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