Nucleon structure functions from ν_µ-Fe interactions and a study of the valence quark distribution

Data were taken in 1979-80 by the CCFRR high energy neutrino experiment at Fermilab. A total of 150,000 neutrino and 23,000 antineutrino charged current events in the approximate energy range 25 < E_v < 250GeV are measured and analyzed. The structure functions F2 and xF_3 are extracted for three assumptions about σ_L/σ_T:R=0., R=0.1 and R= a QCD based expression. Systematic errors are estimated and their significance is discussed. Comparisons or the X and Q^2 behaviour or the structure functions with results from other experiments are made.

We find that statistical errors currently dominate our knowledge of the valence quark distribution, which is studied in this thesis. xF_3 from different experiments has, within errors and apart from level differences, the same dependence on x and Q^2, except for the HPWF results. The CDHS F_2 shows a clear fall-off at low-x from the CCFRR and EMC results, again apart from level differences which are calculable from cross-sections.

The result for the the GLS rule is found to be 2.83±.15±.09±.10 where the first error is statistical, the second is an overall level error and the third covers the rest of the systematic errors. QCD studies of xF_3 to leading and second order have been done. The QCD evolution of xF_3, which is independent of R and the strange sea, does not depend on the gluon distribution and fits yield

ʌ_(LO) = 88^(+163)_(-78) ^(+113)_(-70) MeV

The systematic errors are smaller than the statistical errors. Second order fits give somewhat different values of ʌ, although α_s (at Q^2_0 = 12.6 GeV^2) is not so different.

A fit using the better determined F_2 in place of xF_3 for x > 0.4 i.e., assuming q = 0 in that region, gives

ʌ_(LO) = 266^(+114)_(-104) ^(+85)_(-79) MeV

Again, the statistical errors are larger than the systematic errors. An attempt to measure R was made and the measurements are described. Utilizing the inequality q(x)≥0 we find that in the region x > .4 R is less than 0.55 at the 90% confidence level.

Iso-specific Ziegler-Natta polymerization of α-olefins with a single-component organoyttrium catalyst

The synthesis of a sterically tailored ligand array (M)_2((C_5H_2-2-Si(CH_3)_3-4-C(CH_3)_3)S_2i(CH_3)_2]("M_2Bp") (M = Li, 16; K, 19) is described. Transmetallation of Li_2Bp with YCl_3(THF)_3 affords exclusively the C_2 symmetric product rac-[BpY(µ_2-Cl)_2Li(THF)_2], 20. A X-ray crystal structure of 20 has been determined; triclinic, P1, a= 13.110 (8), b = 17.163 (15), c = 20.623 (14) Å, α = 104.02 (7), β = 99.38 (5), γ = 100.24 (6)° , Z = 4, R = 0.056. Transmetallation of K_2Bp with YCl_3(THF)_3 affords the halide free complex rac-BpYCl, 23. The corresponding rac-BpLaCl, 28, is prepared in an anlogous manner. In all cases the achiral meso isomer is not obtained since only for the racemic isomers are the unfavorable steric interactions between the Si(CH3)_3 groups in the narrow portion of the [Cp-M'-Cp] wedge avoided. Alkylation of 20 or 23 with LiCH(Si(CH_3)_3)_2 affords rac-BpYCH(Si(CH_3)_3)_2, 26 in good yield. Alkylation of 28 with LiCH(Si(CH_3)_3)_2 affords rac-BpLaCH(Si(CH_3)_3)_2 29. Hydrogenation of 26 cleanly affords the bridging hydride species [BpY(µ_2-H)]_2, 27, as the homochiral (R,R) and (S,S) dimeric pairs. 26 is an efficient initiator for the polymerization of ethylene to high molecular weight linear polyethylene. 27 catalyzes the polymerization of propylene (25% v/v in methylcyclohexane) and neat samples of 1-butene, 1-pentene, 1-hexene to moderately high molecular weight polymers: polypropylene (M_n = 4,200, PDI 2.32, T_m 157 °C); poly-1-butene (M_n = 8,500, PDI 3.44, T_m 105 °C); poly-1-pentene (M_n = 20,000, PDI 1.99, T_m 73 °C); poly-1-hexene (M_n = 24,000, PDI 1.75, T_m < 25 °C). ^(13)C NMR spectra at the pentad analysis level indicates that the degree of isotacticity is 99% mmmm for all polymer samples. 27 is the first single component iso-specific α-olefin polymerization catalyst. The presumed origins of the high isospecificity are presented.

