A RESEARCH AND DEVELOPMENT PROGRAM TO CONTINUE THE DEVELOPMENT OF PRECISION INSTRUMENTATION FOR THE STUDY OF MUONS IN THE TeV REGION

title: Search for flavor-changing non-standard neutrino interactions by MINOS
abstract: We report new constraints on flavor-changing non-standard neutrino interactions from the MINOS experiment, in which neutrino versus antineutrino interactions can be distinguished on an event-by-event basis. We analyzed a combined set of beam neutrino and antineutrino data from the well-understood NuMI beam, and found no evidence for deviations from standard neutrino mixing. The observed energy spectra constrain the non-standard neutrino interactions parameter to the range −0.20

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: The MINOS scintillator calorimeter system
abstract: The MINOS detectors will use extruded plastic scintillator strips, which are readout by wavelength-shifting fibres coupled to multi-pixel photodetectors. This technique provides excellent energy and spatial resolution. The MINOS detectors are described in detail along with results from the light output tests.

title: Ultrahigh energy cosmic ray composition from surface air shower and underground muon measurements at Soudan 2.
abstract: The Soudan 2 experiment has performed time-coincident cosmic ray air shower and underground muon measurements. Comparisons to Monte Carlo predictions show that such measurements can make statistically significant tests of the primary composition in the knee region of the cosmic ray spectrum. The results do not support any significant increase in the average primary mass with energy in the range of {similar_to}10{sup 4} TeV per nucleus. Some systematic uncertainties remain, however, particularly in the Monte Carlo modeling of the cosmic ray shower.

title: Search for magnetic monopoles with the Soudan 2 detector.
abstract: A search for grand unified theory magnetic monopoles making highly ionizing tracks in argon gas has been conducted using the Soudan 2 nucleon decay detector. This underground detector is a large fine-grained tracking calorimeter comprised of long drift tubes read out by proportional wires. No monopole candidates were observed in data taken over almost three years, yielding an upper flux limit of 8.7{times}10{sup {minus}15} cm{sup {minus}2}s{sup {minus}1}sr{sup {minus}1} for monopole velocities of .

title: Matrix operator symmetries of the Dirac equation and separation of variables
abstract: The set of all matrix‐valued first‐order differential operators that commute with the Dirac equation in n‐dimensional complex Euclidean space is computed. In four dimensions it is shown that all matrix‐valued second‐order differential operators that commute with the Dirac operator in four dimensions are obtained as products of first‐order operators that commute with the Dirac operator. Finally some additional coordinate systems for which the Dirac equation in Minkowski space can be solved by separation of variables are presented. These new systems are comparable to the separation in oblate spheroidal coordinates discussed by Chandrasekhar [S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford U.P., Oxford, 1983)].

title: CLEBSCH--GORDAN COEFFICIENTS AND SPECIAL FUNCTION IDENTITIES. II. THE ROTATION AND LORENTZ GROUPS IN 3-SPACE.
abstract: It is shown that the construction of concrete models of Clebsch‐Gordan decompositions for tensor products of irreducible group representations leads to a wide variety of special function identities. In this paper the representation theory of the rotation and Lorentz groups in 3‐space is used to give elegant derivations of identities involving Languerre, Gegenbauer, hypergeometric, and generalized hypergeometric functions. Some of these identities may be new in this general form.

title: Coulomb-oscillator duality in spaces of constant curvature
abstract: In this paper we construct generalizations to spheres of the well-known Levi-Civita, Kustaanheimo–Steifel, and Hurwitz regularizing transformations in Euclidean spaces of dimensions two, three, and five. The corresponding classical and quantum mechanical analogs of the Kepler–Coulomb problem on these spheres are discussed.

title: Lie theory and the wave equation in space–time. 3. Semisubgroup coordinates
abstract: We classify and study those coordinate systems which permit R separation of variables for the wave equation in four‐dimensional space–time and such that at least one of the variables corresponds to a one‐parameter symmetry group of the wave equation. We discuss over 100 such systems and relate them to orbits of triplets of commuting operators in the enveloping algebra of the conformal group SO(4,2).

title: Lie theory and the wave equation in space-time. 4. The Klein-Gordon equation and the Poincaré group
abstract: 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.