Lie theory and the wave equation in space-time. 4. The Klein-Gordon equation and the Poincaré group
A detailed classification is made of all orthogonal coordinate systems for which the Klein–Gordon equation in space–time, ψtt−Δ3ψ=λψ, admits a separation of variables. We show that the Klein–Gordon equation is separable in 261 orthogonal coordinate systems. In each case the coordinate systems presented are characterized in terms of three symmetric second order commuting operators in the enveloping algebra of the Poincare group. This paper also consitutes an important step in the study of separation of variables for the wave equation in space–time ψtt−Δ3ψ=0, and its relation to the underlying conformal symmetry group O(4,2) of this equation.

title: Superintegrability on the two-dimensional hyperboloid. II
abstract: In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras.

title: Separation of variables in Einstein spaces. I. Two ignorable and one null coordinate
abstract: Computes and classifies all Einstein spaces and their corresponding coordinate systems such that the Hamilton-Jacobi equation admits a separation of variables with two ignorable and one essential null coordinates. The authors find that all such spaces correspond to plane-fronted gravitational waves of Petrov type N. They also give necessary conditions which a general space-time must have in order to admit coordinates of the type studied. Furthermore, the integrability conditions for Helmholtz (Schrodinger) separability are completely solved.

title: Lie theory and separation of variables. 11. The EPD equation
abstract: We show that the Euler–Poisson–Darboux equation {∂tt−∂rr−[(2m+1)/r]∂r}Θ=0 separates in exactly nine coordinate systems corresponding to nine orbits of symmetric second‐order operators in the enveloping algebra of SL(2,R), the symmetry group of this equation. We employ techniques developed in earlier papers from this series and use the representation theory of SL(2,R) to derive special function identities relating the separated solutions. We also show that the complex EPD equation separates in exactly five coordinate systems corresponding to five orbits of symmetric second‐order operators in the enveloping algebra of SL(2,C).

title: Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials
abstract: As a continuation of Paper 6 we study the separable basis eigenfunctions and their relationships for the harmonic oscillator Hamiltonian in two space variables with special emphasis on products of Ince polynomials, the eigenfunctions obtained when one separates variables in elliptic coordinates. The overlaps connecting this basis to the polar and Cartesian coordinate bases are obtained by computing in a simpler Bargmann Hilbert space model of the problem. We also show that Ince polynomials are intimately connected with the representation theory of SU (2), the group responsible for the eigenvalue degeneracy of the oscillator Hamiltonian.

title: Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)
abstract: We consider the ``missing label'' problem for basis vectors of SU(3) representations in a basis corresponding to the group reduction SU(3)⊃O(3)⊃O(2). We prove that only two independent O (3) scalars exist in the enveloping algebra of S U (3), in addition to the obvious ones, namely the angular momentum L2 and the two SU(3) Casimir operators C(2) and C(3). Any one of these two operators (of third and fourth order in the generators) can be added to C(2), C(3), L2, and L3 to form a complete set of commuting operators. The eigenvalues of the third and fourth order scalars X(3) and X(4) are calculated analytically or numerically for many cases of physical interest. The methods developed in this article can be used to resolve a missing label problem for any semisimple group G, when reduced to any semisimple subgroup H.

title: Improved measurement of muon antineutrino disappearance in MINOS.
abstract: We report an improved measurement of ν(μ) disappearance over a distance of 735 km using the MINOS detectors and the Fermilab Main Injector neutrino beam in a ν(μ)-enhanced configuration. From a total exposure of 2.95×10(20) protons on target, of which 42% have not been previously analyzed, we make the most precise measurement of Δm2=[2.62(-0.28)(+0.31)(stat)±0.09(syst)]×10(-3)  eV2 and constrain the ν(μ) mixing angle sin2(2θ)>0.75 (90% C.L.). These values are in agreement with Δm2 and sin2(2θ) measured for ν(μ), removing the tension reported in [P. Adamson et al. (MINOS),  (2011).].