Reactivity of titanocene methylidene with metal halides, alkene sulfides, and alkene oxides

Titanocene metallacyclobutanes show a wide variety of reactivites with organic and inorganic reagents. Their reactions include methylene transfer to organic carbonyls, formation of enolates, electron transfer from activated alkyl chlorides, olefin metathesis, ring opening polymerization. Recently, preparations of heterobinuclear µ-methylene complexes were reported. In this thesis, mechanistic, synthetic, and structural studies of the heterobinuclear µ-methylene complexes will be described. Also, the reaction of titanocene methylidene trimethylphosphine complex with alkene sulfide and styrene sulfide will be presented.

Heterobinuclear µ-methylene-µ-methyl complexes C_(p2)Ti(µ-CH_2)( µ-CH_3)M(1,5-COD) have been prepared (M = Rh, Ir). X-ray crystallography showed that the methyl group of the complex was bonded to the rhodium and bridges to the titanium through an agostic bond. The ^(1)H,^(13)CNMR, IR spectra along with partial deuteration studies supported the structure in both solution and solid state. Activation of the agostic bond is demonstrated by the equilibration of the µ-CH_3 and µ-CH_2 groups. A nonlinear Arrhenius plot, an unusually large kinetic isotope effect (24(5)), and a large negative activation entropy (-64(3)eu) can be explained by the quantum-mechanical tunneling. Calculated rate constants with Bell-type barrier fitted well with the observed one. This equilibration was best explained by a 4e-4c mechanism (or σ bond metathesis) with the character of quantum-mechanical tunneling.

Heterobinuclear µ-methylene-µ-phenyl complexes were synthesized. Structural study of C_(p2)Ti(µ-CH_(2))(µ-p-Me_(2)NC_(6)H_(4))Rh(l,5-COD) showed that the two metal atoms are bridged by the methylene carbon and the ipso carbon of the p-N,N-dimethylarninophenyl group. The analogous structure of C_(p2))Ti(µ-CH_(2))(µ-o-MeOC_(6)H_(4))Rh(1,5-COD) has been verified by the differential NOE. The aromaticity of the phenyl group observed by ^(1)H NMR, was confirmed by the comparison of the C-C bond lengths in the crystallographic structure. The unusual downfield shifts of the ipso carbon in the ^(13)C NMR are assumed to be an indication of the interaction between the ipso carbon and electron-deficient titanium.

Titanium-platinum heterobinuclear µ-methylene complexes C_(p2)Ti(µ-CH_(2))(µ -X)Pt(Me)(PM_(2)Ph) have been prepared (X= Cl, Me). Structural studies indicate the following:(1) the Ti-CH2 bond possesses residual double bond character, (2) there is a dative Pt→Ti interaction which may be regarded as a π back donation from the platinum atom to the 'Ti=CH_(2)'' group, and (3) the µ-CH_3 group is bound to the titanium atom through a three-center, two-electron agostic bond.

Titanocene (η^(2)-thioformaldehyde)•PMe_3 was prepared from C_(p2)Ti=CH_(2)•PMe_3 and sulfur-containing organic compounds (e.g. alkene sulfide, triphenylphosphine sulfide) including elemental sulfur. Mechanistic studies utilizing trans-styrene sulfide-d_1 suggested the stepwise reaction to explain equimolar mixture of trans- and cis-styrene-d_1 as by-products. The product reacted with methyl iodide to produce cationic titanocene (η_(2)-thiomethoxymethyl) complex. Complexes having less coordinating anion like BF_4 or BPh_4 could be obtained through metathesis. Together with structural analyses, the further reactivities of the complexes have been explored.

