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Optimum Resolution of CMS Experiment for Muon Momentum Study

This study presents the analysis of the optimal momentum resolution for the CMS Experiment conducted by Timothy McDonald under the mentorship of Darin Acosta. The research focuses on the Compact Muon Solenoid project at CERN, aiming to achieve precise measurements of muon momentum in high-energy particle collisions. Data handling challenges and the need for accurate muon momentum measurement trigger development goals to identify interesting physics events efficiently. The methodology involves parameterizing momentum as a function of detector measurements, accounting for azimuthal and polar angles. Different rapidity regions and detector field variations are considered using simulation data in the CMSIM tool to characterize muon behavior. By analyzing angle changes between detector stations, likelihood functions are used to estimate momentum via the method of maximum likelihood. The study demonstrates improved resolution with the three-station momentum assignment compared to the two-station setup, aiming for a resolution of 15% with the four-station approach. Future steps involve leveraging direction vectors assigned by CSC chambers for further refinement.

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Optimum Resolution of CMS Experiment for Muon Momentum Study

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  1. Study of the Optimum Momentum Resolution of CMS Experiment Presented by: Timothy McDonald Faculty Mentor: Darin Acosta

  2. The Compact Muon Solenoid • To be completed 2005 at CERN • At Large Hadron Collider • Collides proton bunches at 7 times Fermilab energy (7 TeV)

  3. The Compact Muon Solenoid

  4. The Compact Muon Solenoid

  5. Project focus Endcap Muon System

  6. CMS Endcap Muon System • Disk composed of 100 or 200 muon detectors • Four stations of detectors • Predominantly Only muons penetrate this much iron 4 Stations 100 or 200

  7. Endcap Detector Station • Each Station Contains 6 cathode strip chambers • Anode wires: polar angle theta • Cathode strips: azimuthal angle phi Cathode Strip Chambers

  8. More data is produced than can be easily handled • 40,000,000 collisions per second • 1 megabyte of data per collision bunch • 40 terabytes of data per second

  9. Need to measure Muon Momentum • Trigger must select interesting events (Higgs, Z, W Bosons) • Heavy, interesting particles often decay into high momentum muons • Trigger must quickly measure muon momentum

  10. Resolution Goals

  11. Amount of Bending Proportional to Momentum • 4 tesla magnet bends escaping charged particles in azimuthal direction • high momentum muons bend less • momentum can be obtained based on bending between four detector stations

  12. Parameterize momentum as a function of measurements • Can use 2,3, or 4 detector stations • Must consider change in azimuthal angle • Must consider the polar angle as well • Use simulation data to determine constants

  13. Different rapidity regions • Rapidity is transformation of polar angle (eta=-ln tan /2) • Equations must consider rapidity region • Many layers of iron and detectors means field varies

  14. CMSIM simulates detectors • Mean change in angle at 15 GeV and in the eta region 1.4 to 1.5 • Data is fit to a normal curve • Provides information of how muons will behave in the experiment

  15. Two station assignment • Change in muon track’s angle is inversely related to momentum • This relationship varies depending on the region of the detector

  16. The Three Station Momentum Assignment • Attempts to get a better resolution • Uses more information about muon track Uses change in angle from: *Station 1 to Station 2 *Station 2 to Station 3

  17. Likelihood function • Estimate momentum from measured parameters using method of maximum likelihood • Correlation between two change in angle values must be considered • First derivative = 0 maximizes

  18. Solve for momentum • Solve the likelihood function for 1/momentum • The mean and RMS spread parameterized from simulation data • results in function that depends on rapidity and change in phi angles

  19. Graph of momentum assignment function versus generated data

  20. Resolution based on 3 station measurement • Resolution is about 21% for low momentum muons

  21. Four Station Momentum Assignment • Attempts to bring resolution to lowest possible: 15% • Uses three change in angle values from the four stations • Not as much bending between third and fourth • Resolution same as three station assignment

  22. Next Possible Step • Each station has 6 CSC chambers • They assign a direction vector • The direction can be used in the assignment

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