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Study of the Optimum Study of the Optimum Momentum Resolution of Momentum Resolution of CMS ExperimentCMS Experiment
Presented by: Presented by:
Timothy Timothy McDonaldMcDonald
Faculty Faculty Mentor:Mentor:
Darin AcostaDarin Acosta
The Compact Muon The Compact Muon SolenoidSolenoid
To be To be completed 2005 completed 2005 at CERNat CERN
At Large At Large Hadron ColliderHadron Collider
Collides proton Collides proton bunches at 7 bunches at 7 times Fermilab times Fermilab energy (7 TeV)energy (7 TeV)
The Compact Muon The Compact Muon SolenoidSolenoid
The Compact Muon The Compact Muon SolenoidSolenoid
Project focus Endcap Muon Project focus Endcap Muon SystemSystem
CMS Endcap Muon SystemCMS Endcap Muon System
100 or 200
Disk composed of 10Disk composed of 100 0 or or 202000 muon detectors muon detectors
Four stations of Four stations of detectorsdetectors
Predominantly Only Predominantly Only muons penetrate this muons penetrate this much iron much iron
4 Stations
Endcap Detector StationEndcap Detector Station
Each Station Contains 6 Each Station Contains 6 cathode strip chamberscathode strip chambers
Anode wires: polar angle Anode wires: polar angle thetatheta
Cathode strips: azimuthal Cathode strips: azimuthal angle phiangle phi
Cathode Strip Chambers
More data is produced More data is produced than can be easily handledthan can be easily handled
40,000,000 collisions per second40,000,000 collisions per second 1 megabyte of data per collision 1 megabyte of data per collision
bunchbunch 40 terabytes of data per second40 terabytes of data per second
Need to measure Muon Need to measure Muon MomentumMomentum
Trigger must select Trigger must select interesting events interesting events (Higgs, Z, W Bosons)(Higgs, Z, W Bosons)
Heavy, interesting Heavy, interesting particles often decay particles often decay into high momentum into high momentum muonsmuons
Trigger must quickly Trigger must quickly measure muon measure muon momentummomentum
Resolution GoalsResolution Goals
Amount of Bending Amount of Bending Proportional to MomentumProportional to Momentum
4 tesla magnet bends 4 tesla magnet bends escaping charged escaping charged particles in azimuthal particles in azimuthal directiondirection
high momentum high momentum muons bend lessmuons bend less
momentum can be momentum can be obtained based on obtained based on bending between bending between four detector stationsfour detector stations
Parameterize momentum as Parameterize momentum as a function of measurementsa function of measurements
Can use 2,3, or 4 Can use 2,3, or 4 detector stationsdetector stations
Must consider Must consider change in azimuthal change in azimuthal angleangle
Must consider the Must consider the polar angle as wellpolar angle as well
Use simulation data Use simulation data to determine to determine constantsconstants
Different rapidity regionsDifferent rapidity regions
Rapidity is Rapidity is transformation of transformation of polar angle polar angle (eta=-ln tan /2)
Equations must Equations must consider rapidity consider rapidity regionregion
Many layers of iron Many layers of iron and detectors means and detectors means field variesfield varies
CMSIM simulates detectorsCMSIM simulates detectors
Mean change in Mean change in angle at 15 GeV and angle at 15 GeV and in the eta region 1.4 in the eta region 1.4 to 1.5to 1.5
Data is fit to a Data is fit to a normal curvenormal curve
Provides Provides information of how information of how muons will behave muons will behave in the experimentin the experiment
Two station assignmentTwo station assignment
Pta /)( Change in muon track’s angle is Change in muon track’s angle is
inversely related to momentuminversely related to momentum This relationship varies depending This relationship varies depending
on the region of the detectoron the region of the detector
Uses change in angle from:
*Station 1 to Station 2
*Station 2 to Station 3
The Three Station The Three Station Momentum AssignmentMomentum Assignment
Attempts to get a Attempts to get a better resolutionbetter resolution
Uses more Uses more information about information about muon trackmuon track
Likelihood functionLikelihood function
Estimate momentum Estimate momentum from measured from measured parameters using parameters using method of maximum method of maximum likelihoodlikelihood
Correlation between Correlation between two change in angle two change in angle values must be values must be consideredconsidered
First derivative = 0 First derivative = 0 maximizesmaximizes 0),,( 2312
PtfPt
Solve for momentumSolve for momentum
Solve the likelihood function for Solve the likelihood function for 1/momentum1/momentum
The mean and RMS spread The mean and RMS spread parameterized from simulation dataparameterized from simulation data
results in function that depends on results in function that depends on rapidity and change in phi anglesrapidity and change in phi angles
Resolution based on 3 Resolution based on 3 station measurementstation measurement
Resolution is about 21% for low Resolution is about 21% for low momentum muonsmomentum muons
Four Station Momentum Four Station Momentum AssignmentAssignment
Attempts to bring resolution to Attempts to bring resolution to lowest possible: 15%lowest possible: 15%
Uses three change in angle values Uses three change in angle values from the four stationsfrom the four stations
Not as much bending between third Not as much bending between third and fourthand fourth
Resolution same as three station Resolution same as three station assignmentassignment
Next Possible StepNext Possible Step
Each station has 6 Each station has 6 CSC chambers CSC chambers
They assign a They assign a direction vector direction vector
The direction can The direction can be used in the be used in the assignmentassignment