The complex C_(p2)TiOCH_(2)CH(Ph)CH_2 was prepared from the compound C_(p2)Ti=CH_(2)-PMe_3 and styrene oxide. The product was characterized with ^(1)H-^(1)H correlated 2-dimensional NMR, selective decoupling of ^(1)H NMR, and differential NOE. Stereospecificity of deuterium in the product was lost when trans-styrene oxide-d_1 was allowed to react. Relative rates of the reaction were measured with varying substituents on the phenyl ring. Better linearity (r = -0.98, p^(+) = -0.79) was observed with σ_(p)^(+)than σ(r = -0.87, p = -1.26). The small magnitude of p^+ value and stereospecificity loss during the formation of product were best explained by the generation of biradicals, but partial generation of charge cannot be excluded. Carbonylation of the product followed by exposure to iodine yields the corresponding β-phenyl γ-lactone.

Testing inflationary cosmology with the BICEP1 and BICEP2 experiments

Recent observations of the temperature anisotropies of the cosmic microwave background (CMB) favor an inflationary paradigm in which the scale factor of the universe inflated by many orders of magnitude at some very early time. Such a scenario would produce the observed large-scale isotropy and homogeneity of the universe, as well as the scale-invariant perturbations responsible for the observed (10 parts per million) anisotropies in the CMB. An inflationary epoch is also theorized to produce a background of gravitational waves (or tensor perturbations), the effects of which can be observed in the polarization of the CMB. The E-mode (or parity even) polarization of the CMB, which is produced by scalar perturbations, has now been measured with high significance. Con- trastingly, today the B-mode (or parity odd) polarization, which is sourced by tensor perturbations, has yet to be observed. A detection of the B-mode polarization of the CMB would provide strong evidence for an inflationary epoch early in the universe’s history.

In this work, we explore experimental techniques and analysis methods used to probe the B- mode polarization of the CMB. These experimental techniques have been used to build the Bicep2 telescope, which was deployed to the South Pole in 2009. After three years of observations, Bicep2 has acquired one of the deepest observations of the degree-scale polarization of the CMB to date. Similarly, this work describes analysis methods developed for the Bicep1 three-year data analysis, which includes the full data set acquired by Bicep1. This analysis has produced the tightest constraint on the B-mode polarization of the CMB to date, corresponding to a tensor-to-scalar ratio estimate of r = 0.04±0.32, or a Bayesian 95% credible interval of r < 0.70. These analysis methods, in addition to producing this new constraint, are directly applicable to future analyses of Bicep2 data. Taken together, the experimental techniques and analysis methods described herein promise to open a new observational window into the inflationary epoch and the initial conditions of our universe.

Characterization of detectors and instrument systematics for the SPIDER CMB polarimeter

We know from the CMB and observations of large-scale structure that the universe is extremely flat, homogenous, and isotropic. The current favored mechanism for generating these characteristics is inflation, a theorized period of exponential expansion of the universe that occurred shortly after the Big Bang. Most theories of inflation generically predict a background of stochastic gravitational waves. These gravitational waves should leave their unique imprint on the polarization of the CMB via Thompson scattering. Scalar perturbations of the metric will cause a pattern of polarization with no curl (E-mode). Tensor perturbations (gravitational waves) will cause a unique pattern of polarization on the CMB that includes a curl component (B-mode). A measurement of the ratio of the tensor to scalar perturbations (r) tells us the energy scale of inflation. Recent measurements by the BICEP2 team detect the B-mode spectrum with a tensor-to-scalar ratio of r = 0.2 (+0.05, −0.07). An independent confirmation of this result is the next step towards understanding the inflationary universe.

