《粒子物理与核物理实验方法（二）》track_fitting.pdf

A review of fast circleand helix ?ttingR. Fr¨uhwirth(HEPHY, Vienna, Austria)A. Strandlie (CERN, Geneva, Switzerland)W. Waltenberger (HEPHY, Vienna, Austria)J. Wroldsen (Gj?vik University College, Norway)ACAT 2002, Moscow, ?Introduction and background?Circle ?tting?Helix ?tting?ConclusionR. Fr¨uhwirth ACAT 2002, Moscow 2Introduction and background?In adetector embedded in a ic ?eld, the particle trajectories arehelices.?Examples: Inner trackers in CMS and ATLAS.?LHC track reconstruction methods have to bepreciseandfast?Themethod of choicewill very likely depend on therequirements of the actual physics . Fr¨uhwirth ACAT 2002, Moscow 3Introduction and backgroundTrack ?tting methodscan roughly be divided intotwoseparate categories:?Precise and slow?Approximate and fastThose of thelatter category mainly work for2Ddata— . data ing from a2Ddetectororprojected data from a3DdetectorR. Fr¨uhwirth ACAT 2002, Moscow 4Introduction and backgroundThe global least-squares method:?Used formany decadesinHEP experiments.?Proper treatmentofelastic, multiple Coulombscatteringincluded in the methodduring the 70’s.?Close to optimalin precision, but may putationally quite expensivewith alargenumber of measurementsand/or alarge numberof scattering . Fr¨uhwirth ACAT 2002, Moscow 5Introduction and backgroundThe Kalman ?lter:?Recursive least-squares estimation.?Thereforesuitable bined track ?ndingand ?tting?Equivalenttoglobal least-squares methodincluding allcorrelations between measurementsdue tomultiple scattering.?Probably themost widely used method . Fr¨uhwirth ACAT 2002, Moscow 6Introduction and backgroundBoth the global LS ?t and the Kalman ?lter may needprevious knowledgeof the track:?as an expansion point (reference track) of thelinearization procedure,?for putation of the multiple scatteringcovariance isparticularly importantfor tracks withlargecurvature (low momentum). Thereforefastpreliminary ?tsare . Fr¨