Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 278.882 LHC PhysicsExperimental Methods and MeasurementsTrack Reconstruction and Fitting[Lecture 8, March 2, 2009]C.Paus, LHC Physics: Track Reconstruction and Fitting 2Organizational IssuesDue days for the documented analyses●project 1 is due March 12TWiki●updated the documentation to include Monte Carlo instructionsC.Paus, LHC Physics: Track Reconstruction and Fitting 3Lecture Outline Track reconstruction and fitting●basics: alignment, particles in B field and matter●real life tracking issues●Monte Carlo methods and GEANT●tracking strategies and fitting●inside-out and outside-in tracking●combining track algorithms●typical failures of tracking algorithms●calibration of the tracking●efficiencies●momentum scale calibration●material calibrationC.Paus, LHC Physics: Track Reconstruction and Fitting 4Tracking – The DefinitionIn In particle physicsparticle physics, the tracking is the act of , the tracking is the act of measuring the measuring the directiondirection and magnitude of and magnitude of charged charged particlesparticles momentamomenta..Taken from wikipedia.org: “Tracking (particle physics)” Taken from wikipedia.org: “Tracking (particle physics)” Tracking also includes the act of determining Tracking also includes the act of determining the particle position.the particle position.Lesson: Lesson: not everything found on the Web is completenot everything found on the Web is completeC.Paus, LHC Physics: Track Reconstruction and Fitting 5Detector Alignment To perform tracking, detector has to be aligned Alignment●detector positions have to be known to micrometer level●survey of each component is a must●knowledge of possible component shifts crucial to simplify alignment model●bootstrap: use tracks make them fit better by adjusting positions (careful effects have to be disentangled)●alignment need to be redone regularly●detector opening and closing●temperature variations●detector sinking●detector breathes with magnetic field switching on and off, ....C.Paus, LHC Physics: Track Reconstruction and Fitting 6Track Reconstruction: Outline Reconstruct hits●space points, sometimes called clusters●determine space point uncertainties Perform pattern recognition●lay out all hits and find helical trajectories●identify the hits which seem to belong to trajectory Fit identified hits to expected trajectory (helix)●use space points and their uncertainties and find helix which optimally describes those hits●knowledge of detector material and detailed magnetic field crucial: think multiple scattering and energy loss Often the steps are not separated but integrated for best performanceC.Paus, LHC Physics: Track Reconstruction and Fitting 7Charged Particles in Magnetic Field Lorentz force●magnetic field: no change to momentum size, only changes direction●electrical field irrelevant Assume B field along z●xy-plane motion: circle●direction determines charge●momentum component in z remains constant●3 dimensional: helixBxy Real life●magnetic fields never completely homogeneousC.Paus, LHC Physics: Track Reconstruction and Fitting 8Helix Parameters●particle mass (m)●creation point (x,y,z)●momentum vector (px,py,pz) Tracking determines●trajectory of the particle●per se mass not included●our cases of tracking: exact creation point not determined because of 1 dimensional ambiguity Helix parameters must be 5●2 dim: curvature ρ (~1/pT), azimuthal angle φ0, impact parameter d0 ●3 dim: z0 and cotθ (=λ) Description of particle in phase space (7 params)C.Paus, LHC Physics: Track Reconstruction and Fitting 9Particles Interactions in Matter Multiple Scattering - Coulomb scattering approx.: x – traversed thickness, X0 – material radiation lengthalways checkout PDG or GEANT implementation for referenceC.Paus, LHC Physics: Track Reconstruction and Fitting 10Particle Interactions with Matter Energy loss (Bethe Bloch formula)always checkout PDG or GEANT implementation for reference●for moderately relativistic particles●depends only on β Very well studied effect●theoretically complex●measured in many materials●good documentation●useful for particle IdC.Paus, LHC Physics: Track Reconstruction and Fitting 11Real Life Issues for Tracking Particle follow helix, but ....●inhomogeneous B field: helix gets bend out of shape●multiple scattering: blurs helix, momentum up and down●energy loss: helix radius decreases Tracking should be precise to micrometer level:●those effects have to be taken into account in details●detector simulation programs are used to implement all those issues in detailC.Paus, LHC Physics: Track Reconstruction and Fitting 12Monte Carlo MethodThey [Monte Carlo methods] are distinguished from other simulation methods (such as molecular dynamics) by being stochastic, that is nondeterministic in some manner – usually by using random numbers (or, more often, pseudo-random numbers) – as opposed to deterministic algorithms.as usual from wikipedia.org: “Monte Carlo method” In High Energy physics complex systems with many components need to be simulated .... Monte Carlo technique is a must in modern HEP and is only adequate since the advent of large computers.C.Paus, LHC Physics: Track Reconstruction and Fitting 13Detector Simulation: GEANT GEometry ANd Tracking software package●originally developed in Fortran at CERN (1974) for HEP experiments, now available as Geant4 in C++●based on Monte Carlo methods Features●allows complex detector descriptions: definitions of volumes of certain material(s)●implements detailed particle interaction with material●multiple scattering, energy loss, particle decay, particle creation, motion of charged particles in magnetic field●various plugins: digitization, hadronic showers etc. Output of GEANT simulation●usually – fully digitized detector response, i.e. hitsC.Paus, LHC Physics: Track Reconstruction and Fitting 14GEANT Basic Tracking GEANT tracks particle through given detector●any particle and their “children” can be tracked●track is not calculated as a whole but rather in fine grained steps●many effects can be linearized●account for inhomogeneous magnetic field●particle interaction and decay