Kerr metric, static observers and Fermi coordinates

The coordinate transformation which maps the Kerr metric written in standard Boyer-Lindquist coordinates to its corresponding form adapted to the natural local coordinates of an observer at rest at a fixed position in the equatorial plane, i.e., Fermi coordinates for the neighborhood of a static observer world line, is derived and discussed in a way which extends to any uniformly circularly orbiting observer there.Comment: 15 page latex iopart class documen

The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges

We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular (plus some regular) points, which are then matched numerically with high accuracy. The expansions allow a fast and precise numerical calculation of the three master integrals (better than 15 digits with less than 30 terms in the whole real axis). A conspicuous relation with the equal-mass sunrise in two dimensions is found. Comparison with a previous large momentum expansion is made finding complete agreement.Comment: 42 pages, 1 figur

Spin precession in the Schwarzschild spacetime: circular orbits

We study the behavior of nonzero rest mass spinning test particles moving along circular orbits in the Schwarzschild spacetime in the case in which the components of the spin tensor are allowed to vary along the orbit, generalizing some previous work.Comment: To appear on Classical and Quantum Gravity, 200

Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies and extends most known work on hypersurface-homogeneous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, like Brans-Dicke or higher-dimensional theories.Comment: 41 pages, REVTEX/LaTeX 2.09 file (don't use LaTeX2e !!!) Accepted for publication in Phys. Rev.

Radiative corrections to W-boson hadroproduction: higher-order electroweak and supersymmetric effects

The high accuracy envisaged for future measurements of W-boson production at hadron colliders has to be matched by precise theoretical predictions. We study the impact of electroweak radiative corrections on W-boson production cross sections and differential distributions at the Tevatron and at the LHC. In particular, we include photon-induced processes, which contribute at O(alpha), and leading radiative corrections beyond O(alpha) in the high-energy Sudakov regime and from multi-photon final-state radiation. We furthermore present the calculation of the complete supersymmetric next-to-leading-order electroweak and QCD corrections to W-boson hadroproduction within the MSSM. The supersymmetric corrections turn out to be negligible in the vicinity of the W resonance in general, reaching the percent level only at high lepton transverse momentum and for specific choices of the supersymmetric parameters.Comment: 30 pages, 10 figures, 2 new sections, including a comparison with previous results on multi-photon radiation; version published in PR

The General Solution of Bianchi Type VIIhVII_h Vacuum Cosmology

The theory of symmetries of systems of coupled, ordinary differential equations (ODE) is used to develop a concise algorithm in order to obtain the entire space of solutions to vacuum Bianchi Einstein Field Equations (EFEs). The symmetries used are the well known automorphisms of the Lie algebra for the corresponding isometry group of each Bianchi Type, as well as the scaling and the time re-parametrization symmetry. The application of the method to Type VII_h results in (a) obtaining the general solution of Type VII_0 with the aid of the third Painlev\'{e} transcendental (b) obtaining the general solution of Type $VII_h$ with the aid of the sixth Painlev\'{e} transcendental (c) the recovery of all known solutions (six in total) without a prior assumption of any extra symmetry (d) The discovery of a new solution (the line element given in closed form) with a G_3 isometry group acting on T_3, i.e. on time-like hyper-surfaces, along with the emergence of the line element describing the flat vacuum Type VII_0 Bianchi Cosmology.Comment: latex2e source file, 27 pages, 2 tables, no fiure

Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC

Previous work on electroweak radiative corrections to high energy scattering using soft-collinear effective theory (SCET) has been extended to include external transverse and longitudinal gauge bosons and Higgs bosons. This allows one to compute radiative corrections to all parton-level hard scattering amplitudes in the standard model to NLL order, including QCD and electroweak radiative corrections, mass effects, and Higgs exchange corrections, if the high-scale matching, which is suppressed by two orders in the log counting, and contains no large logs, is known. The factorization structure of the effective theory places strong constraints on the form of gauge theory amplitudes at high energy for massless and massive gauge theories, which are discussed in detail in the paper. The radiative corrections can be written as the sum of process-independent one-particle collinear functions, and a universal soft function. We give plots for the radiative corrections to q qbar -> W_T W_T, Z_T Z_T, W_L W_L, and Z_L H, and gg -> W_T W_T to illustrate our results. The purely electroweak corrections are large, ranging from 12% at 500 GeV to 37% at 2 TeV for transverse W pair production, and increasing rapidly with energy. The estimated theoretical uncertainty to the partonic (hard) cross-section in most cases is below one percent, smaller than uncertainties in the parton distribution functions (PDFs). We discuss the relation between SCET and other factorization methods, and derive the Magnea-Sterman equations for the Sudakov form factor using SCET, for massless and massive gauge theories, and for light and heavy external particles.Comment: 44 pages, 30 figures. Refs added, typos fixed. ZL ZL plots removed because of a possible subtlet

EVALUATION OF THE IMPACT OF THE DEFENSE WASTE PROCESSING FACILITY (DWPF) LABORATORY GERMANIUM OXIDE USE ON RECYCLE TRANSFERS TO THE H-TANK FARM

