Path integral formulations for the Smorodinsky‐Winternitz potentials in two‐ and three‐dimensional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky‐Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is not possible, we list in all soluble cases the path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave‐functions.

We report test beam studies of 11% of the production ATLAS Tile Calorimeter modules. The modules were equipped with production front-end electronics and all the calibration systems planned for the final detector. The studies used muon, electron and hadron beams ranging in energy from 3 to 350 GeV. Two independent studies showed that the light yield of the calorimeter was similar to 70 pe/GeV, exceeding the design goal by 40%. Electron beams provided a calibration of the modules at the electromagnetic energy scale. Over 200 calorimeter cells the variation of the response was 2.4%. The linearity with energy was also measured. Muon beams provided an intercalibration of the response of all calorimeter cells. The response to muons entering in the ATLAS projective geometry showed an RMS variation of 2.5% for 91 measurements over a range of rapidities and modules. The mean response to hadrons of fixed energy had an RMS variation of 1.4% for the modules and projective angles studied. The response to hadrons normalized to incident beam energy showed an 8% increase between 10 and 350 GeV, fully consistent with expectations for a noncompensating calorimeter. The measured energy resolution for hadrons of sigma/E = 52.9%/root E circle plus 5.7% was also consistent with expectations. Other auxiliary studies were made of saturation recovery of the readout system, the time resolution of the calorimeter and the performance of the trigger signals from the calorimeter. (C) 2009 Elsevier B.V. All rights reserved

Steps towards path integral formulations for Smorodinsky‐Winternitz potentials, respectively systems with accidental degeneracies, on the two‐ and three‐dimensional sphere, and a complete classification of super‐integrable systems on spaces of constant curvature are presented. We mention all coordinate systems which separate the Smorodinsky‐Winternitz potentials on a sphere, and state the corresponding path integral formulations. Whereas in many coordinate systems explicit path integral solutions are not possible, we list in all soluble cases the path integral in terms of the propagator, respectively the spectral expansion into the wave functions and the energy spectrum.

The COMPASS experiment at the CERN SPS has studied the diffractive dissociation of negative pions into the π- π- π+ final state using a 190  GeV/c pion beam hitting a lead target. A partial wave analysis has been performed on a sample of 420,000 events taken at values of the squared 4-momentum transfer t' between 0.1 and 1  GeV2/c2. The well-known resonances a1(1260), a2(1320), and π2(1670) are clearly observed. In addition, the data show a significant natural-parity exchange production of a resonance with spin-exotic quantum numbers J(PC)=1-+ at 1.66  GeV/c2 decaying to ρπ. The resonant nature of this wave is evident from the mass-dependent phase differences to the J(PC)=2-+ and 1++ waves. From a mass-dependent fit a resonance mass of (1660±10(-64)(+0))  MeV/c2 and a width of (269±21(-64)(+42))  MeV/c2 are deduced, with an intensity of (1.7±0.2)% of the total intensity.

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