had not been characterized in the literature. For 3-carboxy proxyl, it is found that ΔH^G_pp(0) = 1.04 ± 0.01 G independent of solvent polarity. Precision values of the¹⁴N hyperfine coupling constant for 3-carboxy proxyl at 9.5°C are as follows: 14.128 ± 0.001 G in CCl₄and 16.230 ± 0.002 G in aqueous buffer. The temperature dependence of ΔH^G_pp(0) and the¹⁴N hyperfine coupling constant are reported as empirical equations. Results of the present work taken together with previously published data permits accurate correction for the effects of inhomogeneous broadening due to unresolved hyperfine structure and modulation broadening for the majority of spin probes in common use.     

Millimeter-Wave Spectroscopy, High-Resolution Infrared Spectrum, ab Initio Calculations, and Molecular Geometry of FPS

The transient thiophosphenous fluoride FPS was produced by pyrolysis of 2.5% F₂PSPF₂ in Ar at 1300–1800°C. High-resolution (≥0.004 cm⁻¹) Fourier transform infrared spectra of the a-type ν₁ and b-type ν₂ bands, centered respectively at 803.249 and 726.268 cm⁻¹, were measured and fitted to rotational and quartic centrifugal distortion parameters. The millimeter-wave spectrum, essentially b-type, was measured between 300 and 370 GHz in the ground state and in the ν₃ excited state for FP³²S and in the ground state for FP³⁴S. The frequencies were fitted to a Watson-type A-reduced Hamiltonian up to sextic distortion terms. High level ab initio calculations with large basis sets were performed on FPS and supported the first identification of its infrared and millimeter wave spectra. The calculated anharmonic force field provided precise ab initio rovibrational α constants which were combined with the experimental molecular parameters to determine an accurate equilibrium structure of the molecule: r_e(PS)=188.86 pm, r_e(PF)=158.70 pm, θ(FPS)=109.28°. The collision-controlled 1/e lifetime measured in a 10-Pa (1 : 20) F₂PSPF₂/Ar mixture was 2 s, more than two orders of magnitude larger than that of FPO under the same experimental conditions.     

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.     

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).     

Separation of the ortho and para NMR signals in solid deuterium via DQ filtering

Double quantum (DQ) filtering is shown to lead to an effective separation of the NMR signals from the para (I = 1) and ortho (I = 2) molecules in solid deuterium. The separation is achieved by the pulse sequence 90_φ^°–t_pr–90_φ^°–t_ev–90_x^°–t, where the phase-cycled first two pulses create the DQ coherence. Two components are observed after the third pulse; the para signal shows the maximum at a short time t while the ortho signal reaches the maximum at a longer t. The observed signal can be expressed as ∑_I [F_I(t_pr − t) − F_I(t_pr + t)], where F_I(t) is a proper fitting function for the free induction signal of the para and ortho molecules (with I = 1 or 2, respectively). Numerical fits to experimental data at 4.2 and 2 K show that this method can be used to determine the ratio F₁(0)/F₂(0) and thus, because the initial value F_I(0) is proportional to the respective magnetization before the pulse sequence, the ortho and para concentrations in solid deuterium.     

An energy-momentum tensor in gauge theories

We consider the renormalization of the twist two, dimension four gauge invariant operator O_μν⁽¹⁾ = − F_μσF_νσ − g_{μν 0}. By using the general theory of renormalization of gauge invariant operators, we find the gauge noninvariant operator O⁽²⁾ with which it mixes. We construct a finite combination of O⁽¹⁾ and O⁽²⁾ and show that it is an acceptable energy momentum tensor for gauge theories. We compare our energy momentum tensor with that constructed by Freedman, Muzinich, and Weinberg.     

Measurement of the mass of the Λb baryon

In a data sample of four million hadronic Z decays collected with the ALEPH detector at LEP, four Λ_b baryon candidates are exclusively reconstructed in the Λ_b → Λ_c⁺π⁻ channel, with the Λ_c⁺ decaying into pK⁻π⁺, , or Λπ⁺π⁺π⁻. The probability of the observed signal to be due to a background fluctuation is estimated to be 4.2 × 10⁻⁴. The mass of the Λ_b is measured to be 5614±21 (stat.) ± 4 (syst.) MeV/c².     

Three-dimensional stationary cyclic symmetric Einstein–Maxwell solutions; black holes

From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the (2 + 1)-dimensional gravity the uniqueness of wide families of exact solutions is established. Among them, all uniform electromagnetic solutions possessing electromagnetic fields with vanishing covariant derivatives, all fields having constant electromagnetic invariants F_μνF^μν and T_μνT^μν, the whole classes of hybrid electromagnetic solutions, and also wide classes of stationary solutions are derived for a third-order nonlinear key equation. Certain of these families can be thought of as black hole solutions. For the most general set of Einstein–Maxwell equations, reducible to three nonlinear equations for the three unknown functions, two new classes of solutions – having anti-de Sitter spinning metric limit – are derived. The relationship of various families with those reported by different authors’ solutions has been established. Among the classes of solutions with cosmological constant a relevant place is occupied by the electrostatic and magnetostatic Peldan solutions, the stationary uniform and spinning Clement classes, the constant electromagnetic invariant branches with the particular Kamata–Koikawa solution, the hybrid cyclic symmetric stationary black hole fields, and the non-less important solutions generated via SL(2,R)-transformations where the Clement spinning charged solution, the Martinez–Teitelboim–Zanelli black hole solution, and Dias–Lemos metric merit mention.     