When processing High Level Waste (HLW) glass, the Defense Waste Processing Facility (DWPF) cannot wait until the melt or waste glass has been made to assess its acceptability, since by then no further changes to the glass composition and acceptability are possible. Therefore, the acceptability decision is made on the upstream feed stream, rather than on the downstream melt or glass product. This strategy is known as 'feed forward statistical process control.' The DWPF depends on chemical analysis of the feed streams from the Sludge Receipt and Adjustment Tank (SRAT) and the Slurry Mix Evaporator (SME) where the frit plus adjusted sludge from the SRAT are mixed. The SME is the last vessel in which any chemical adjustments or frit additions can be made. Once the analyses of the SME product are deemed acceptable, the SME product is transferred to the Melter Feed Tank (MFT) and onto the melter. The SRAT and SME analyses have been analyzed by the DWPF laboratory using a 'Cold Chemical' method but this dissolution did not adequately dissolve all the elemental components. A new dissolution method which fuses the SRAT or SME product with cesium nitrate (CsNO{sub 3}), germanium (IV) oxide (GeO{sub 2}) and cesium carbonate (Cs{sub 2}CO{sub 3}) into a cesium germanate glass at 1050 C in platinum crucibles has been developed. Once the germanium glass is formed in that fusion, it is readily dissolved by concentrated nitric acid (about 1M) to solubilize all the elements in the SRAT and/or SME product for elemental analysis. When the chemical analyses are completed the acidic cesium-germanate solution is transferred from the DWPF analytic laboratory to the Recycle Collection Tank (RCT) where the pH is increased to {approx}12 M to be released back to the tank farm and the 2H evaporator. Therefore, about 2.5 kg/yr of GeO{sub 2}/year will be diluted into 1.4 million gallons of recycle. This 2.5 kg/yr of GeO{sub 2} may increase to 4 kg/yr when improvements are implemented to attain an annual canister production goal of 400 canisters. Since no Waste Acceptance Criteria (WAC) exists for germanium in the Tank Farm, the Effluent Treatment Project, or the Saltstone Production Facility, DWPF has requested an evaluation of the fate of the germanium in the caustic environment of the RCT, the 2H evaporator, and the tank farm. This report evaluates the effect of the addition of germanium to the tank farm based on: (1) the large dilution of Ge in the RCT and tank farm; (2) the solubility of germanium in caustic solutions (pH 12-13); (3) the potential of germanium to precipitate as germanium sodalites in the 2H Evaporator; and (4) the potential of germanium compounds to precipitate in the evaporator feed tank. This study concludes that the impacts of transferring up to 4 kg/yr germanium to the RCT (and subsequently the 2H evaporator feed tank and the 2H evaporator) results in <2 ppm per year (1.834 mg/L) which is the maximum instantaneous concentration expected from DWPF. This concentration is insignificant as most sodium germanates are soluble at the high pH of the feed tank and evaporator solutions. Even if sodium aluminosilicates form in the 2H evaporator, the Ge will likely substitute for some small amount of the Si in these structures and will be insignificant. It is recommended that the DWPF continue with their strategy to add germanium as a laboratory chemical to Attachment 8.2 of the DWPF Waste Compliance Plan (WCP)

Role of Manganese Reduction/Oxidation (REDOX) on Foaming and Melt Rate in High Level Waste (HLW) Melters (U)

High-level nuclear waste is being immobilized at the Savannah River Site (SRS) by vitrification into borosilicate glass at the Defense Waste Processing Facility (DWPF). Control of the Reduction/Oxidation (REDOX) equilibrium in the DWPF melter is critical for processing high level liquid wastes. Foaming, cold cap roll-overs, and off-gas surges all have an impact on pouring and melt rate during processing of high-level waste (HLW) glass. All of these phenomena can impact waste throughput and attainment in Joule heated melters such as the DWPF. These phenomena are caused by gas-glass disequilibrium when components in the melter feeds convert to glass and liberate gases such as H{sub 2}O vapor (steam), CO{sub 2}, O{sub 2}, H{sub 2}, NO{sub x}, and/or N{sub 2}. During the feed-to-glass conversion in the DWPF melter, multiple types of reactions occur in the cold cap and in the melt pool that release gaseous products. The various gaseous products can cause foaming at the melt pool surface. Foaming should be avoided as much as possible because an insulative layer of foam on the melt surface retards heat transfer to the cold cap and results in low melt rates. Uncontrolled foaming can also result in a blockage of critical melter or melter off-gas components. Foaming can also increase the potential for melter pressure surges, which would then make it difficult to maintain a constant pressure differential between the DWPF melter and the pour spout. Pressure surges can cause erratic pour streams and possible pluggage of the bellows as well. For these reasons, the DWPF uses a REDOX strategy and controls the melt REDOX between 0.09 {le} Fe{sup 2+}/{summation}Fe {le} 0.33. Controlling the DWPF melter at an equilibrium of Fe{sup +2}/{summation}Fe {le} 0.33 prevents metallic and sulfide rich species from forming nodules that can accumulate on the floor of the melter. Control of foaming, due to deoxygenation of manganic species, is achieved by converting oxidized MnO{sub 2} or Mn{sub 2}O{sub 3} species to MnO during melter preprocessing. At the lower redox limit of Fe{sup +2}/{summation}Fe {approx} 0.09 about 99% of the Mn{sup +4}/Mn{sup +3} is converted to Mn{sup +2}. Therefore, the lower REDOX limits eliminates melter foaming from deoxygenation

Restricted infinitesimal deformations of restricted simple Lie algebras

We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic different from 2 and 3.Comment: 15 pages; final version, to appear in Journal of Algebra and Its Application