120152328
Lie theory and separation of variables. 11. The EPD equation
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).
55017968
Series solutions for the Dirac equation in Kerr-Newman space-time
The Dirac equation is solved for an electron in a Kerr–Newman geometry using an adaptation of the procedure of Chandrasekhar. The corresponding eigenfunctions obtained can be represented as series of Jacobi polynomials. The spectrum of eigenvalues can be calculated using continued fraction techniques. Representations for the eigenvalues and eigenfunctions are obtained for various ranges of the parameters appearing in the Kerr–Newman metric. Some comments concerning the bag model of nucleons are made.
17212560
Superintegrability on the two-dimensional hyperboloid. II
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.
119430316
Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)
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.
120717466
Matrix operator symmetries of the Dirac equation and separation of variables
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)].
122430224
Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials
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.
7735148
Improved measurement of muon antineutrino disappearance in MINOS.
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), Phys. Rev. Lett. 107, 021801 (2011).].
1159458
Study of quasielastic scattering using charged-current νμ -iron interactions in the MINOS near detector
Kinematic distributions from an inclusive sample of 1.41×10^6 charged-current ν_μ interactions on iron, obtained using the MINOS near detector exposed to a wide-band beam with peak flux at 3 GeV, are compared to a conventional treatment of neutrino scattering within a Fermi gas nucleus. Results are used to guide the selection of a subsample enriched in quasielastic ν_μFe interactions, containing an estimated 123,000 quasielastic events of incident energies 1<E_ν<8  GeV, with ⟨E_ν⟩=2.79  GeV. Four additional subsamples representing topological and kinematic sideband regions to quasielastic scattering are also selected for the purpose of evaluating backgrounds. Comparisons using subsample distributions in four-momentum transfer Q^2 show the Monte Carlo model to be inadequate at low Q^2. Its shortcomings are remedied via inclusion of a Q^2-dependent suppression function for baryon resonance production, developed from the data. A chi-square fit of the resulting Monte Carlo simulation to the shape of the Q^2 distribution for the quasielastic-enriched sample is carried out with the axial-vector mass M_A of the dipole axial-vector form factor of the neutron as a free parameter. The effective M_A which best describes the data is 1.23^(+0.13)_(−0.09)(fit)^(+0.12)_(−0.15)(syst)  GeV.
119270975
The 2010 Interim Report of the Long-Baseline Neutrino Experiment Collaboration Physics Working Groups
In early 2010, the Long-Baseline Neutrino Experiment (LBNE) science collaboration initiated a study to investigate the physics potential of the experiment with a broad set of different beam, nearand far-detector configurations. Nine initial topics were identified as scientific areas that motivate construction of a long-baseline neutrino experiment with a very large far detector. We summarize the scientific justification for each topic and the estimated performance for a set of far detector reference configurations. We report also on a study of optimized beam parameters and the physics capability of proposed Near Detector configurations. This document was presented to the collaboration in fall 2010 and updated with minor modifications in early 2011. PACS numbers: 14.60.Lm, 14.60.Pq, 95.85.Ry, 13.15+g, 13.30.Ce, 11.30.Fs, 14.20.Dh, 26.65.+t, 25.30.Pt, 29.40.Ka, 29.40.Gx ∗ Corresponding author: bob.wilson@colostate.edu
118469809
Underground muons observed in the Soudan 2 detector from the directions of x-ray sources
We report on observations of underground muons made with the Soudan 2 proton decay detector at a depth of 2090 mwe from the directions of the binaries Hercules X-1 and 1E2259+586 and the Crab pulsar.
122216729
Underground Muons from the Direction of Cygnus X-3 during the January 1991 Radio Flare
Abstract Muons recorded in the Soudan 2 underground nucleon decay detector from January 1989 to February 1991 have been examined for any correlation with the radio flares of Cygnus X-3 observed during this period. On two nearby days during the radio flare of January 1991 a total of 32 muons within 2.0° of the Cygnus X-3 direction were observed when 11.4 were expected.