The Euclidean matching problem

Résumé. 2014 Nous étudions le problème du couplage (« matching ») en dimension finie. Les corrélations euclidiennes entre les distances peuvent être prises en compte de manière systématique. Par rapport au cas des distances aléatoires indépendantes que nous avions étudiées précédemment, les corrélations triangulaires euclidiennes engendrent des corrections qui s'annulent dans la limite où la dimension de l'espace tend vers l'infini, et restent relativement petites à toute dimension. Abstract. 2014 We study the matching problem in finite dimensions. The Euclidean correlations of the distances can be taken into account in a systematic way. With respect to the case of independent random distances which we have studied before, the adjonction of Euclidean triangular correlations gives rise to corrections which vanish when the dimension of space goes to infinity, and remain relatively small in any dimensions

Higher spin symmetry and #NU#=4 SYM

We assemble the spectrum of single-trace operators in free N = 4 SU(N) SYM theory into irreducible representations of the Higher Spin symmetry algebra hs(2, 2 vertical stroke 4). Higher Spin representations or YT-pletons are associated to Young tableaux (YT) corresponding to representations of the symmetric group compatible with the cyclicity of color traces. After turning on interactions g_Y_M #not =# 0, YT-pletons decompose into infinite towers of representations of the superconformal algebra psu(2, 2 vertical stroke 4) and anomalous dimensions are generated. We work out the decompositions of tripletons with respect to the N = 4 superconformal algebra psu(2, 2 vertical stroke 4) and compute their anomalous dimensions to lowest non-trivial order in g_Y_M"2N at large N. We then focus on operators/states sitting in semishort multiplets of psu(2, 2 vertical stroke 4). By passing them through a semishort-sieve that removes superdescendants, we derive compact expressions for the partition function of semishort primaries. (orig.)Available from TIB Hannover: RA 2999(04-058) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

SEEDING EXPERIMENTS AT SPARC

The SPARC Free Electron Laser can be operated in both SASE and seeded modes. A major part of the second stage of the commissioning, now undergoing, is dedicated to the characterization of the SASE radiation. Simultaneously, we are finalizing the experimental setup for seeding. We present an in-situ characterization of the two input seeds that are foreseen: both are obtained via harmonic generation, the first one in crystal (400 and 266 nm) and the second in rare gas (Argon). We also describe the specific diagnostics implemented for the electron-seed overlap in the undulator, together with the diagnostics for radiation analysis (2D spectrometer and FROG). The seeding will enable the operation of the SPARC FEL in original cascaded configurations