This thesis describes my work on a balloon-borne polarimeter called SPIDER, which is designed to illuminate the physics of the early universe through measurements of the cosmic microwave background polarization. SPIDER consists of six single-frequency, on-axis refracting telescopes contained in a shared-vacuum liquid-helium cryostat. Its large format arrays of millimeter-wave detectors and tight control of systematics will give it unprecedented sensitivity. This thesis describes how the SPIDER detectors are characterized and calibrated for flight, as well as how the systematics requirements for the SPIDER system are simulated and measured.

Measurement of the Polarization of the Cosmic Microwave Background with the BICEP2 and Keck Array Telescopes

Precision polarimetry of the cosmic microwave background (CMB) has become a mainstay of observational cosmology. The ΛCDM model predicts a polarization of the CMB at the level of a few μK, with a characteristic E-mode pattern. On small angular scales, a B-mode pattern arises from the gravitational lensing of E-mode power by the large scale structure of the universe. Inflationary gravitational waves (IGW) may be a source of B-mode power on large angular scales, and their relative contribution to primordial fluctuations is parameterized by a tensor-to-scalar ratio r. BICEP2 and Keck Array are a pair of CMB polarimeters at the South Pole designed and built for optimal sensitivity to the primordial B-mode peak around multipole l ~ 100. The BICEP2/Keck Array program intends to achieve a sensitivity to r ≥ 0.02. Auxiliary science goals include the study of gravitational lensing of E-mode into B-mode signal at medium angular scales and a high precision survey of Galactic polarization. These goals require low noise and tight control of systematics. We describe the design and calibration of the instrument. We also describe the analysis of the first three years of science data. BICEP2 observes a significant B-mode signal at 150 GHz in excess of the level predicted by the lensed-ΛCDM model, and Keck Array confirms the excess signal at > 5σ. We combine the maps from the two experiments to produce 150 GHz Q and U maps which have a depth of 57 nK deg (3.4 μK arcmin) over an effective area of 400 deg² for an equivalent survey weight of 248000 μK². We also show preliminary Keck Array 95 GHz maps. A joint analysis with the Planck collaboration reveals that much of BICEP2/Keck Array's observed 150 GHz signal at low l is more likely a Galactic dust foreground than a measurement of r. Marginalizing over dust and r, lensing B-modes are detected at 7.0σ significance.

Locally convex Riesz spaces and Archimedean quotient spaces

A Riesz space with a Hausdorff, locally convex topology determined by Riesz seminorms is called a locally convex Riesz space. A sequence {x_n} in a locally convex Riesz space L is said to converge locally to x ϵ L if for some topologically bounded set B and every real r ˃ 0 there exists N (r) and n ≥ N (r) implies x – x_n ϵ r^b. Local Cauchy sequences are defined analogously, and L is said to be locally complete if every local Cauchy sequence converges locally. Then L is locally complete if and only if every monotone local Cauchy sequence has a least upper bound. This is a somewhat more general form of the completeness criterion for Riesz – normed Riesz spaces given by Luxemburg and Zaanen. Locally complete, bound, locally convex Riesz spaces are barrelled. If the space is metrizable, local completeness and topological completeness are equivalent.

Two measures of the non-archimedean character of a non-archimedean Riesz space L are the smallest ideal A_o (L) such that quotient space is Archimedean and the ideal I (L) = { x ϵ L: for some 0 ≤ v ϵ L, n |x| ≤ v for n = 1, 2, …}. In general A_o (L) ᴝ I (L). If L is itself a quotient space, a necessary and sufficient condition that A_o (L) = I (L) is given. There is an example where A_o (L) ≠ I (L).

A necessary and sufficient condition that a Riesz space L have every quotient space Archimedean is that for every 0 ≤ u, v ϵ L there exist u₁ = sup (inf (n v, u): n = 1, 2, …), and real numbers m₁ and m₂ such that m₁ u₁ ≥ v₁ and m₂ v₁ ≥ u₁. If, in addition, L is Dedekind σ – complete, then L may be represented as the space of all functions which vanish off finite subsets of some non-empty set.