Letter of Intent by the Solenoidal Detector Collaboration to construct and operate a detector at the Superconducting Super Collider

title: Search for B ---> K lepton+ lepton- and B ---> K* lepton+ lepton- decays

title: Study of charmless hadronic B meson decays to pseudoscalar-vector final states.
abstract: We report results of searches for charmless hadronic B meson decays to pseudoscalar( pi(+/-), K+/-, pi(0), or K(0)(S))-vector( rho, K(*), or omega) final states. By using 9.7x10(6) BB pairs collected with the CLEO detector, we report the first observation of B(-)--->pi(-)rho(0), B(0)-->pi(+/-)rho(-/+), and B(-)-->pi(-)omega, which are expected to be dominated by hadronic b-->u transitions. The measured branching fractions are (10.4(+3.3)(-3.4)+/-2.1)x10(-6), (27.6(+8.4)(-7.4)+/-4.2)x10(-6), and (11.3(+3.3)(-2.9)+/-1. 4)x10(-6), respectively. Branching fraction upper limits are set for all of the other decay modes investigated.

title: Measurement of Cabibbo-suppressed decays of the tau lepton.
abstract: Branching ratios for the dominant Cabibbo-suppressed decays of the [tau] lepton have been measured by CLEO II in [ital e][sup +][ital e][sup [minus]] annihilation at the Cornell Electron Storage Ring ([radical][ital s] [similar to]10.6 GeV) using kaons with momenta below 0.7 GeV/[ital c]. The inclusive branching ratio into one charged kaon is (1.60[plus minus]0.12[plus minus]0.19)%. For the exclusive decays, [ital B]([tau][sup [minus]][r arrow][ital K][sup [minus]][nu][sub [tau]])=(0.66[plus minus]0.07[plus minus]0.09)%, [ital B]([tau][sup [minus]][r arrow][ital K][sup [minus]][pi][sup 0][nu][sub [tau]])=(0.51 [plus minus]0.10[plus minus]0.07)%, and, based on three events, [ital B]([tau][sup [minus]][r arrow][ital K][sup [minus]]2[pi][sup 0][nu][sub [tau]])[lt]0.3% at the 90% confidence level. These represent significant improvements over previous results. ) is measured for the first time with exclusive [pi][sup 0] reconstruction.

title: Measurement of B (tau- ---> tau-neutrino K- K0) and b (tau- ---> tau-neutrino K- K0 pi0)

title: Observation of radiative leptonic decay of the tau lepton
abstract: Using 4.68 fb(-1) of e(+)e(-) annihilation data collected with the CLEO II detector at the Cornell Electron Storage Ring, we have studied tau radiative decays tau(-)-->nu(tau)&mgr;(-)nu;(&mgr;)gamma and tau(-)-->nu(tau)e(-)nu;(e)gamma. For a 10 MeV minimum photon energy in the tau rest frame, the branching fraction for radiative tau decay to a muon or electron is measured to be (3.61+/-0.16+/-0. 35)x10(-3) or (1.75+/-0.06+/-0.17)x10(-2), respectively. The branching fractions are in agreement with standard model theoretical predictions.

title: Hopfish structure and modules over irrational rotation algebras
abstract: Inspired by the group structure on $S^1/ \bbZ$, we introduce a weak hopfish structure on an irrational rotation algebra $A$ of finite Fourier series. We consider a class of simple $A$-modules defined by invertible elements, and we compute the tensor product between these modules defined by the hopfish structure. This class of simple modules turns out to generate an interesting commutative unital ring.

title: GROUPOID SYMMETRY AND CONSTRAINTS IN GENERAL RELATIVITY
abstract: When the vacuum Einstein equations are cast in the form of Hamiltonian evolution equations, the initial data lie in the cotangent bundle of the manifold of Riemannian metrics on a Cauchy hypersurface Σ. As in every Lagrangian field theory with symmetries, the initial data must satisfy constraints. But, unlike those of gauge theories, the constraints of general relativity do not arise as momenta of any Hamiltonian group action. In this paper, we show that the bracket relations among the constraints of general relativity are identical to the bracket relations in the Lie algebroid of a groupoid consisting of diffeomorphisms between space-like hypersurfaces in spacetimes. A direct connection is still missing between the constraints themselves, whose definition is closely related to the Einstein equations, and our groupoid, in which the Einstein equations play no role at all. We discuss some of the difficulties involved in making such a connection. In an appendix, we develop some aspects of diffeology, the basic framework for our treatment of function spaces.

title: Detection of VER J2019+407 (G78.2+2.1) and Tycho's Supernova Remnant with VERITAS

title: A universal phase space for particles in Yang-Mills fields
abstract: Given a principal G-bundle P over M and a Hamiltonian G-space Q, one may construct the reduced symplectic manifold (T*P x Q)0. When a connection on P is chosen, this manifold becomes a bundle over T*M with fibre Q. It is shown that this bundle is precisely the phase space constructed by Sternberg for a classical particle in a Yang-Mills field.

title: Reduction and quantization for singular momentum mappings
abstract: When a Hamiltonian action of Lie group on a symplectic manifold has a singular momentum mapping, the reduced manifold may not exist. Nevertheless, we may always construct a Poisson algebra which corresponds to the functions on the reduced manifold in the regular case. The ideas of geometric quantization are extended to Poisson algebras, and it is shown in an example that quantization may be carried out before or after reduction, with isomorphic results.