Isoscalar quadrupole strength in Ca from the (p,p′α0) reaction at Ep = 100 MeV

The ⁴⁰Ca(p,p′ α) reaction has been studied at an incident proton energy E_p = 99.5 MeV for proton laboratory scattering angles Θ_p^lab = 17°, 23° and 27°. Emission of α particles coincident with the scattered proton has been measured for an angular range Θ_α 0° − 180° relative to the recoil axis. A multipole decomposition for the α₀-decay channel to the ³⁶Ar ground state has been performed from the angular-correlation functions. The energy distribution of the dominating E2 strength deduced in the excitation energy range E_x = 11–21 MeV agrees reasonably well with the results from electron and α-induced α₀-decay investigations. The exhaustion of the E2 energy-weighted sum rule in this channel up to an energy of 17 MeV is 16.1(4.0)%, in accord with the study of the (α, α′ α₀) reaction. However, this value is twice what is found in the (e,e′ α₀) experiment in the same energy region. Thus, the puzzling discrepancy in the E2 strengths derived from electromagnetic and hadronic probes remains unsolved.     

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.     

Analysis of the Δv = 0 sequence of the β(cΦ - aΔ) system of the TiO molecule

Rotational analyses have been performed on the emission spectra of the 0-0, 1-1, 2-2, and 3-3 bands of the β system (c¹Φ - a¹Δ) of the TiO molecule, excited in a microwave discharge through a mixture of helium, oxygen and TiCl₄ vapor. Rotational constants were obtained for all the bands from which the following equilibrium constants were derived. Be^‘=0.52301±0.00008 cm⁻, αe^‘=0.00313±0.0006 cm⁻, re⁻=1.6391±0.0001 AHigher order constants, D_v and H_v, were calculated for the various vibrational levels.     

Correlator of the quark scalar currents and Γtot(H → hadrons) at O(αs) in pQCD

We present the results of the analytical evaluation of the massless four-loop

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(α³_s) correction to the correlator of the quark scalar currents and the Higgs decay rate into hadrons. In numerical form we found (in

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scheme) that Γ (H →

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b ) = (3G_F/4

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π) M_Hm²_b (M_H) [1 + 5.667α_s/π + (35.94 − 1.359n_f) (α_s/π)² + (164.139 − 25.771n_f + 0.259n²_f) (α_s/π)³] where n_f is the number of quark flavour and α_s = α_s(M_H).     

Water incorporation into the Ba2(In1 − xMx)2O5‪ (M = Sc 0 ≤ x < 0.5 and M = Y 0 ≤ x < 0.35) system and protonic conduction

Ba₂(In_1 − xM_x)₂O_{5 − y / 2}(OH)_y‪□_{1 − y / 2} (y ≤ 2; M = Sc³⁺ 0 ≤ x < 0.5 and M = Y³⁺ 0 ≤ x < 0.35) compounds were prepared by reacting Ba₂(In_1 − xM_x)₂O₅‪ phases with water vapor. This reaction is reversible. Analyses of the hydration process by TG and XRD studies show that the thermal stability of hydrated phases increases when x increases and that the incorporation of water is not a single-phase reaction inducing either a crystal system or space group modification. Fully hydrated (y = 2) and dehydrated (y = 0) samples have been stabilized at room temperature and characterized for all compositions. In wet air, all phases show a proton contribution to the total conductivity at temperatures between 350 and 600 °C. At a given temperature, proton conductivity increases with the substitution ratio and reaches at 350 °C, 5.4 10^− 3 S cm^− 1 for Ba₂(In_0.65Sc_0.35)₂O_4.2□_0.2(OH)_1.6.     

Carbon-13 and Fluorine-19 NMR Spectroscopy of the Supramolecular Solid p-tert-Butylcalix[4]arene ·α,α,α-trifluorotoluene

The supramolecular 1 : 1 host–guest inclusion compound, p-tert-butylcalix[4]arene ·α,α,α-trifluorotoluene, 1, is characterized by ¹⁹F and ¹³C solid-state NMR spectroscopy. Whereas the ¹³C NMR spectra are easily interpreted in the context of earlier work on similar host–guest compounds, the ¹⁹F NMR spectra of solid 1 are, initially, more difficult to understand. The ¹⁹F{¹H} NMR spectrum obtained under cross-polarization and magic-angle spinning conditions shows a single isotropic resonance with a significant spinning sideband manifold. The static ¹⁹F{¹H} CP NMR spectrum consists of a powder pattern dominated by the contributions of the anisotropic chemical shift and the homonuclear dipolar interactions. The ¹⁹F MREV-8 experiment, which minimizes the ¹⁹F–¹⁹F dipolar contribution, helps to identify the chemical shift contribution as an axial lineshape. The full static ¹⁹F{¹H} CP NMR spectrum is analysed using subspectral analysis and subsequently simulated as a function of the ¹⁹F–¹⁹F internuclear distance (D_FF = 2.25 ± 0.01 Å) of the rapidly rotating CF₃ group without including contributions from additional libration motions and the anisotropy in the scalar tensor. The shielding span is found to be 56 ppm. The width of the centerband in the ¹⁹F{¹H} sample-spinning CP NMR spectrum is very sensitive to the angle between the rotor and the magnetic field. Compound 1 is thus an attractive standard for setting the magic angle for NMR probes containing a fluorine channel with a proton-decoupling facility.