title: Development of Large Area Integrated Silicon Tracking Elements for the LHC Luminosity Upgrade
abstract: A natural upgrade of the CERN LHC would be to increase the luminosity to 1035 cm-2s-1. For charged particle tracking at this Super-LHC, all-silicon systems are considered appropriate. For tracking in an upgraded ATLAS detector, outside a radius of 20 cm, large area integrated elements ("staves") containing silicon strip detectors are under design and development. Each stave would hold of order 30 individual modules and contain integrated electrical services, mechanical support, and cooling. Prototype tests of such staves are reported here including studies of noise, interference, and a comparison of power distribution by parallel and serial current flow. Mechanical design and simulation on full length staves are presented as well.

title: The Cleo III silicon vertex detector
abstract: The CLEO collaboration has embarked on an ambitious upgrade of the CLEO detector to match the upgrade of the CESR accelerator to luminosities of 2 × 10 33 cm −2 sec −1 . This will bring a factor ten improvement in the measurement of rare B decays and hence, increased sensitivity to physics at high mass scales and also the possibility of measuring CP violation. The upgrade includes a new four layer double-sided silicon detector. Each double-sided silicon wafer is 2.6 cmx 5.1 cm × 300 μ m . To maximize solid angle coverage with minimal material in the detector volume the detector chains are very long, up to 5 detectors per electronic readout channel, resulting in large series resistance and large detector capacitance. Moderate backgrounds permit the electronics to operate with a 1–3 μ s shaping time. A new front-end low noise preamplifier is being developed to maximize the signal to noise ratio, along with a modified SVX chip used for analog to digital conversion and sparsification. The detectors are connected to the electronics hybrid by a thin double sided kapton flex circuit. The length of the detector chains also requires novel mechanical support structures — CVD diamond beams axe the baseline solution. We are currently near the end of the prototype stage for all aspects for the project and will move into production by late summer. The detector will be installed in early 1998.

title: Testing Lorentz invariance and CPT conservation with NuMI neutrinos in the MINOS near detector.
abstract: A search for a sidereal modulation in the MINOS near detector neutrino data was performed. If present, this signature could be a consequence of Lorentz and CPT violation as predicted by the effective field theory called the standard-model extension. No evidence for a sidereal signal in the data set was found, implying that there is no significant change in neutrino propagation that depends on the direction of the neutrino beam in a sun-centered inertial frame. Upper limits on the magnitudes of the Lorentz and CPT violating terms in the standard-model extension lie between 10(-4) and 10(-2) of the maximum expected, assuming a suppression of these signatures by a factor of 10(-17).

title: Search for sterile neutrino mixing in the MINOS long-baseline experiment
abstract: A search for depletion of the combined flux of active neutrino species over a 735 km baseline is reported using neutral-current interaction data recorded by the MINOS detectors in the NuMI neutrino beam. Such a depletion is not expected according to conventional interpretations of neutrino oscillation data involving the three known neutrino flavors. A depletion would be a signature of oscillations or decay to postulated noninteracting sterile neutrinos, scenarios not ruled out by existing data. From an exposure of 3.18×10^(20) protons on target in which neutrinos of energies between ∼500  MeV and 120 GeV are produced predominantly as ν_μ, the visible energy spectrum of candidate neutral-current reactions in the MINOS far detector is reconstructed. Comparison of this spectrum to that inferred from a similarly selected near-detector sample shows that of the portion of the ν_μ flux observed to disappear in charged-current interaction data, the fraction that could be converting to a sterile state is less than 52% at 90% confidence level (C.L.). The hypothesis that active neutrinos mix with a single sterile neutrino via oscillations is tested by fitting the data to various models. In the particular four-neutrino models considered, the mixing angles θ_(24) and ) are constrained to be less than 11° and 56° at 90% C.L., respectively. The possibility that active neutrinos may decay to sterile neutrinos is also investigated. Pure neutrino decay without oscillations is ruled out at 5.4 standard deviations. For the scenario in which active neutrinos decay into sterile states concurrently with neutrino oscillations, a lower limit is established for the neutrino decay lifetime τ_3/m_3>2.1×10^(-12) s/eV at 90% C.L.