Alignment of the CMS Muon System with Cosmic-Ray and Beam-Halo Muons

Abstract The CMS muon system has been aligned using cosmic-ray muons collected in 2008 and beam-halo muons from the 2008 LHC circulating beam tests. After alignment, the resolution of the most sensitive coordinate is 80 microns for the relative positions of superlayers in the same barrel chamber and 270 microns for the relative positions of endcap chambers in the same ring structure. The resolution on the position of the central barrel chambers relative to the tracker is comprised between two extreme estimates, 200 and 700 microns, provided by two complementary studies. With minor modifications, the alignment procedures can be applied using muons from LHC collisions, leading to additional significant improvements. * See Appendix A for the list of collaboration members arXiv:0911.4022v2 [physics.ins-det] 8 Feb 2010 FERMILAB-PUB-10-163-CMS Introduction The primary goal of the Compact Muon Solenoid (CMS) experiment [1] is to explore particle physics at the TeV energy scale exploiting the proton-proton collisions delivered by the Large Hadron Collider (LHC) The muon system consists of hundreds of independent tracking chambers mounted within the CMS magnetic field return yoke. Three technologies are employed: Drift Tube (DT) chambers on the five modular wheels of the barrel section, Cathode Strip Chambers (CSC) on the six endcap disks (illustrated in Figs. 1 and 2) and Resistive Plate Chambers (RPC) throughout. The DTs and CSCs are sufficiently precise to contribute to the momentum resolution of highmomentum muons (several hundred GeV/c) assuming that these chambers are well-aligned relative to the CMS tracker, a one-meter radius silicon strip and pixel detector. Between the tracker and the muon system are electromagnetic and hadronic calorimeters (ECAL and HCAL, respectively) for particle identification and energy measurement, as well as the solenoid coil for producing an operating magnetic field strength of 3.8 T in which to measure charged-particle momenta (all shown in The CMS collaboration is developing multiple techniques to align the DT and CSC chambers and their internal layers. Photogrammetry and in-situ measurement devices [3] provide realtime monitoring of potential chamber movements on short timescales and measurements of degrees of freedom to which tracks are only weakly sensitive. Track-based alignment, the subject of this paper, optimizes component positions for a given set of tracks, directly relating the active elements of the detectors traversed by the charged particles in a shared coordinate frame. Methods using tracks are employed both to align nearby components relative to one another and to align all muon chambers relative to the tracker. A challenge to track-based alignment in the CMS muon system is the presence of large quantities of material between the chambers. As a central design feature of the detector, 20-60 cm layers of steel are sandwiched between the chambers to concentrate the magnetic field and absorb beam-produced hadrons. Consequently, uncertainties in track trajectories become significant as muons propagate through the material, making it necessary to develop alignment procedures that are insensitive to scattering, even though typical deviations in the muon trajectories (3-8 mm) are large compared to the intrinsic spatial resolution (100-300 µm). Two types of approaches are presented in this paper: the relative alignment of nearby structures, which avoids extrapolation of tracks through material but does not relate distant coordinate frames to each other, and the alignment using tracks reconstructed in the tracker, which allows for a more sophisticated treatment of propagation effects by simplifying the interdependence of alignment parameters. This paper begins with a brief overview of the geometry of the muon system and conventions to be used thereafter (Section 2), followed by presentations of three alignment procedures: (a) internal alignment of layers within DT chambers using a combination of locally fitted track segments and survey measurements (Section 3); (b) alignment of groups of overlapping CSC chambers relative to one another, using only (c) alignment of each chamber relative to the tracker, using the tracks from the tracker, propagated to the muon system with a detailed map of the magnetic field and material distribution of CMS (Section 5). Procedure (c), above, completes the alignment, relating all local coordinate frames to a shared frame. Its performance is greatly improved by supplying internally aligned chambers from procedure (a), such that only rigid-body transformations of whole chambers need to be considered. Procedures (b) and (c) both align CSC chambers relative to one another, but in different ways: (b) does not need many tracks, only about 1000 per chamber, to achieve high precision, and (c) additionally links the chambers to the tracker. With the first LHC collisions, groups of CSCs will be interaligned using (b) and these rigidbody groups will be aligned relative to the tracker with (c). As more data become available, comparisons of results from (b) and (c) yield highly sensitive tests of systematic errors in (c). Although the ideal tracks for these procedures are muons from LHC collisions, this paper focuses on application of the procedures using currently available data, namely cosmic rays (a and c) and beam-halo muons from circulating LHC beam tests in September 2008 (b). In particular, (c) requires a magnetic field to select high-quality, high-momentum muons and concurrent operation of the tracker and muon systems. The CMS Collaboration conducted a monthlong data-taking exercise known as the Cosmic Run At Four Tesla (CRAFT) during OctoberNovember 2008, with the goal of commissioning the experiment for extended operation The formalism and results of each procedure are presented together. Details of the data transfer and the computing model which were used to implement these procedures are described in Ref. Geometry of the Muon System and Definitions Muon chambers are independent, modular track detectors, each containing 6-12 measurement layers, sufficient to determine the position and direction of a passing muon from the intersections of its trajectory with the layer planes ("hits"). The DT layers are oriented nearly perpendicular to lines radially projected from the beamline, and CSC layers are perpendicular to lines parallel with the beamline. Hits are initially expressed in a local coordinate frame (x, y, z) defined by the layers: z = 0 is the plane of the layer and x is the more precisely measured (or the only measured) of the two plane coordinates. On CSC layers, the most precise measurement is given by cathode strips, which fan radially from the beamline A semi-local coordinate system for the entire chamber is defined with x, y, and z axes nominally parallel to the layers' axes, but with a single origin. Within this common frame, the positions of hits from different layers can be related to each other and combined by a linear fit into segments with position (x,ȳ) and direction ( dx dz , dy dz ). The nominal x direction of every chamber is perpendicular to the beamline and radial projections from the beamline